A humanoid robot flexible interaction metamaterial topology optimization system and method

Abstract

The present application relates to a kind of humanoid robot flexible interaction metamaterial topology optimization system and method, specifically relates to the field of humanoid robot, the weight of the leg structure of humanoid robot is significantly reduced by the topology optimization of mechanical metamaterial, while enhancing its energy absorption and impact resistance, using isogeometric analysis and customized microstructure design, provide lightweight filling structure with negative poisson ratio characteristics for foot and ankle, significantly improve flexibility under the premise of guaranteeing structural strength, this method effectively solves the contradiction between the strength deficiency of traditional flexible material and the excessive weight of rigid element, makes humanoid robot show more safe buffer characteristics and more stable dynamic control performance when interacting with environment, significantly improves the overall interaction safety and complex environment adaptability of robot.

Description

Technical Field

[0001] This invention relates to the field of humanoid robots, and more specifically, to a flexible interactive metamaterial topology optimization system and method for humanoid robots. Background Technology

[0002] Humanoid robots are a current research hotspot in the fields of artificial intelligence and robotics, and also one of the key industries for future development. Because humanoid robots have a similar appearance and way of moving as humans, they have good affinity and can quickly integrate into human living environments without modifying the environment for robot applications. Since humanoid robots need to complete various complex tasks in human production and living environments, they need to frequently interact with the environment, other robots, and even humans in this process. Therefore, the flexible interaction of humanoid robots is crucial to the safety and stability of robot applications.

[0003] Flexible interaction in humanoid robots is mainly divided into active flexible interaction and passive flexible interaction. Active flexible interaction refers to flexible interaction achieved by adjusting the robot's force-position characteristics through compliant control or admittance control algorithms, reinforcement learning, and multimodal sensory feedback in real-time control. However, real-time control in practical robot applications is often delayed due to signal transmission, controller calculation, and filters in the control algorithm. This prevents the robot from buffering external impacts in time, weakening the role and significance of active flexible interaction. Therefore, humanoid robots need to combine passive compliant interaction with active flexible interaction to ensure safe interaction with the environment, other robots, and even humans by reducing peak impact forces and absorbing energy. In addition, passive compliance can improve the robot's control performance: on the one hand, passive compliance can expand the adjustment range of active compliance by coupling with active compliance, forming an active-passive compliant control system; on the other hand, passive compliance has anti-interference and energy absorption capabilities, and can improve the robustness of the control system by absorbing high-frequency noise. Therefore, passive compliant interaction is very important for humanoid robots.

[0004] Generally speaking, flexible interaction in humanoid robots can be achieved through two methods: flexible mechanisms represented by series elastic actuators (SEAs) and flexible structures made of flexible materials such as rubber. Meanwhile, the interaction positions of humanoid robots are generally at the limb ends, such as robotic hands and robotic feet. These positions are quite sensitive to structural weight. Therefore, it is of great significance to achieve lightweight and flexible design of the interaction mechanism and structure of the robot's end effector.

[0005] The main drawback of existing technologies is that in flexible interactive mechanisms, SEAs generally require one or more heavy springs to match the output range of the actuators, resulting in a large weight. Furthermore, the springs are often soft, which can easily cause controller oscillations and reduce the control bandwidth. In flexible interactive structures, flexible materials such as rubber have the disadvantage of low structural strength, which reduces the stability and accuracy of robot applications.

[0006] To address the aforementioned shortcomings, a microstructure design of mechanical metamaterials using topology optimization methods can achieve lightweighting while maintaining flexibility and good strength. Mechanical metamaterials are artificially designed negative Poisson's ratio composite structures exhibiting mechanical properties distinct from conventional structures: they contract laterally when compressed and expand laterally when stretched. The unique mechanical properties of mechanical metamaterials primarily depend on the mesh structure of the microstructure rather than material properties, and they possess several excellent characteristics that meet the requirements of flexible interaction in humanoid robots: lightweight, high strength, good energy absorption, and good impact resistance. Therefore, they are suitable for the passive flexible interaction design of humanoid robots. By optimizing the microstructure of the robot's interactive end effector using metamaterials and designing the microstructure filling of the flexible interaction mechanism and structure, it is possible to effectively improve the flexible interaction performance of humanoid robots while achieving lightweighting, which is of significant research value. Summary of the Invention

[0007] This invention addresses the technical problems existing in the prior art by providing a flexible interactive metamaterial topology optimization system and method for humanoid robots. Through topology optimization of mechanical metamaterials, the weight of the humanoid robot's leg structure is significantly reduced, while its energy absorption and impact resistance are enhanced. By employing isogeometric analysis and customized microstructure design, a lightweight filling structure with negative Poisson bit properties is provided for the foot and ankle joints, significantly improving compliance while ensuring structural strength, thereby solving the problems mentioned in the background art.

