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 surface force solving method, device and equipment based on a flexible body. The surface force solving method based on the flexible body comprises the following steps: obtaining current displacement information of a measurement node of a finite element model of the flexible body, wherein the measurement node is part of nodes in the finite element model; establishing a current objective function of an optimization problem of a static force balance equation based on the current displacement information of the measurement node, wherein a preset constraint condition is added to the current objective function; and solving the optimization problem to obtain the surface force of the flexible body. The technical scheme adopted by the application can improve the efficiency of force surface force solving.

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 field of force / tactile sensors as an example, for force / tactile sensors including flexible bodies, the existing technology discloses a three-dimensional contact force measurement method for visual tactile sensors based on inverse finite element analysis. Since the nodal displacement information in the finite element is relatively rich, the three-dimensional force can be directly calculated. However, if only the displacement information of some nodes is known, the nodal displacement information of the three-dimensional solid finite element is relatively small, which often makes it difficult to quickly solve the surface force of the flexible body. Summary of the Invention

[0004] The purpose of this application is to provide a method, apparatus, and device for solving the surface forces of flexible bodies, so as to improve the efficiency of solving surface forces.

[0005] 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:

[0006] A method for solving surface forces based on flexible bodies, the method comprising the following steps:

[0007] Obtain the current displacement information of the measurement nodes of the finite element model of the flexible body; the measurement nodes are some nodes in the finite element model;

[0008] Based on the current displacement information of the measurement node, a current objective function is established for the optimization problem of the static equilibrium equation; wherein, a preset constraint condition is added to the current objective function;

[0009] Solve the optimization problem to obtain the surface forces of the flexible body.

[0010] Furthermore, establishing the current objective function for the optimization problem of the static equilibrium equation based on the current displacement information of the measurement node specifically includes the following steps:

[0011] Obtain the objective function (3.1) of the optimization problem constructed based on the static equilibrium equation;

[0012] min(Kx-F) T (Kx-F) (3.1)

[0013] Where K is the overall stiffness matrix; x is the current displacement information of the measurement node; F is the surface force; the constraint conditions include: preset friction cone constraint conditions and boundary force constraints;

[0014] The current displacement information of the measurement node is substituted into the objective function (3.1) to obtain the current objective function. Further, solving the optimization problem to obtain the surface force of the flexible body specifically includes the following steps:

[0015] The optimization problem is transformed into a quadratic programming problem under the constraints.

[0016] Solve the quadratic programming problem to obtain the surface force.

[0017] Furthermore, transforming the optimization problem into a quadratic programming problem under the constraints specifically includes the following steps:

[0018] The current objective function is expanded twice to obtain the quadratic expansion of the gradient and Hessian matrix.

[0019] Add the aforementioned constraints as constraints to the quadratic expansion; and / or,

[0020] Solving the quadratic programming problem to obtain the surface force specifically includes the following steps:

[0021] The quadratic programming problem is solved using an iterative method until a preset termination condition is met.

[0022] The surface force at which the preset termination condition is met is taken as the final surface force.

[0023] Furthermore, solving the optimization problem to obtain the surface force of the flexible body specifically includes the following steps:

[0024] Based on the current displacement and current surface force of the unknown node, determine whether the objective function has reached the preset convergence condition;

[0025] If it is determined that the preset convergence condition has been met, the surface force corresponding to the time when the preset convergence condition is met shall be taken as the final surface force.

[0026] If it is determined that the preset convergence condition has not been met, repeat the above method steps until it is determined that the preset convergence condition has been met.

[0027] Furthermore, before establishing the current objective function of the optimization problem for the static equilibrium equation based on the current displacement information of the measurement node, the following steps are also included:

[0028] Stress-strain matrix is ​​constructed based on a nonlinear material constitutive model of flexible bodies;

[0029] The strain-displacement matrix is ​​constructed based on the finite element model of the flexible body.

[0030] By combining the stress-strain matrix and the strain-displacement matrix, the overall stiffness matrix of the flexible body is generated.

[0031] Based on the overall stiffness matrix, the static equilibrium equations are constructed.

[0032] Establish the objective function of the optimization problem for the static equilibrium equations; and / or,

[0033] Before obtaining the current displacement information of the measurement nodes of the finite element model of the flexible body, the following steps are also included:

[0034] Construct the finite element model of the flexible body.

