Dielectric elastomer driven soft robot topology optimization method

Abstract

The application provides a dielectric elastomer driven soft robot topology optimization method, including defining design parameters and boundary conditions; establishing an interpolation relationship between unit elastic modulus and unit density; converting the Laplace equation of electric potential into an integral weak form; representing and integrating the Maxwell stress field to obtain equivalent node force; constructing a topology optimization mathematical model of the dielectric elastomer driven soft robot, solving corresponding sensitivity information; performing binary processing on the topology density field of the topology optimization mathematical model and extracting skeleton features; dynamically applying minimum size constraints and forcing unit density values; updating design variables and judging whether iteration meets convergence conditions, if yes, outputting a dielectric elastomer driven soft robot topology structure meeting minimum size requirements, and the application can effectively avoid the generation of adverse structures such as thin rods and single-node hinges, and significantly improve the manufacturability and mechanical performance matching degree of flexible driving structures.

Description

Technical Field

[0001] This invention belongs to the technical field of soft robot design, and specifically relates to a topology optimization method for a dielectric elastomer-driven soft robot. Background Technology

[0002] Dielectric elastomers (DEEs) are intelligent materials with large deformation capabilities and are widely used in the field of soft robotics. Through electric field excitation, DEEs can achieve complex deformations, thereby driving soft robots to complete various tasks, demonstrating enormous application potential in cutting-edge fields such as flexible grasping, biomimetic robots, and artificial muscles. In existing technologies, traditional topology optimization in DEE-driven soft robot design often results in thin rod structures and single-node hinge-like structures. These structures not only increase manufacturing difficulty but also severely weaken the load-bearing capacity of the mechanism. Furthermore, existing topology optimization processes often suffer from insufficient feature recognition accuracy due to intermediate density element problems and lack dynamic constraints on the minimum feature size, easily leading to premature convergence of the optimization results to local optima. Ultimately, this results in soft robots that fail to meet both manufacturability and mechanical performance requirements. Currently, conventional topology optimization design methods have not effectively suppressed unfavorable structural features. Therefore, there is an urgent need in this field for a topology optimization method for DEE-driven soft robots that can precisely control feature sizes while balancing mechanical performance and manufacturability. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes a topology optimization method for dielectric elastomer-driven soft robots, thereby overcoming the shortcomings of the existing technologies.

[0004] In a first aspect, the present invention provides the following technical solution: a topology optimization method for a dielectric elastomer-driven soft robot, comprising: Define the design parameters and boundary conditions for the dielectric elastomer-driven soft robot; An improved SIMP method is used to establish the interpolation relationship between the element elastic modulus and element density in the design parameters. The design domain is discretized into finite elements, a shape function matrix is ​​defined for each finite element, and the Laplace equation of the potential is transformed into a weak integral form based on the Galerkin method. Calculate the nodal loads of the finite element, express the Maxwell stress field as equivalent body forces, and integrate the equivalent body forces to obtain the equivalent nodal forces; With maximizing the output displacement of the soft robot as the objective function and volume fraction, strain energy, and minimum feature size as constraints, a topology optimization mathematical model for the dielectric elastomer-driven soft robot is constructed, and the sensitivity information of the objective function and constraints of the topology optimization mathematical model to the design variables is solved. The topological density field of the topology optimization mathematical model is binarized using the Otsu threshold segmentation algorithm, and skeleton features are extracted using a parallel topology thinning algorithm. Based on the skeleton features, a minimum size constraint is dynamically applied, and the cell density value is forced to be constrained through the sweep control domain. The design variables are updated using the moving asymptote algorithm, and it is determined whether the iteration meets the convergence condition. If so, the topology configuration of the dielectric elastomer-driven soft robot that meets the minimum size requirement is output.

[0005] Compared to existing technologies, the advantages of this invention are as follows: By combining Otsu threshold segmentation with parallel refinement algorithms, this invention achieves accurate binarization of the topological density field and extraction of skeleton features, effectively suppressing the generation of thin rod structures and single-node hinge-like structures. The optimized topological configuration fully meets the minimum feature size requirements, significantly improving the manufacturability and load-bearing capacity of the structure. Employing a dynamic constraint method for the minimum feature size, size constraints are applied in a timely manner based on the monitoring results of the proportion of intermediate density units during the optimization process. This ensures both the degrees of freedom in the initial optimization stage and precise control of geometric accuracy in critical stages, avoiding premature convergence to local optima. By comprehensively considering volume fraction, strain energy, and minimum structural scale constraints, a multi-constraint optimization model is constructed, ensuring that the optimization results meet performance requirements while possessing good engineering applicability. The use of the moving asymptote algorithm to handle non-convex optimization problems, combined with sensitivity analysis, significantly improves computational efficiency. Simulation results show that the error between theoretical calculations and experimental results is only 2% to 4%, verifying the effectiveness and robustness of the method. It can generate reasonable topological configurations under different volume fractions and size constraints, providing a new idea for high-performance topology optimization of dielectric elastomer-driven soft robots, and has broad application prospects.