[0008] The technical solution of this invention to solve the above-mentioned technical problems is as follows: a humanoid robot flexible interactive metamaterial topology optimization system, specifically including: an initial design module, an isogeometric analysis module, a topology optimization module, and an array generation module, wherein... Initial design module: Receives the geometric dimensions and material parameters of the humanoid robot's leg structure, establishes the control points and node parameters of the mechanical metamaterial microstructure through non-uniform rational B-spline basis functions, including chiral microstructures or concave microstructures, and outputs a parameterized geometric model file; Iso-geometric analysis module: Receives parameterized geometric model files, uses an energy-based homogenization method to calculate the equivalent elastic properties of the microstructure at the macroscale, and outputs homogenized elastic tensor data; Topology optimization module: Receives homogenized elastic tensor data, constructs an isogeometric topology optimization model through the node density distribution function, adopts a multi-objective optimization strategy of minimizing strain energy and maximizing negative Poisson's ratio effect, and outputs optimized microstructure configuration data; Array generation module: Receives optimized microstructure configuration data, performs periodic arrangement of microstructures and cylindrical surface curling operations according to the size of the humanoid robot's feet and the installation space requirements of the series elastic actuators, and outputs three-dimensional model data of the mechanical metamaterial infill structure; In a preferred embodiment, the construction process of the non-uniform rational B-spline basis functions in the initial design module is as follows: First, the CAD geometric file of the humanoid robot's leg structure is read, and the contour curve data of the foot contact surface and ankle joint connection are extracted. The number and position of control points are set according to the contour curvature characteristics. The node vector values ​​are calculated using the chord length parameterization method. The boundary curve of the mechanical metamaterial unit cell is fitted by the back calculation control point technology. The mapping relationship from the two-dimensional parameterized space to the three-dimensional physical space is established. Finally, a parameterized geometric model file containing control point coordinates, node vector sequence and basis function order is generated. This file is transferred to the isogeometric analysis module for finite element mesh generation. The number of control points is dynamically adjusted according to the rate of change of contour curvature. The node vector sequence is generated using the uniform parameterization method. The order of the basis function is set to quadratic or cubic to achieve curve smoothness. The entire construction process iteratively optimizes the position of control points to reduce fitting error and achieves high-precision representation of the geometric model.

[0009] In a preferred embodiment, the execution process of the energy-based homogenization method in the isogeometric analysis module is as follows: The non-uniform rational spline basis function information is read from the parametric geometric model file. Gaussian integration points and weight coefficients are generated in the parameter space. The derivatives and Jacobian matrix determinants of the basis functions at each integration point are calculated. The micro-stiffness matrix is ​​obtained by integrating the product of the constitutive relation matrix and the strain-displacement matrix. The micro-displacement response under the unit test strain field is solved. The values ​​of each component of the macro-equivalent elastic tensor, including Young's modulus, shear modulus and Poisson's ratio, are calculated according to the mean stress-strain relationship. These parameters are transmitted to the topology optimization module as homogenized elastic tensor data. The number of Gaussian integration points is automatically selected based on the order of the basis functions, the determinant of the Jacobian matrix is ​​used to achieve integration accuracy, the micro-displacement response is solved using the conjugate gradient method, and the mean stress-strain relationship is obtained through volume averaging.

[0010] In a preferred embodiment, the process of establishing the node density distribution function in the topology optimization module is as follows: A density variable allocation scheme corresponding to control points is adopted, with each control point associated with a density value between zero and one. A continuous mapping from control point density to field point density is achieved through radial basis function interpolation. A penalty factor is introduced to suppress intermediate density values. Sensitivity analysis is used to calculate the derivative of the objective function with respect to the density variable. The density variable values ​​are updated using the optimization criterion method. The optimization process that satisfies volume constraints is completed by using the moving asymptote algorithm. After iterative calculation, the optimal density distribution field is output. The initial value of the density variable is set to 0.5, the radial basis function kernel radius is adaptively adjusted according to the control point spacing, the penalty factor is between two and four, the sensitivity analysis adopts the adjoint variable method, the volume constraint is implemented by the Lagrange multiplier method, and the iterative calculation is performed until the density change is less than the threshold.