[0035] Secondly, embodiments of this application provide a surface force calculation device for a flexible body, the device comprising:

[0036] The information acquisition module is used to acquire the current displacement information of the measurement nodes of the finite element model of the flexible body; the measurement nodes are some nodes in the finite element model.

[0037] The optimization and transformation module is used to establish the current objective function of the optimization problem of the static equilibrium equation based on the current displacement information of the measurement node, wherein the current objective function is subject to preset constraints.

[0038] The force calculation module is used to solve the optimization problem to obtain the surface force of the flexible body.

[0039] Thirdly, embodiments of this application provide a surface force solving system based on a flexible body, the system including a nodal displacement measuring device and a controller;

[0040] The node displacement measuring device and the controller are communicatively connected;

[0041] The node displacement measuring device is used to measure the current displacement information of the measuring node;

[0042] The controller is used to implement the steps of the surface force solution method for flexible bodies described in any of the above-mentioned methods.

[0043] Fourthly, 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.

[0044] Fifthly, 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.

[0045] Compared with the prior art, the embodiments of this application have the following main advantages:

[0046] This application embodiment constructs an optimization problem of static equilibrium equations based on the known current node displacement information of some nodes of a flexible body, adds preset constraints, and obtains the surface force of the flexible body at the current moment by solving the optimization problem. Since the surface force of the flexible body can be obtained based only on the current node displacement information of some nodes of the flexible body, it is more versatile and can be mass-produced compared to neural network methods, which do not require the collection of a large amount of sample data. In addition, by constructing an optimization problem of static equilibrium equations and then solving the optimization problem to obtain the surface force of the flexible body, the computational efficiency is high compared to directly solving the surface force of the flexible body based on the static equilibrium equations, and it can meet the real-time requirements. Attached Figure Description

[0047] 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.

[0048] Figure 1 This is an exemplary system architecture diagram in which this application can be applied.

[0049] Figure 2 This is a flowchart illustrating an embodiment of the surface force solution method based on flexible bodies according to this application;

[0050] Figure 3 This is a schematic diagram of the structure of one embodiment of the surface force solving device based on flexible bodies of this application;

[0051] Figure 4 This is a schematic diagram of the structure of one embodiment of the computer device of this application. Detailed Implementation

[0052] 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.

[0053] 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.

[0054] 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.

[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] 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.

[0058] 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 "nodal displacement measuring device 110" can be a force / tactile sensor, and the force / tactile sensor described in the application embodiment includes a flexible body.

[0059] 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.

[0060] 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.

[0061] In an optional embodiment of this application, a nodal displacement measuring device is used to collect the current displacement information of the measuring nodes of the flexible body; wherein, the measuring nodes are some nodes in the finite element model.

[0062] It should be noted that, in another optional embodiment of this application, some intermediate data (such as sensing signals) can also be collected by a node displacement measuring device, and then the intermediate data can be processed by a controller to obtain the current displacement information described in the embodiment of this application.

[0063] Specifically, the nodal displacement measuring device can employ measuring devices based on different principles (such as magnetic field sensing, resistance sensing, voltage sensing, capacitance sensing, or optical sensing) depending on the actual situation. Based on the previous embodiments, this application takes the nodal displacement measuring device as a force / tactile sensor as an example. The force / tactile sensor can use devices based on principles such as magnetic field sensing, resistance sensing, voltage sensing, capacitance sensing, or optical sensing to solve for surface forces.

[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 nodal displacement measuring device as an example of a force / tactile sensor, each sensor unit of the force / tactile sensor 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 and distributed within the flexible body. When the flexible body deforms under the action of an external force, it can cause the magnetic source, etc., to displace. The sensing unit is used to generate displacement information of the measuring nodes based on the acquired signals or to obtain intermediate data for displacement information. For example, the displacement of some nodes in the flexible body 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 1 As shown, taking the node displacement measuring device 110 as an example of a force / tactile sensor 110, the acquisition unit of the force / tactile sensor 110 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 disposed on a circuit board. The sensing unit senses the 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 displacement information. Continuing with the example of the force / tactile sensor 110 being disposed 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 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] In an optional embodiment of this application, the displacement information of the flexible body can also be directly measured by a node displacement measuring device (e.g., an image sensor based on the principle of optical sensing). (That is, the position information of the nodes is identified sequentially by the image sensor at a preset time interval, and the displacement information of the nodes is obtained based on the position information at two adjacent times.)