[0006] Preferably, the design parameters and boundary conditions include: design domain, fixed constraints, input voltage, allowable volume fraction, minimum filter radius, minimum size control radius, spring stiffness, penalty coefficient, Neo-Hookean model parameters, elastic modulus of solid material and elastic modulus of void material.

[0007] Preferably, the step of establishing the interpolation relationship between the element elastic modulus and element density in the design parameters using the improved SIMP method includes: The elastic modulus of the solid material and the elastic modulus of the void material are introduced as the upper and lower limits of stiffness interpolation, respectively. The unit density is used as the independent variable, and the unit density is penalized using the penalty coefficient to obtain the penalized density. The penalized density is used as the weight to perform interpolation calculation between the elastic modulus of the void material and the elastic modulus of the solid material to establish a mathematical mapping relationship between the unit density and the unit elastic modulus.

[0008] Preferably, the step of binarizing the topological density field of the topology optimization mathematical model using the Otsu thresholding algorithm includes: Calculate the density distribution and probability of the topological density field; The topological density field is divided into a background region and a target region by an arbitrary density value, and the intra-class variance and inter-class variance of the background region and the target region are calculated respectively. The optimal segmentation threshold is determined by maximizing the inter-class variance. The topological density field is segmented based on the optimal segmentation threshold to eliminate intermediate density values ​​and obtain a binarized unit density field.

[0009] Preferably, the step of extracting skeleton features using a parallel topology refinement algorithm includes: Based on the binarized unit density field, initialize the corresponding unit density matrix; A two-stage iterative scan is performed on the cell density matrix to identify and remove redundant boundary cells that satisfy the preset topological connectivity conditions; The two-stage iterative scan is performed repeatedly until the topological configuration of the entity cells in the cell density matrix no longer changes, and the skeleton feature of a single cell width is output.

[0010] Preferably, the step of dynamically applying a minimum size constraint based on the skeleton features and forcing the constraint cell density value through a sweep control domain includes: Monitor the proportion of intermediate density units during the topology optimization iteration process; When the proportion of intermediate density units is less than a preset proportion threshold, the minimum size constraint condition is dynamically activated. After activating the minimum size constraint, a sweep control domain is generated with the centroid of the skeleton unit in the skeleton feature as the center and the minimum size control radius as the radius. In subsequent optimization iterations, the density values ​​of all cells within the sweep control domain are forcibly constrained to 1.

[0011] Preferably, the expression for the topology optimization mathematical model of the dielectric elastomer-driven soft robot is: ; ; ; ; ; ; ; ; ; In the formula, Let be the objective function. This is the position vector for output displacement. It is a displacement vector. For the overall current density matrix, Here is the electric field intensity matrix. For the overall stiffness matrix, For the overall nodal force array, This is the global transformation matrix. This represents the Maxwell stress matrix of a dielectric elastic body under an electric field. This represents the current volume fraction. For permissible volume fraction, For current strain energy, For the defined strain energy, For the current structural feature size, For the minimum feature size, As a correction factor, For the current density, For the first The cell density of each cell, These are volume constraints and strain energy constraints, respectively. To control the radius to the minimum size, For the minimum unit density, For the first The cell density of each cell, This is the unit density after density filtering. The physical density after projection. This represents the total number of units.

[0012] Preferably, the step of solving the objective function and the sensitivity information of the constraints of the topology optimization mathematical model to the design variables includes: The sensitivity of the objective function, volume fraction constraint, and strain energy constraint to the design variables is calculated using the adjoint variable method. The sensitivity of the minimum feature size constraint to the design variables is calculated based on the chain rule.