[0011] In a preferred embodiment, the geometric topology optimization model in the topology optimization module is constructed as follows: Using the minimization of the compliance of the micro-unit cell and the maximization of the negative Poisson's ratio effect as dual objective functions, the multi-objective process is transformed into a single-objective optimization process through the weighted summation method. The macroscopic equivalent performance parameters are calculated using an energy-based homogenization method, and the amount of material used is limited by the volume fraction constraint. The constraint optimization process is realized through the Lagrange multiplier method, and the sensitivity of the objective function to the design variables is calculated using the adjoint variable method. The gradient-based optimization algorithm is used for iterative solution. Each iteration requires recalculation of the homogenization elastic tensor and sensitivity information, and finally, microstructure configuration data with negative Poisson's ratio properties are obtained. Among them, compliance is defined as the strain energy density integral, the negative Poisson's ratio effect is quantified by the principal Poisson's ratio, the weight coefficients of the weighted summation method are adjusted according to the application requirements, the upper limit of the volume fraction constraint is set to 0.3 of the material volume fraction, and the gradient-based algorithm adopts the MMA method.

[0012] In a preferred embodiment, the process of periodically arranging the microstructures in the array generation module is as follows: The array layout area is determined based on the shape of the foot sole of the humanoid robot. The microstructure units are arranged in a hexagonal close-packing manner. Boolean operations are used to realize the connection relationship between adjacent microstructures to maintain the continuity of the force flow path. Incomplete units at the edge are trimmed and transitioned. A radial arrangement is used in the ankle joint mounting area to adapt to the cylindrical space constraint. Finally, parameterized array data containing unit position coordinates, rotation angles and scaling ratios are generated. The array arrangement area is obtained by discretizing the foot surface, the hexagonal stacking spacing is calculated based on the microstructure unit size, Boolean operation uses union operation to achieve structural connectivity, edge trimming uses adaptive mesh refinement technology, and the radial arrangement angle is evenly distributed according to the installation space.

[0013] In a preferred embodiment, the specific steps of the cylindrical surface curling operation in the array generation module are as follows: First, the radius and height parameters of the target cylindrical surface of the series elastic actuator are determined. A mapping function from the planar coordinate system to the cylindrical surface coordinate system is established. The geometric properties of the microstructure unit are kept unchanged by conformal transformation technology. The mesh distortion adjustment during the curling process is achieved by piecewise linear interpolation. The connection area is smoothly transitioned to achieve structural continuity. Finally, STL format surface model data that can be used for 3D printing manufacturing is generated. The cylindrical radius is set according to the ankle joint size, the height parameter is matched with the foot length, the mapping function uses polar coordinate transformation, the conformal transformation maintains the angle and length ratio unchanged, the piecewise linear interpolation is adjusted based on the grid node position, and the smooth transition uses B-spline curve fitting.

[0014] In a preferred embodiment, the optimization design process of the chiral microstructure mechanical metamaterial is as follows: An initial design configuration with central symmetry was adopted. Anisotropy control was achieved by adjusting the beam element width and connection angle. During the optimization process, the numerical changes of the main and secondary Poisson ratios were monitored. The design variables that contribute the most to the negative Poisson ratio were identified through sensitivity analysis. The structural connectivity and manufacturability were achieved by using a constrained optimization algorithm. Finally, chiral-type microstructure configuration data that exhibits a rotational deformation mechanism under axial load were obtained. The initial design configuration is a hexagonal honeycomb structure. The beam element width ranges from 0.1 to 1 millimeter, the connection angle ranges from 30 to 60 degrees, the main Poisson's ratio is calculated using the homogenization method, the sensitivity analysis uses the finite difference method, and the constraint optimization algorithm includes stress constraints and geometric constraints.

[0015] In a preferred embodiment, the optimization design process of the concave microstructure mechanical metamaterial is as follows: The initial design configuration using rectangular holes was adopted. Negative Poisson's ratio characteristics were achieved by controlling the rib thickness and inclination angle. During the optimization process, the off-diagonal element values ​​of the macroscopic elastic tensor were monitored. The orthogonal anisotropy of the structure was maintained by symmetry constraints. Stress constraints were used to reduce the stress concentration. Finally, re-entrant microstructure configuration data that exhibits an inward contraction deformation mechanism under compressive load were obtained. The initial design configuration is a square grid, the rib thickness ranges from 0.2 to 2 mm, the tilt angle ranges from 10 to 45 degrees, the off-diagonal elements of the macroscopic elastic tensor are obtained through homogenization, symmetry constraints are applied to the design variables, and stress constraints are based on the Von Mises stress criterion.