[0068] 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.

[0069] The controller and the nodal displacement measuring instrument communicate with each other via wired or wireless means.

[0070] 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 4 The computer equipment shown.

[0071] 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.

[0072] First, for ease of understanding, some concepts involved in the embodiments of this application will be explained.

[0073] A "nonlinear material constitutive model" refers to a mechanical behavior description model in materials mechanics that describes the nonlinear relationship between the deformation of a flexible body under stress and the applied force. Specifically, nonlinear material constitutive models can be, but are not limited to, elastoplastic models, viscoelastic-plastic models, and inherently nonlinear models. For ease of understanding and to adapt to the solution of surface forces in the aforementioned flexible bodies, the embodiments of this application will primarily use the Mooney-Rivlin hyperelastic nonlinear material model as an example for detailed explanation.

[0074] The "finite element model" refers to discretizing the 3D model of a flexible body into a mesh formed by multiple polyhedral elements, with the connection points between the polyhedral elements being nodes. The motion of the flexible body after being subjected to external forces is described by the displacement of the nodes.

[0075] A "node" refers to the connection point between the finite element solid elements in a finite element model. Specifically, the 3D model of a flexible body can be discretized into multiple virtual finite element solid elements (such as tetrahedral elements, hexahedral elements, etc.), thereby forming a virtual mesh (i.e., a finite element model) corresponding to the flexible body, composed of multiple solid elements. The connection points between the solid elements within the mesh are referred to as the aforementioned "nodes".

[0076] The "static equilibrium equation" is a data physics equation that describes the relationship between external forces and the deformation of a structure (such as a flexible body) in a static equilibrium state.

[0077] like Figure 2 As shown, Figure 2 This is a flowchart illustrating an embodiment of the surface force solution method based on flexible bodies according to this application.

[0078] 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 a controller. The above-mentioned method for solving surface forces based on flexible bodies may include the following steps:

[0079] Step 210: Obtain the current displacement information of the measurement nodes of the finite element model of the flexible body; the measurement nodes are some nodes in the finite element model.

[0080] Step 220: Based on the current displacement information of the measurement nodes, establish the current objective function of the optimization problem through the static equilibrium equation, wherein preset constraints are added to the current objective function.

[0081] Step 230 solves the optimization problem to obtain the surface forces of the flexible body.

[0082] This application embodiment constructs an optimization problem of static equilibrium equations based on the known current node displacement information of some nodes of a flexible body, adds preset constraints, and obtains the surface force of the flexible body at the current moment by solving the optimization problem. Since the surface force of the flexible body can be obtained based only on the current node displacement information of some nodes of the flexible body, it is more versatile and can be mass-produced compared to neural network methods, which do not require the collection of a large amount of sample data. In addition, by constructing an optimization problem of static equilibrium equations and then solving the optimization problem to obtain the surface force of the flexible body, the computational efficiency is high compared to directly solving the surface force of the flexible body based on the static equilibrium equations, and it can meet the real-time requirements.

[0083] To facilitate understanding, the above methods and steps will be explained in further detail below.

[0084] Step 210: Obtain the current displacement information of the measurement nodes of the finite element model of the flexible body; the measurement nodes are some nodes in the finite element model.

[0085] In an optional embodiment of this application, the controller obtains the current displacement information of the measurement node at the current time or the current time period from the memory or server according to a preset address.

[0086] In this embodiment, the measurement nodes are a subset of nodes in the finite element model. That is, it is not necessary to obtain the displacement information of all nodes in the finite element model of the flexible body; only the displacement information of a subset of nodes is required. For example, a predetermined number (e.g., 9 nodes) evenly distributed in the finite element model of the flexible body can be selected as measurement nodes. A predetermined sensing unit corresponds to the position of each measurement node, thereby acquiring the current displacement information of each measurement node based on each sensing unit. Alternatively, some intermediate data can be acquired through each measurement node, and then the controller performs certain processing on the intermediate data to obtain the current displacement information described in this embodiment.

[0087] Specifically, the current displacement information of the measurement node can be obtained directly from the output of the node displacement measuring device; or it can be obtained from the discrete current sensing signal (i.e., current intermediate data) of the measurement node collected by the node displacement measuring device, and then the controller can obtain the current displacement information of the measurement node based on the current sensing signal, etc., all of which fall within the scope of protection of this application.