[0013] Preferably, after the step of determining whether the iteration meets the convergence condition, the method further includes: if the iteration does not meet the convergence condition, repeating the steps of calculating the nodal loads of the finite element, representing the Maxwell stress field as an equivalent body force, and integrating the equivalent body force to obtain the equivalent nodal force. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a flowchart of the topology optimization method for a dielectric elastomer-driven soft robot in an embodiment of the present invention; Figure 2 This is a schematic diagram of the clamp boundary conditions in an embodiment of the present invention; Figure 3 This is a schematic diagram of the topology and skeleton of the size-constrained gripper in an embodiment of the present invention; Figure 4 This is a schematic diagram of the topology and skeleton of the dimension constraint clamp in an embodiment of the present invention; Figure 5 This is a constraint condition iteration diagram in an embodiment of the present invention; Figure 6 This is the output displacement curve in an embodiment of the present invention; Figure 7 This is a stress cloud diagram from an Abaqus simulation in an embodiment of the present invention.

[0016] The embodiments of the present invention will be further described below with reference to the accompanying drawings. Detailed Implementation

[0017] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain embodiments of the present invention, and should not be construed as limiting the present invention.

[0018] Example 1 In Embodiment 1 of the present invention, as Figure 1 As shown, a topology optimization method for a dielectric elastomer-driven soft robot includes: S1. Define the design parameters and boundary conditions of the dielectric elastomer-driven soft robot; The design parameters and boundary conditions include: design domain, fixed constraints, input voltage, allowable volume fraction, minimum filter radius, minimum size control radius, spring stiffness, penalty coefficient, Neo-Hookean model parameters, elastic modulus of solid materials and elastic modulus of void materials.

[0019] S2. Using the improved SIMP method, establish the interpolation relationship between the element elastic modulus and element density in the design parameters; Specifically, step S2 includes: The elastic modulus of the solid material and the elastic modulus of the void material are introduced as the upper and lower limits of stiffness interpolation, respectively. The unit density is used as the independent variable, and the unit density is penalized using the penalty coefficient to obtain the penalized density. The penalized density is used as the weight to perform interpolation calculation between the elastic modulus of the void material and the elastic modulus of the solid material to establish a mathematical mapping relationship between the unit density and the unit elastic modulus.

[0020] Specifically, it employs the improved Solid Isotropic Material with Penalization (SIMP) method to describe the relationship between the element elastic modulus and design variables. It can be represented as: ; In the formula, Representation unit The elastic modulus, The penalty coefficient is 3. It is the elastic modulus of solid materials. Let be the elastic modulus of the void material, and take a value of . To avoid singularities in the element stiffness matrix, For the first Cell density of each cell; S3. Discretize the design domain into finite elements, define a shape function matrix for each finite element, and transform the Laplace equation of the potential into an integral weak form based on the Galerkin method. It is understandable to consider an infinitesimal volume unit. Under steady-state conditions, the amount of current flowing in is equal to the amount of current flowing out. According to the law of conservation of charge, we can conclude that: ; In the formula, There are three directions respectively. This is the voltage drop. They are respectively Current in the direction, This represents the total change in current. Substituting into the equation yields Laplace's equation for the electric potential: ; In the formula, For electrical conductivity, The electric potential distribution function; To avoid directly dealing with the second derivative, the Galerkin method is used to transform the differential equation into a weak integral form, and a trial function is chosen. Transform the differential equation into an integral equation: ; Each of them All are made by Constructed using the same basis functions, where N represents the total number of elements. The design domain... Discretize into finite elements, with each element defining a shape function matrix. : ; in, These are the basis functions for nodes 1-4, respectively. Cell potential. From nodal potential Interpolation yields: ; In the formula, the nodal potential Similarly, the interpolation expression for the trial function can be obtained. : ; In the formula, For the first The trial function for each unit, The potential of nodes 1-4; Using integration by parts and Green's theorem, the expression can be expanded as follows: ; In the formula, For surface Boundary normal, This is the current volume fraction, here Become , For the boundary The trial function value at point [0, 1] is obtained by substituting the weak form into the form function according to the above formula: ; In the formula, the gradient matrix , Represents shape function, Indicates the external reference potential. The global transformation matrix can be simplified to:

[0021] in, For the overall charge density matrix, Here is the electric field intensity matrix. For the overall load vector; S4. Calculate the nodal loads of the finite element, express the Maxwell stress field as equivalent body force, and integrate the equivalent body force to obtain the equivalent nodal force. Specifically, it can be understood that when converting the stress field of a nonlinear material into equivalent nodal loads, the calculation of the stress field itself already takes into account the nonlinearity of the material. The conversion process of nodal forces (i.e., the integration process) depends only on the current stress field and element geometry, and does not require further consideration of the nonlinear or linear properties of the material. Therefore, this process is simply force transfer, and the integration of nodal forces is based on the gradients of the stress tensor and shape functions.