[0016] This application also provides a topology optimization method for flexible interactive metamaterials in humanoid robots, which specifically includes the following steps: Step S1: Receive the geometric dimension parameters and material property parameters of the humanoid robot's leg structure, and use non-uniform rational B-spline basis functions to construct a mechanical metamaterial microstructure geometric model containing control point coordinates and node vector sequences, generating a parameterized geometric model file; Step S2: Read the basis function information and control point data in the parameterized geometric model file, perform an energy-based homogenization calculation process to obtain the equivalent elastic parameters of the microstructure at the macro scale, and output a homogenized elastic tensor dataset containing Young's modulus, shear modulus and Poisson's ratio parameters. Step S3: Obtain the homogenized elastic tensor dataset, establish the mapping relationship between the node density distribution function and the isogeometric topology optimization model, implement the optimization calculation process with the goal of minimizing strain energy density and maximizing negative Poisson's ratio effect, and generate the optimized microstructure configuration data file; Step S4: Receive the optimized microstructure configuration data file. Based on the contour dimensions of the humanoid robot's foot surface and the spatial constraints of the series elastic actuator installation, complete the periodic array arrangement of the microstructure units and the cylindrical surface curling transformation operation to generate a three-dimensional model data of a mechanical metamaterial infill structure that can be used for additive manufacturing. The beneficial effects of this invention are: by optimizing the topology of mechanical metamaterials, the weight of the humanoid robot's leg structure is significantly reduced, while its energy absorption and impact resistance are enhanced. By using isogeometric analysis and customized microstructure design, a lightweight filling structure with negative Poisson bit properties is provided for the foot and ankle joints, which significantly improves compliance while ensuring structural strength. This method effectively solves the contradiction between the insufficient strength of traditional flexible materials and the excessive weight of rigid components, enabling the humanoid robot to exhibit safer buffering characteristics and more stable dynamic control performance when interacting with the environment, and significantly improving the robot's overall interactive safety and adaptability to complex environments. Attached Figure Description

[0017] Figure 1 This invention provides a framework for the optimized design of mechanical metamaterials for flexible interaction in humanoid robots. Figure 2 This is the optimization result of the first chiral microstructure mechanical metamaterial provided by the present invention, wherein (a) is the optimized microstructure unit, (b) is the 5x5 array arrangement result of the optimized microstructure, and (c) is the deformation mechanism of the 5x5 array of the optimized microstructure when subjected to a downward force. Figure 3This is the optimization result of the second chiral microstructure mechanical metamaterial provided by the present invention, wherein (a) is the optimized microstructure unit, (b) is the 5x5 array arrangement result of the optimized microstructure, and (c) is the deformation mechanism of the 5x5 array of the optimized microstructure when subjected to a downward force. Figure 4 The microstructure filling results of the chiral microstructure mechanical metamaterial optimized by the present invention are used as the elastomer in the SEA flexible mechanism of a humanoid robot, wherein (a) is a 12x14 array of the first chiral microstructure mechanical metamaterial, (b) is a 20x22 array of the first chiral microstructure mechanical metamaterial, (c) is a 12x14 array of the second chiral microstructure mechanical metamaterial, and (d) is a 20x22 array of the second chiral microstructure mechanical metamaterial; Figure 5 This is a deformation simulation of the chiral microstructure mechanical metamaterial filling structure of the elastic body in the SEA flexible mechanism of the humanoid robot when subjected to a downward force. Among them, (a) is a 12x14 array of the first chiral microstructure mechanical metamaterial, (b) is a 20x22 array of the first chiral microstructure mechanical metamaterial, (c) is a 12x14 array of the second chiral microstructure mechanical metamaterial, and (d) is a 20x22 array of the second chiral microstructure mechanical metamaterial. Figure 6 The first concave microstructure mechanical metamaterial provided by the present invention is the optimization result, wherein (a) is the optimized microstructure unit, (b) is the 5x5 array arrangement result of the optimized microstructure, and (c) is the deformation mechanism of the 5x5 array of the optimized microstructure when subjected to a downward force. Figure 7 This is the optimization result of the second type of concave microstructure mechanical metamaterial provided by the present invention, wherein (a) is the optimized microstructure unit, (b) is the 5x5 array arrangement result of the optimized microstructure, and (c) is the deformation mechanism of the 5x5 array of the optimized microstructure when subjected to a downward force. Figure 8 The microstructure filling result of the concave microstructure mechanical metamaterial optimized by this invention is used for the flexible structure of the foot of humanoid robots. Figure 9 It is a simulation of the deformation of the concave microstructure mechanical metamaterial filling structure of the flexible structure of the foot of a humanoid robot when subjected to a downward force. Figure 10 It is a simulation of the deformation of the concave microstructure mechanical metamaterial filling structure of the flexible structure of the foot of a humanoid robot when subjected to a force from right to left. Figure 11 This is a side view schematic diagram of the leg structure of a humanoid robot. Figure 12This is a schematic diagram of a series elastic actuator (SEA) applied to the leg structure of a humanoid robot, including 1-servo valve, 2-hydraulic cylinder and 3-elastic body; Figure 13 This is an actual picture of the leg structure of a humanoid robot. Detailed Implementation