[0088] In an optional embodiment of this application, before step 210 obtains the current displacement information of the measurement nodes of the finite element model of the flexible body, the method of this embodiment may further include the following method steps:

[0089] Step 290: Construct the finite element model of the flexible body.

[0090] In an optional embodiment of this application, the 3D model of the flexible body can be discretized into multiple virtual finite element solid units (such as tetrahedral units, hexahedral units, etc.) in advance, either offline or in real time, thereby forming a virtual mesh (i.e., finite element model) corresponding to the flexible body, which is composed of multiple solid units.

[0091] For example, taking hexahedral elements as an example, the 3D model of the flexible body of the force / tactile sensor to be measured can be meshed offline in advance or in real time to obtain a hexahedral mesh composed of multiple hexahedral elements, each hexahedral element including eight nodes. In this embodiment of the application, the 3D model of the flexible body to be measured can be meshed offline in advance or in real time to obtain a hexahedral mesh composed of multiple hexahedral elements, each hexahedral element including eight nodes. Specifically, meshing can be performed using various existing or future meshing tools / software, such as Code_aster and Gmsh.

[0092] Step 220: Based on the current displacement information of the measurement nodes, establish the current objective function of the optimization problem through the static equilibrium equation, wherein preset constraints are added to the current objective function.

[0093] In an optional embodiment of this application, the preset constraints may include: preset friction cone constraints and boundary force constraints.

[0094] In an optional embodiment of this application, the controller may obtain preset friction cone constraints and boundary force constraints from a memory or server according to a preset address, and add the friction cone constraints and boundary force constraints as constraints of the objective function.

[0095] For example, the friction cone constraint (3.2) is as follows:

[0096] st|f i，x |<0.7071μ|f i，z |

[0097] |f i，y |<0.7071μ|f i，z | (3.2)

[0098] Equation (3.2) represents the force |f| in the x-direction of the friction cone. i，x |force in the y-direction|f i，y |less than the maximum sliding friction (normal force)|f i，z | Multiplied by the sliding friction coefficient 0.7071μ).

[0099] For example, the boundary force constraint (3.3) is as follows:

[0100] x min ≤x i ≤x max

[0101] f x，min ≤f i，x ≤f x，max

[0102] f y，min ≤f i，y ≤f y，max

[0103] f z，min ≤f i，z ≤f z，max (3.3)

[0104] Equation (3.3) represents the maximum surface force constraint in the three directions (x, y, z) of a certain node i, which is artificially defined.

[0105] The embodiments of this application are based on actual application scenarios. For example, in actual target object grasping application scenarios, by adopting friction cone constraints, since there is no relative displacement between the target object and the tactile sensor located on the actuator during the grasping process, the tangential force can be made less than the maximum static friction force by setting friction cone constraint conditions to prevent the object from sliding relative to the sensor. In addition, the actuator usually presets the threshold range of the force during the grasping process, so the boundary force constraint of the force can be set. By setting the boundary force constraint, the calculation of invalid data outside the boundary can be reduced, and the calculation efficiency of the final surface force can be improved.

[0106] It should be noted that, in addition to adding friction cone constraints and boundary force constraints as constraints as described in the above embodiments, other constraints may be used as needed in the embodiments of this application.

[0107] In an optional embodiment of this application, step 220 establishes the current objective function of the static equilibrium equation optimization problem based on the current displacement information of the measurement node, which may specifically include the following method steps:

[0108] Step 221 Obtain the objective function of the optimization problem constructed based on the static equilibrium equation.

[0109] In an optional embodiment of this application, the controller can retrieve the objective function of the optimization problem based on the static equilibrium equation, which is generated offline or in real time, from a memory or server according to a preset address.

[0110] In an optional embodiment of this application, based on the static equilibrium equation (1.4) described in the following embodiment, the objective function (3.1) of the optimization problem of the static equilibrium equation (1.4) can be obtained:

[0111] min(Kx-F)T(Kx-F) (3.1)

[0112] Where K is the overall stiffness matrix; x is the current displacement information of the measurement node; and F is the surface force of the flexible body.

[0113] In this embodiment, since the known node displacement is less than the node where the surface force of the object is actually obtained, the static equation is an underdeterminate problem. It cannot be solved directly based on the linear static equilibrium equation (1.4). Therefore, it can be transformed into a least squares problem, that is, constructing the objective function (3.1) of the optimization problem of the static equilibrium equation (1.4) to facilitate the solution of the surface force.