[0022] Representing the Maxwell stress field as equivalent body forces, the force balance equations can be expressed as follows: ; In the formula, , , These are the components of body force in three directions. For stress, in the plane case Indicating thickness, in a plane, The formula can be written as:

[0023] In discretization design, for example... , The gradient matrix, For the first The element stress vector within each element. (Based on body forces) and traction The generated external fundamental force It can be represented as: ; In the formula, , Let be a matrix of shape functions, where It is an identity matrix. Traction force is not considered in this paper. The function, set The formula can be simplified to: ; In the global form, nodal loads With global transformation matrix and global stress vector The relationship is: ; In the formula, the global transformation matrix Transformation matrix of units The assembly is achieved by using Maxwell stress vectors based on the Neo-Hookean hyperelastic model.

[0024] S5. Using maximizing the output displacement of the soft robot as the objective function and volume fraction, strain energy, and minimum feature size as constraints, construct a topology optimization mathematical model for the dielectric elastomer-driven soft robot, and solve for the sensitivity information of the objective function and constraints of the topology optimization mathematical model to the design variables. The expression for the topology optimization mathematical model of the dielectric elastomer-driven soft robot is as follows: ; ; ; ; ; ; ; ; ; In the formula, Let be the objective function. This is the position vector for output displacement. It is a displacement vector. For the overall current density matrix, Here is the electric field intensity matrix. For the overall stiffness matrix, For the overall nodal force array, This is the global transformation matrix. This represents the Maxwell stress matrix of a dielectric elastic body under an electric field. This represents the current volume fraction. For permissible volume fraction, For current strain energy, For the defined strain energy, For the current structural feature size, For the minimum feature size, As a correction factor, For the current density, For the first The cell density of each cell, These are volume constraints and strain energy constraints, respectively. To control the radius to the minimum size, For the minimum unit density, For the first The cell density of each cell, For the first The density of each unit after density filtering. For the first The density of each cell after processing by the Heaviside filtering algorithm. This represents the total number of units.

[0025] The step of solving the objective function and the sensitivity information of the constraints of the topology optimization mathematical model to the design variables includes: S51. Calculate the sensitivity of the objective function, volume fraction constraint, and strain energy constraint to the design variables using the adjoint variable method; Understandably, the Lagrangian function of the topology optimization mathematical model of the dielectric elastomer-driven soft robot based on minimum size control is established by using the adjoint variable method to solve for displacement sensitivity. ; In the formula, For Lagrange functions, The objective function is the representation of the Lagrange function. They are respectively And the adjoint vector of the mechanical equilibrium equation, The current iteration step The global current density matrix, electric field intensity matrix, global stiffness matrix, displacement vector, and global stress vector; Differentiating with respect to the design variables, we get: ; In the formula, The current iteration step Next The density of each cell after processing by the Heaviside filtering algorithm. This can be further simplified to: ;

[0026] In the formula, This is the combined coefficient term for the implicit partial derivatives of the displacement. This is the combined coefficient term for the implicit partial derivatives of the electric field intensity. The vector of partial derivatives of the objective function with respect to the displacement vector; Pick ,get: ; The final sensitivity is: ; constraint The sensitivities to the design variables are as follows: ; ; in, To allow strain energy, The total solid volume of the design domain. For the volume of a single finite element, finally, using the chain rule, the objective and constraint derivatives with respect to the design variables are determined as follows: ; In the formula, The current iteration step Next The density of each unit after density filtering; S52. Calculate the sensitivity of the minimum feature size constraint to the design variables based on the chain rule.

[0027] Understandably, based on minimum size control, calculating the minimum size constraint sensitivity based on the skeleton control domain first involves refining the topology to obtain a single-pixel skeleton. Then, a global sweep is performed with the centroid of each skeleton unit as the center and the preset minimum control size as the diameter, generating the corresponding size control domain. During iterative optimization, the density value of all units within the constraint control domain is forced to be 1. Its mathematical model can be expressed as: ; In the formula: Indicates the target volume fraction; This represents the current material volume fraction; This is a control parameter, and its value is 5; while It is a correction factor, and satisfies .