[0018] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0019] In the description of this application, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0020] In the description of this application, the term "for example" is used to mean "used as an example, illustration, or description." Any embodiment described as "for example" in this application is not necessarily to be construed as being more preferred or advantageous than other embodiments. The following description is provided to enable any person skilled in the art to make and use the invention. Details are set forth in the following description for purposes of explanation. It should be understood that those skilled in the art will recognize that the invention can be made without using these specific details. In other instances, well-known structures and processes will not be described in detail to avoid obscuring the description of the invention with unnecessary detail. Therefore, the invention is not intended to be limited to the embodiments shown, but is consistent with the broadest scope of the principles and features disclosed in this application. Example

[0021] Please see Figure 1This invention provides a framework for the optimization design of mechanical metamaterials for flexible interaction in humanoid robots. The framework begins with an initial design of the mechanical metamaterial to facilitate subsequent isogeometric topology optimization. First, isogeometric analysis (IGA) is performed using non-uniform rational B-splines (NURBS) basis functions. This involves approximating, describing, and parameterizing the geometric model of the structure to be optimized through control points and node parameters. Since the overall structure is composed of microstructures, an energy-based homogenization method (EBHM) is used to predict the macroscopic effective performance of the overall structure. Subsequently, each control point is assigned a node density to construct a density distribution function (DF). The DDF can be used to design and optimize the microstructure of the mechanical metamaterial, while IGA can be used to solve for the structural response within the microstructure. Throughout the parametric modeling and optimization process, the NURBS basis functions connect the geometric model, numerical analysis model, density distribution function, and topology optimization formula, thus effectively improving the computational efficiency of the optimization process. Then, isogeometric topology optimization is performed, and the formula is: in, Represents node density, including the density of all nodes. And all are in the range of 0 to 1. It is the objective function. These are weight parameters. It is an unknown displacement field in the microstructure of the material. It is the DDF in the structural domain. Since the deformation behavior mechanism within mechanical metamaterials is closely related to the rotational effect in the material's microstructure, the objective function is to minimize... Item and maximize This ensures the generation of the mechanical metamaterial configuration layout, thereby enabling the structure to possess metamaterial mechanical characteristics. It is the area of ​​the microstructure. It is a volume constraint. It is the volume fraction of the structure, and its value is not greater than . It belongs to the permissible displacement space The virtual displacement field, and These are the bilinear energy function and the linear load function, expressed as: in It is a penalty parameter. It is the constitutive elastic tensor of the basic material. It is the aspect ratio between the microscopic structural scale and the overall macroscopic structure.

[0022] After topology optimization is completed, mechanical metamaterial microstructures can be obtained according to different initial designs and optimization objectives. Typical mechanical metamaterial microstructures include concave microstructures and chiral microstructures. Concave microstructure metamaterials have a negative Poisson's ratio (NPR) characteristic: when a uniaxial tensile load is applied, it expands in the transverse direction and vice versa; while chiral microstructure metamaterials mainly achieve the NPR effect through rotation, and it will twist and rotate under axial load.

[0023] By arranging the optimized metamaterial microstructures in an array, a macroscopic metamaterial structure based on the metamaterial microstructure can be obtained. Depending on the configuration and arrangement of its microstructure, it will exhibit mechanical properties different from those of conventional structural materials: it will shrink or twist when subjected to pressure.

[0024] By performing filling designs such as curling and thickening on the obtained macroscopic metamaterial structure, mechanical metamaterials that can be used for flexible interaction in humanoid robots can be obtained, and further applied to the flexible mechanisms or flexible structures of robots.