[0114] Step 222: Substitute the current displacement information of the measured node into the objective function (3.1) to obtain the current objective function.

[0115] In this embodiment of the application, the current displacement information x of the above-mentioned measurement node is substituted into the objective function (3.1) to realize the above-mentioned "the current objective function of the optimization problem of establishing static equilibrium equation based on the current displacement information of the measurement node".

[0116] In an optional embodiment of this application, before step 220 establishes the current objective function of the static equilibrium equation optimization problem based on the current displacement information of the measurement node, the method of this embodiment may further include the following method steps:

[0117] Step 270: Construct the static equilibrium equations.

[0118] Step 280: Establish the objective function for the optimization problem of the static equilibrium equations.

[0119] This application embodiment constructs a static equilibrium equation, then establishes an objective function for the optimization problem of the static equilibrium equation, and subsequently obtains the surface force by solving the optimization problem.

[0120] Furthermore, in an optional embodiment of this application, step 270, which constructs the static equilibrium equations, may specifically include the following method steps:

[0121] Step 271: Construct the stress-strain matrix based on the nonlinear material constitutive model of the flexible body.

[0122] For example, the stress-strain matrix obtained from the constitutive model of a Mooney-Rivlin hyperelastic nonlinear material is used as an example for illustration. The strain energy function W of the Mooney-Rivlin hyperelastic material is as follows:

[0123] W=C 10 (I1-3)+C 01 (I²⁻³) + C 20 (I1-3) 2 +C 11 (I1-3)(I2-3)

[0124] +C 02 (I2-3) 2 +C 30 (I1-3) 3 +C 21 (I1-3) 2 (I2-3)

[0125] +C 12 (I1-3)(I2-3) 2 +C 03 (I2-3) 3 +D1(exp(D2(I1-3))-1)

[0126] The deformation gradient tensor F is as follows:

[0127]

[0128] Let the right Cauchy-Green tensor be C, with the first invariant being I1 and the second invariant being I2.

[0129]

[0130] Cauchy stress

[0131]

[0132] Take the partial derivative of the strain energy function with respect to the right Cauchy-Green tensor C (retaining 5 terms):

[0133]

[0134] The stress-strain matrix D(1.1) is as follows:

[0135]

[0136] Step 272: Construct the strain-displacement matrix based on the finite element model of the flexible body. For example, the stiffness matrix is ​​established using a first-order hexahedral element:

[0137]

[0138]

[0139] The strain matrix of node i is as follows:

[0140] ∈ i =[∈ x,i ,∈ y,i ,∈ z,i ,τ xy,i ,τ yz,i ,τ xz,i ] T

[0141] The displacement matrix of node i is as follows:

[0142] u i =[u x,i ,u y,i ,u z,i ]

[0143] The strain-displacement matrix B(1.2) of node i is as follows:

[0144] ∈ i =Bu i

[0145]

[0146] Step 273 combines the stress-strain matrix and the strain-displacement matrix to generate the stiffness matrix.

[0147] For example, the stiffness matrix (1.3) of the element is as follows:

[0148]

[0149] Based on the previous embodiments, where D is the element stress-strain matrix; B is the strain-displacement matrix; K e dΩ represents the element stiffness matrix; dΩ represents the volume integral.

[0150] Then the element stiffness matrix K e Assemble the components according to their degree of freedom numbers to form the overall stiffness matrix K.

[0151] Step 274 generates static equilibrium equations based on the stiffness matrix.

[0152] In an optional embodiment of this application, the static equilibrium equation can be equation (1.4):

[0153] K·x=F (1.4)

[0154] Where K is the overall stiffness matrix; x is the current displacement information of the measurement node; and F is the surface force of the flexible body.

[0155] It should be noted that the aforementioned nonlinear material constitutive models, stress-strain matrices, strain-displacement matrices, element stiffness matrices, global stiffness matrices, and static equilibrium equations are merely illustrative examples. Therefore, in addition to the examples listed in the above embodiments, various existing or future nonlinear material constitutive models, stress-strain matrices, strain-displacement matrices, stiffness matrices, and static equilibrium equations can be used as needed, and all fall within the scope of protection of this application.