[0028] It is important to note that the structural evolution in topology optimization depends on the dynamic process of void generation and merging. Applying a minimum size constraint directly at the beginning of the iteration will inhibit the dynamic reconstruction of the material phase and void phase, causing the optimization to converge prematurely to a local optimum. Among these factors, the grayscale ratio... The calculation formula is: ; in, The total number of units, For the first The unit density of each element is processed by the Heaviside filtering algorithm. Minimum size control is applied when the grayscale ratio is less than 15%. This threshold design monitors the global material distribution to ensure that size constraints only intervene after the initial structural framework is formed, maintaining freedom in the early optimization stages while achieving precise geometric control in critical phases. Based on the above formula, the sensitivity of the minimum size constraint can be obtained as: ; S6. The topology density field of the topology optimization mathematical model is binarized using the Otsu threshold segmentation algorithm, and skeleton features are extracted using a parallel topology refinement algorithm. Step S6 includes: S611. Calculate the density value distribution and probability of the topological density field; Understandably, in this embodiment, the core of the Otsu algorithm is to determine an adaptive segmentation threshold by maximizing the inter-class variance criterion, thereby achieving image binarization. Essentially, it divides the image's grayscale histogram into foreground (target region) and background classes, and iteratively calculates the optimal threshold that maximizes the statistical difference between the two classes. For grayscale images generated in topology optimization problems, their grayscale distribution range is defined as... , The maximum gray level is , where the gray level is . The number of units is Then the total number of elements in the design domain satisfies: ; No. The probability of gray levels appearing It can be represented as: ; For the topology optimization problem of a single material system, a single-threshold segmentation strategy is adopted. The segmentation threshold is set to... grayscale image Divided into background areas and target area Their gray levels satisfy the following conditions: ; In the formula, Indicates a low-density area (background); The target structure (foreground) of the topological configuration is the topological configuration itself. The probability distribution of the two regions is shown. and class mean The calculations are as follows: ; ; Overall average gray value of the image It can be represented as: ; S612. Divide the topological density field into a background region and a target region using an arbitrary density value as the boundary, and calculate the intra-class variance and inter-class variance of the background region and the target region respectively. The within-class variance can be calculated according to step S61. and inter-class variance They are respectively: ; ; S613. Determine the optimal segmentation threshold by maximizing the inter-class variance; The optimal threshold that maximizes the statistical difference between the two classes is found through iterative calculation; based on the Otsu method's between-class variance maximization criterion, a corresponding objective function is constructed to measure the between-class variance between the target region and the background region. It can be calculated using the following mathematical expression: ; Optimal splitting threshold under the maximizing inter-class variance criterion It can be determined by the following formula: ; In the formula, For the threshold is Inter-class variance between the target region and the background region at that time; S614. Based on the optimal segmentation threshold, the topological density field is segmented by thresholding to eliminate intermediate density values ​​and obtain a binarized unit density field. Normalization preprocessing is employed to ensure a strict correspondence between gray levels and unit densities. Threshold segmentation is applied to the original filter density field to obtain topological boundaries with clear physical meaning. To achieve binarization of the topological density field, the original filter density field is further processed. Apply threshold segmentation: ; in, This represents the binarized element density field. Normalization preprocessing ensures a strict correspondence between gray levels and element densities, thus yielding topological boundaries with clear physical meaning.

[0029] Step S6 further includes: S621. Based on the binarized unit density field, initialize the corresponding unit density matrix; Understandably, a fast parallel topology refinement algorithm is used to extract skeleton features from a binary density field. Background regions (pixel values ​​0) and target regions (pixel values ​​1) are defined within the binary density field. Redundant boundary pixels are removed through two complementary iterative sub-processes (southeast boundary-northwest corner elimination stage and northwest boundary-southeast corner elimination stage). The deletion condition for each pixel is based on its 8-neighborhood distribution. Skeleton breakage is prevented and only valid boundary points are processed by limiting the number of 0 / 1 patterns and the total number of non-zero pixels. A single-pixel-width skeleton structure is generated through initialization, two-stage iteration, iterative optimization, and output results. S622. Perform a two-stage iterative scan on the unit density matrix to identify and remove boundary redundant units that meet the preset topological connectivity conditions.

[0030] S623. Execute the two-stage iterative scan repeatedly until the topological configuration of the entity cells in the cell density matrix no longer changes, and output the skeleton feature of a single cell width.

[0031] S7. Dynamically apply minimum size constraints based on the skeleton features, and force the constraint on the cell density value through the sweep control domain; Specifically, step S7 includes: S71. Monitor the proportion of intermediate density units during the topology optimization iteration process; S72. When the proportion of intermediate density units is less than the preset proportion threshold, the minimum size constraint condition is dynamically activated. S73. After activating the minimum size constraint, a sweep control domain is generated with the centroid of the skeleton unit in the skeleton feature as the center and the minimum size control radius as the radius. S74. In subsequent optimization iterations, all cell density values ​​within the sweep control domain are forcibly constrained to 1.

[0032] Specifically, a fast parallel topology thinning algorithm is used to perform a southeast-northwest corner point elimination stage on the binary density field: processing the boundary features of the lower right region of the image; The deletion condition for each pixel P is based on its 8-neighborhood distribution and must simultaneously satisfy the following four conditions: ; in, It is an ordered neighborhood set , These are the 8 neighboring pixels arranged clockwise. It is the total number of non-zero pixels in the 8-neighborhood, expressed mathematically as: ; A fast parallel topology thinning algorithm is used to perform a northwest boundary-southeast corner point elimination stage on the binary density field: clearing the boundary features of the upper left region of the image.

[0033] The second iteration phase will condition and conditions Make corrections: ; ; It can be proved by solving a system of equations: ; ; This solution set shows that the algorithm precisely eliminates the southeast boundary or the northwest corner point. Exclude isolated points and endpoints, conditions By limiting the number of 01 modes to 1, conditions for skeleton fracture are effectively prevented. and conditions Ensure that only valid boundary points are processed.

[0034] Based on the above analysis, the parallel thinning algorithm for binary images can be systematically implemented according to the following steps: 1. Initialization: Create a copy of the target image and a temporary cache space. 2. Two-stage iteration: Phase 1: Cache the current target image, scan all foreground pixels, and erase when all four topological conditions are met simultaneously; Phase 2: After updating the cache, rescan and erase when the eight-neighborhood meets the four supplementary conditions; 3. Iterative optimization: Perform a two-stage scan repeatedly until the image structure stabilizes and remains unchanged; 4. Output: Output the final skeleton image; The minimum size control domain is determined by sweeping the skeleton with the minimum control size as the diameter. This means that the topological configuration is first refined to obtain a single-pixel skeleton. Then, a global sweep is performed with the centroid of each skeleton unit as the center and the preset minimum control size as the diameter, generating the corresponding size control domain. During iterative optimization, the density of all units within the control domain is forced to be 1. The mathematical model can be expressed as: ; In the formula: Indicates the target volume fraction; This represents the current material volume fraction; This is a control parameter, and its value is 5; while It is a correction factor, and satisfies .

[0035] It should be noted that the structural evolution in topology optimization depends on the dynamic process of void generation and merging. Applying a minimum size constraint directly at the beginning of the iteration will inhibit the dynamic reconstruction of the material phase and void phase, causing the optimization to converge prematurely to a local optimum. The formula for calculating the grayscale ratio is: ; in, This represents the total number of cells. A minimum size control is implemented when the grayscale ratio is less than 15%. This threshold design monitors the global material distribution to ensure that dimensional constraints only intervene after the initial structural framework is formed, maintaining freedom in the early stages of optimization while achieving precise control of geometric accuracy in critical phases.

[0036] S8. Update the design variables using the moving asymptote algorithm and determine whether the iteration meets the convergence condition. If so, output the topology configuration of the dielectric elastomer-driven soft robot that meets the minimum size requirement.

[0037] If the iteration does not meet the convergence condition, the steps of calculating the nodal loads of the finite element, representing the Maxwell stress field as equivalent body forces, and integrating the equivalent body forces to obtain the equivalent nodal forces are repeated.

[0038] Specifically, when the convergence condition is not met, it is necessary to return to the steps of calculating the nodal loads of the finite element, representing the Maxwell stress field as an equivalent body force, integrating the equivalent body force to obtain the equivalent nodal force, and then executing the subsequent steps until the convergence condition is met, and outputting the topology configuration of the dielectric elastomer-driven soft robot that meets the minimum size requirement.

[0039] It should be explained that this method combines deterministic topology optimization with reliability analysis through a two-layer loop architecture, utilizes the MMA algorithm to achieve precise dimensional control, and quantifies the impact of material uncertainties through a hybrid mean method. Numerical examples show that this method is highly effective in suppressing hinge-like structures and improving fatigue reliability, providing an optimization scheme for dielectric elastomer-driven soft robots that balances manufacturability and mechanical performance.

[0040] To further verify the effectiveness of the present invention, the semi-symmetric design domain of the dielectric elastomer with minimum size control, boundary conditions, and input voltage effectiveness are incorporated. This embodiment uses a flexible clamp as an example to explain the present invention.