[0156] In this embodiment, a stress-strain matrix is ​​constructed based on a nonlinear material constitutive model of a flexible body, and a strain-displacement matrix is ​​constructed based on a finite element model of the flexible body. The stiffness matrix is ​​generated by combining the stress-strain matrix and the strain-displacement matrix, and then the stiffness matrix is ​​substituted into the static equilibrium equation. Thus, a static equilibrium equation can be constructed based on the nonlinear material constitutive model and the finite element model.

[0157] Step 230 solves the optimization problem to obtain the surface forces of the flexible body.

[0158] Specifically, the optimization problem can be solved using various existing or future methods.

[0159] In an optional embodiment of this application, step 230, solving the optimization problem to obtain the surface force of the flexible body, may specifically include the following method steps:

[0160] Step 231 transforms the optimization problem into a quadratic programming problem under constraints.

[0161] In an optional embodiment of this application, step 231 transforms the optimization problem into a quadratic programming problem under constraints, which may specifically include the following method steps:

[0162] Step 2311: Perform a second expansion of the current objective function to obtain the second expansion of the gradient and Hessian matrix.

[0163] For example, the quadratic expansion (4) can be expressed as:

[0164]

[0165] Where x is the displacement of the unknown node, F is the surface force, H is the Hessian matrix of the objective function at x0 and F0, and g is the gradient of the objective function at x0 and F0; x0 is the displacement of the unknown node solved in the previous iteration, and F0 is the surface force solved in the previous iteration.

[0166] The values ​​of x0 and F0 during the initial iteration process can be preset.

[0167] For example, based on the objective function (3.1), the corresponding Hessian matrix and gradient can be obtained.

[0168] Step 2312: Add constraints for the quadratic expansion.

[0169] Continuing with the previous example, the constraint can include: friction cone constraint and boundary force constraint. That is, the above quadratic expansion (4) also needs to be limited to certain constraint conditions, such as the friction cone constraint (3.2) and boundary force constraint (3.3) mentioned in the above embodiment.

[0170] In this embodiment, for the measurement node equipped with a data acquisition unit (e.g., a magnet), the displacement of the measurement node can be measured using a node displacement measuring device. Apart from this, the displacements of other nodes in the finite element model are unknown and need to be determined; therefore, they can be called unknown nodes. That is, x and F are the variables that need to be solved.

[0171] Step 233 solves the quadratic programming problem to obtain the surface forces.

[0172] In an optional embodiment of this application, step 233 solves a quadratic programming problem to obtain the surface force, which may specifically include the following method steps:

[0173] Step 2331 solves the quadratic programming problem using an iterative method until a preset termination condition is met.

[0174] Specifically, the termination condition can be set arbitrarily as needed, such as reaching the convergence condition or reaching a preset number of iterations.

[0175] Step 2332: The surface force that satisfies the preset termination condition is taken as the final surface force.

[0176] It should be noted that, in addition to the iterative method for obtaining surface forces based on a quadratic programming problem, other existing or future methods can also be used to solve the quadratic programming problem as needed.

[0177] In this embodiment, the nonlinear problem can be expanded twice within a certain motion limit. Equations 3.2 and 3.3 can be represented as linear constraints, thereby transforming the optimization variables into a quadratic programming (QP) problem within a certain interval, and iterating and solving the problem in sequence until the preset termination conditions such as convergence are met and the iteration stops.

[0178] The embodiments of this application solve the optimization problem by converting it into a quadratic programming problem, which is highly efficient (e.g., compared to gradient descent) and meets real-time requirements. In addition, by adding preset constraints, the final value of the surface force is closer to the actual result.

[0179] In an optional embodiment of this application, step 230, solving the optimization problem to obtain the surface force of the flexible body, may specifically include the following method steps:

[0180] Step 232 determines whether the optimization problem has reached the preset convergence condition based on the current displacement and current surface force of the unknown node.

[0181] The current displacement and current surface force of the unknown node can be the displacement and surface force of the unknown node obtained in the previous iteration. For the initial iteration, the current displacement and current surface force of the unknown node can be preset with initial values.

[0182] Step 234: If the preset convergence condition is met, the surface force in the optimization problem when the preset convergence condition is met is taken as the final surface force.

[0183] If step 236 determines that the preset convergence condition has not been met, repeat the above method steps until the preset convergence condition is met.

[0184] The embodiments of this application can directly solve the optimization problem based on the gradient descent method. That is, based on the current displacement information of the measurement node, it is determined whether the optimization problem has reached the preset convergence condition. If it is determined that the preset convergence condition has been reached, the surface force is output. If it is determined that the preset convergence condition has not been reached, the above method steps are repeated until the preset convergence condition is reached, thereby effectively realizing the solution of the surface force.