[0041] Semi-symmetric design domain, boundary conditions, and input voltage of dielectric elastomers with minimum size control, as shown below. Figure 2 As shown, the clamp design area has dimensions of 200mm × 200mm, and an initial test voltage is applied to the left end of the design area. To facilitate placing an object, a size of [size missing] is set at the bottom right edge. The empty area also has a size of [missing information] near the top left corner. The entity is not in the design domain. The design domain is discretized into 200×200 four-node elements, and the minimum filtering radius is... Permissible volume fraction spring stiffness at the output end N / m is used to simulate the stiffness of the clamped object; the Neo-Hookean model parameters are set as follows: shear modulus C10 = 16000, incompressibility coefficient D1 = 1 × 10⁻⁶. 10 The material's elastic modulus was set to 1 GPa, the tensile ratio to be 3.2, and the minimum dimension control radius was set to... It is 6.

[0042] Figure 3 This is a diagram showing the topology and skeleton of a gripper without dimensional constraints. Figure 4 The topology and skeleton diagram of the dimensionally constrained gripper; from Figure 3 It can be seen that the topology of the unconstrained gripper has a hinge-like structure. This hinge-like structure leads to stress concentration and even fatigue failure, which is different from the size-constrained topology. Figure 4 In comparison, hinge-like structures were effectively suppressed; Figure 5 The constraint iteration diagram shows that the constraint values ​​all converge to the set values, thus satisfying the constraint conditions. Figure 6 The output displacement curve clearly shows that the output displacement gradually increases and tends to converge as the number of iterations increases.

[0043] The obtained topology configuration was imported into Abaqus for simulation analysis. Figure 7 The stress cloud diagram shows that the displacement of the target point measured in the experiment is 5.1672 mm. Compared with the theoretically calculated result of 5.3714 mm, the error is about 4%, which meets the requirements.

[0044] The topology optimization method for dielectric elastomer-driven soft robots provided in Embodiment 1 of this invention achieves accurate binarization of the topological density field and extraction of skeleton features by combining Otsu threshold segmentation and parallel refinement algorithms, effectively suppressing the generation of thin rod structures and single-node hinge-like structures. The optimized topological configuration fully meets the minimum feature size requirements, significantly improving the manufacturability and load-bearing capacity of the structure. A dynamic constraint minimum feature size method is adopted, applying size constraints in a timely manner based on the monitoring results of the proportion of intermediate density units during the optimization process. This ensures both the degrees of freedom in the initial optimization stage and precise control of geometric accuracy in critical stages, avoiding premature convergence to local optima. By comprehensively considering volume fraction, strain energy, and minimum structural scale constraints, a multi-constraint optimization model is constructed, ensuring that the optimization results meet performance requirements while possessing good engineering applicability. The moving asymptote algorithm is used to handle non-convex optimization problems, combined with sensitivity analysis, significantly improving computational efficiency. Simulation results show that the error between theoretical calculations and experimental results is only 2% to 4%, verifying the effectiveness and robustness of the method. It can generate reasonable topological configurations under different volume fractions and size constraints, providing a new idea for high-performance topology optimization of dielectric elastomer-driven soft robots, and has broad application prospects.

[0045] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0046] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A topology optimization method for a dielectric elastomer-driven soft robot, characterized in that, include: Define the design parameters and boundary conditions for the dielectric elastomer-driven soft robot; An improved SIMP method is used to establish the interpolation relationship between the element elastic modulus and element density in the design parameters. The design domain is discretized into finite elements, a shape function matrix is ​​defined for each finite element, and the Laplace equation of the potential is transformed into a weak integral form based on the Galerkin method. Calculate the nodal loads of the finite element, express the Maxwell stress field as equivalent body forces, and integrate the equivalent body forces to obtain the equivalent nodal forces; With maximizing the output displacement of the soft robot as the objective function and volume fraction, strain energy, and minimum feature size as constraints, a topology optimization mathematical model for the dielectric elastomer-driven soft robot is constructed, and the sensitivity information of the objective function and constraints of the topology optimization mathematical model to the design variables is solved. The topological density field of the topology optimization mathematical model is binarized using the Otsu threshold segmentation algorithm, and skeleton features are extracted using a parallel topology thinning algorithm. Based on the skeleton features, a minimum size constraint is dynamically applied, and the cell density value is forced to be constrained through the sweep control domain. The design variables are updated using the moving asymptote algorithm, and it is determined whether the iteration meets the convergence condition. If so, the topology configuration of the dielectric elastomer-driven soft robot that meets the minimum size requirement is output.