[0185] Those skilled in the art will understand that all or part of the processes in 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 above methods. 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).

[0186] 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.

[0187] Further reference Figure 3 As a response to the above Figure 2 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 2 Corresponding to the method embodiment shown, the device can be specifically applied to a controller.

[0188] like Figure 3 As shown, the surface force solving device 400 based on flexible bodies described in this application embodiment may include: an information acquisition module 410, an optimization conversion module 420, and a force value solving module 430.

[0189] The information acquisition module 410 is used to acquire the current displacement information of the measurement nodes of the finite element model of the flexible body; the measurement nodes are some nodes in the finite element model.

[0190] The optimization and transformation module 420 is used to establish the current objective function of the static equilibrium equation optimization problem based on the current displacement information of the measurement nodes; wherein, the current objective function is subject to preset constraints.

[0191] The force calculation module 430 is used to solve optimization problems to obtain the surface forces of the flexible body.

[0192] This application embodiment constructs an optimization problem of static equilibrium equations based on the known current node displacement information of some nodes of a flexible body, adds preset constraints, and obtains the surface force of the flexible body at the current moment by solving the optimization problem. Since the surface force of the flexible body can be obtained based only on the current node displacement information of some nodes of the flexible body, it is more versatile and can be mass-produced compared to neural network methods, which do not require the collection of a large amount of sample data. In addition, by constructing an optimization problem of static equilibrium equations and then solving the optimization problem to obtain the surface force of the flexible body, the computational efficiency is high compared to directly solving the surface force of the flexible body based on the static equilibrium equations, and it can meet the real-time requirements.

[0193] In an optional embodiment of this application, the optimization conversion module 420 may include:

[0194] The function acquisition submodule is used to obtain the objective function (3.1) of the optimization problem constructed based on the static equilibrium equation;

[0195] min (kx-F) T (Kx-F) (3.1)

[0196] Where K is the overall stiffness matrix; x is the current displacement information of the measured node; F is the surface force; the constraints include: preset friction cone constraints and boundary force constraints;

[0197] The function construction submodule is used to input the current displacement information of the measurement node into the objective function (3.1) to obtain the current objective function.

[0198] In an optional embodiment of this application, the force calculation module 430 may include:

[0199] The quadratic programming submodule is used to transform optimization problems into quadratic programming problems under constraints.

[0200] The problem-solving submodule is used to solve a quadratic programming problem to obtain the surface forces.

[0201] In an optional embodiment of this application, the quadratic planning submodule may include:

[0202] The second expansion unit is used to expand the current objective function in a second step to obtain the second expansion of the gradient and Hessian matrix.

[0203] The preset addition unit is used to add constraints as constraints in the quadratic expansion.

[0204] In an optional embodiment of this application, the problem-solving submodule may include:

[0205] The problem-solving unit is used to solve quadratic programming problems using an iterative method until a preset termination condition is met.

[0206] The result determination unit is used to determine the surface force when the preset termination condition is met as the final surface force.

[0207] In an optional embodiment of this application, the force calculation module 430 may include:

[0208] The condition judgment submodule is used to determine whether the objective function has reached the preset convergence condition based on the current displacement and current surface force of the unknown node.

[0209] The force value determination submodule is used to determine the final surface force if a preset convergence condition is met.

[0210] The step repeat submodule is used to repeat the above method steps if the preset convergence condition is not met, until the preset convergence condition is met.

[0211] In an optional embodiment of this application, the surface force solving device 400 based on a flexible body may further include:

[0212] The first building module is used to construct the stress-strain matrix based on the nonlinear material constitutive model of flexible bodies;

[0213] The second building module is used to construct the strain-displacement matrix based on the finite element model of the flexible body;

[0214] The matrix combining module is used to combine the stress-strain matrix and the strain-displacement matrix to generate the overall stiffness matrix of the flexible body.

[0215] The equation building module is used to construct static equilibrium equations based on the global stiffness matrix.

[0216] The function building module is used to establish the objective function for the optimization problem of the static equilibrium equations.

[0217] In an optional embodiment of this application, the surface force solving device 400 based on a flexible body may further include:

[0218] The model building module is used to build finite element models of flexible bodies.

[0219] To address the aforementioned technical problems, embodiments of this application also provide a method such as... Figure 4 The computer equipment shown.

[0220] The computer device can be a terminal or a server.

[0221] 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.

[0222] 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.

[0223] 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.

[0224] 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.

[0225] 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.

[0226] 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.

[0227] 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.

[0228] 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 current displacement information of the measurement nodes of the finite element model of the flexible body; The measurement nodes are some of the nodes in the finite element model; Based on the current displacement information of the measurement node, a current objective function is established for the optimization problem of the static equilibrium equation; wherein, a preset constraint condition is added to the current objective function; Solve the optimization problem to obtain the surface forces of the flexible body.

2. The surface force solution method based on flexible bodies according to claim 1, characterized in that, The objective function for optimizing the static equilibrium equations based on the current displacement information of the measurement nodes, and the addition of preset constraints, specifically includes the following steps: Obtain the objective function (3.1) of the optimization problem constructed based on the static equilibrium equation; min(Kx-F) T (Kx-F) (3.1) Where K is the overall stiffness matrix; x is the current displacement information of the measurement node; F is the surface force; the constraint conditions include: preset friction cone constraint conditions and boundary force constraints; The current displacement information of the measurement node is substituted into the objective function (3.1) to obtain the current objective function.

3. The surface force solution method based on flexible bodies according to claim 1 or 2, characterized in that, Solving the optimization problem to obtain the surface forces of the flexible body specifically includes the following steps: The optimization problem is transformed into a quadratic programming problem under the constraints. Solve the quadratic programming problem to obtain the surface force.

4. The surface force solution method based on flexible bodies according to claim 3, characterized in that, The process of transforming the optimization problem into a quadratic programming problem under the constraints includes the following steps: The current objective function is expanded twice to obtain the quadratic expansion of the gradient and Hessian matrix. Add the aforementioned constraints as constraints to the quadratic expansion; and / or, Solving the quadratic programming problem to obtain the surface force specifically includes the following steps: The quadratic programming problem is solved using an iterative method until a preset termination condition is met. The surface force at which the preset termination condition is met is taken as the final surface force.

5. The surface force solution method based on flexible bodies according to claim 1 or 2, characterized in that, Solving the optimization problem to obtain the surface force of the flexible body specifically includes the following steps: Based on the current displacement and current surface force of the unknown node, determine whether the objective function has reached the preset convergence condition; If it is determined that the preset convergence condition has been met, the surface force corresponding to the time when the preset convergence condition is met shall be taken as the final surface force. If it is determined that the preset convergence condition has not been met, repeat the above method steps until it is determined that the preset convergence condition has been met.

6. The surface force solution method based on flexible bodies according to claim 1 or 2, characterized in that, Before establishing the current objective function of the optimization problem of the static equilibrium equation based on the current displacement information of the measurement node, the following steps are also included: Stress-strain matrix is ​​constructed based on a nonlinear material constitutive model of flexible bodies; The strain-displacement matrix is ​​constructed based on the finite element model of the flexible body. By combining the stress-strain matrix and the strain-displacement matrix, the overall stiffness matrix of the flexible body is generated. Based on the overall stiffness matrix, the static equilibrium equations are constructed. Establish the objective function of the optimization problem for the static equilibrium equations; and / or, Before obtaining the current displacement information of the measurement nodes of the finite element model of the flexible body, the following steps are also included: Construct the finite element model of the flexible body.

7. A surface force solving device for a flexible body, characterized in that, The device includes: The information acquisition module is used to acquire the current displacement information of the measurement nodes of the finite element model of the flexible body; the measurement nodes are some nodes in the finite element model. The optimization and transformation module is used to establish the current objective function of the optimization problem of the static equilibrium equation based on the current displacement information of the measurement node; wherein, the current objective function is subject to preset constraints. The force calculation module is used to solve the optimization problem to obtain the surface force of the flexible body.

8. A surface force solution system based on flexible bodies, characterized in that, The system includes a nodal displacement measuring device and a controller; The node displacement measuring device and the controller are communicatively connected; The node displacement measuring device is used to measure the current displacement information of the measuring node; The controller is used to implement the steps of the surface force solution method for the flexible body according to any one of claims 1 to 6.

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 method for solving the surface force of a flexible body as described in any one of claims 1 to 6.

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 method for solving the surface forces of a flexible body as described in any one of claims 1 to 6.

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