2. The topology optimization method for a dielectric elastomer-driven soft robot according to claim 1, characterized in that, The design parameters and boundary conditions include: design domain, fixed constraints, input voltage, allowable volume fraction, minimum filter radius, minimum size control radius, spring stiffness, penalty coefficient, Neo-Hookean model parameters, elastic modulus of solid materials and elastic modulus of void materials.

3. The topology optimization method for a dielectric elastomer-driven soft robot according to claim 2, characterized in that, The step of establishing the interpolation relationship between the element elastic modulus and element density in the design parameters using the improved SIMP method includes: The elastic modulus of the solid material and the elastic modulus of the void material are introduced as the upper and lower limits of stiffness interpolation, respectively. The unit density is used as the independent variable, and the unit density is penalized using the penalty coefficient to obtain the penalized density. The penalized density is used as the weight to perform interpolation calculation between the elastic modulus of the void material and the elastic modulus of the solid material to establish a mathematical mapping relationship between the unit density and the unit elastic modulus.

4. The topology optimization method for a dielectric elastomer-driven soft robot according to claim 1, characterized in that, The step of binarizing the topology density field of the topology optimization mathematical model using the Otsu threshold segmentation algorithm includes: Calculate the density distribution and probability of the topological density field; The topological density field is divided into a background region and a target region by an arbitrary density value, and the intra-class variance and inter-class variance of the background region and the target region are calculated respectively. The optimal segmentation threshold is determined by maximizing the inter-class variance. The topological density field is segmented based on the optimal segmentation threshold to eliminate intermediate density values ​​and obtain a binarized unit density field.

5. The topology optimization method for a dielectric elastomer-driven soft robot according to claim 4, characterized in that, The step of extracting skeleton features using a parallel topology refinement algorithm includes: Based on the binarized unit density field, initialize the corresponding unit density matrix; A two-stage iterative scan is performed on the cell density matrix to identify and remove redundant boundary cells that satisfy the preset topological connectivity conditions; The two-stage iterative scan is performed repeatedly until the topological configuration of the entity cells in the cell density matrix no longer changes, and the skeleton feature of a single cell width is output.

6. The topology optimization method for a dielectric elastomer-driven soft robot according to claim 1, characterized in that, The step of dynamically applying minimum size constraints based on the skeleton features and forcibly constraining the cell density value through the sweep control domain includes: Monitor the proportion of intermediate density units during the topology optimization iteration process; When the proportion of intermediate density units is less than a preset proportion threshold, the minimum size constraint condition is dynamically activated. After activating the minimum size constraint, a sweep control domain is generated with the centroid of the skeleton unit in the skeleton feature as the center and the minimum size control radius as the radius. In subsequent optimization iterations, the density values ​​of all cells within the sweep control domain are forcibly constrained to 1.

7. The topology optimization method for a dielectric elastomer-driven soft robot according to claim 1, characterized in that, The expression for the topology optimization mathematical model of the dielectric elastomer-driven soft robot is as follows: ； ； ； ； ； ； ； ； ； In the formula, Let be the objective function. This is the position vector for output displacement. It is a displacement vector. For the overall current density matrix, Here is the electric field intensity matrix. For the overall stiffness matrix, For the overall nodal force array, This is the global transformation matrix. This represents the Maxwell stress matrix of a dielectric elastic body under an electric field. This represents the current volume fraction. For permissible volume fraction, For current strain energy, For the defined strain energy, For the current structural feature size, For the minimum feature size, As a correction factor, For the current density, For the first The cell density of each cell, These are volume constraints and strain energy constraints, respectively. To control the radius to the minimum size, For the minimum unit density, For the first The cell density of each cell, This is the unit density after density filtering. The physical density after projection. This represents the total number of units.

8. The topology optimization method for a dielectric elastomer-driven soft robot according to claim 1, characterized in that, The steps for solving the objective function and the sensitivity information of the constraints of the topology optimization mathematical model to the design variables include: The sensitivity of the objective function, volume fraction constraint, and strain energy constraint to the design variables is calculated using the adjoint variable method. The sensitivity of the minimum feature size constraint to the design variables is calculated based on the chain rule.

9. The topology optimization method for a dielectric elastomer-driven soft robot according to claim 1, characterized in that, After the step of determining whether the iteration meets the convergence condition, the method further includes: if the iteration does not meet the convergence condition, repeating the steps of calculating the nodal loads of the finite element, representing the Maxwell stress field as an equivalent body force, and integrating the equivalent body force to obtain the equivalent nodal force.

Images