[0025] Please see Figure 2 , Figure 3 This invention optimizes two chiral microstructures using the given topology optimization method, and presents their microstructural units, 5x5 arrays, and deformation mechanisms of the arrays under longitudinal pressure. The difference between the two chiral microstructures is that the first type is isotropic, while the second is anisotropic. The microstructure rotates clockwise under longitudinal pressure, thus the macrostructure exhibits the following characteristics: Figure 2 (c) and Figure 3 The deformation results are shown in (c). Table 1 also lists the numerical results for the first and second chiral microstructures, including the uniform elastic tensor and the corresponding negative Poisson's ratio.

[0026] Table 1 Numerical results for the two chiral microstructures

[0027] Please see Figure 4 Because chiral microstructures all exhibit the same unidirectional rather than bidirectional lateral deformation, the microstructures of chiral metamaterials can be horizontally connected to form cylinders. The microstructures of both chiral metamaterials are arranged in a periodic cylindrical pattern, with an overall size of [missing information]. The inner diameter of the cylindrical periodic structure was set to 30 mm to avoid out-of-plane buckling. In the cylindrical periodic arrangement of chiral metamaterials, two arrangement strategies were tried for both optimized chiral results: 12 microstructures per layer forming 14 layers (12x14 array) and 20 microstructures per layer forming 22 layers (20x22 array) to discuss the influence of microstructure size and number on the structural properties of chiral metamaterials, and to facilitate the subsequent application and modular replacement of robotic SEAs.

[0028] Please see Figure 4 , Figure 11 , Figure 12 , Figure 13 Two chiral microstructure metamaterial structures are used in the current SEA (Self-Elastomer) as 3-elastics to replace the currently used heavy-duty springs with fixed mechanisms. The external dimensions of the four chiral metamaterial structures are also described. mm and heavy-duty springs with fixing mechanisms at the robot's ankle joint ( Figure 13 The outer dimensions of the area within the red box are basically the same.

[0029] Please see Figure 5 Considering the actual working conditions of the robot, a vertical downward force of 10 kN was applied to the top ring, and the bottom ring was fixed. The numerical bars on the left represent the deformation of the chiral structure in millimeters, and the virtual image behind the deformed chiral structure is the undeformed chiral structure. It can be seen that the four chiral microstructure metamaterials exhibit the same deformation mechanism after being subjected to force, but the degree of deformation differs to some extent.

[0030] To further discuss the impact of structure on control bandwidth, the bandwidth of the hydraulic SEA under 21MPa pressure was calculated based on the stiffness of different structures under several typical working conditions, including the bandwidth under characteristic loads such as the maximum output force of the hydraulic cylinder (5kN, about 500kg), the total weight of the robot (125kg), the weight of the robot's legs (15kg), and the weight of the foot structure (previously 1.55kg for the foot, and 0.88kg for the optimized foot).

[0031] Please see Figure 6 , Figure 7 This invention optimizes two concave microstructures using the given topology optimization method, and presents their microstructural units, 5x5 arrays, and deformation mechanisms of the array under longitudinal pressure. The difference between the two concave microstructures is that the first type is isotropic, while the second is anisotropic. The microstructures contract inward under longitudinal pressure, thus the macrostructure exhibits the following characteristics: Figure 6 (c) and Figure 7 The deformation result shown in (c).

[0033] Please see Figure 8 , Figure 13The first type of concave microstructure was thickened and 60 Two arrays are arranged at the bottom of the robot's foot structure to form the robot's foot sole, and the second type of concave microstructure is thickened and arranged in 8... Two arrays are arranged at the front and rear ends of the robot's foot as anti-collision devices, and are cut according to the shape of the foot. The overall dimensions of the foot are 310. 160 34 mm.

[0034] Please see Figure 9 , Figure 10 Simulation results of foot structure deformation under vertical and horizontal pressures of 10 kN are presented. The bar on the left represents the deformation of the chiral structure, in mm. Based on the simulation results, the stiffness of the sole constructed from the first type of concave microstructure metamaterial is calculated to be 42872.45 N / mm, and the stiffness of the front and rear anti-collision structures constructed from the second type of concave microstructure metamaterial is 18874.33 N / mm. This indicates that the designed concave microstructure metamaterial can provide good cushioning and anti-collision performance for the robot's foot. Furthermore, the overall weight of the foot is 880.52 g, a 43.2% reduction compared to the original foot structure, effectively reducing the rotational inertia of the robot's limb and improving the robot's leg movement performance.

[0035] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0036] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0037] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0038] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0039] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0040] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0041] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A flexible interactive metamaterial topology optimization system for humanoid robots, characterized in that, Specifically, it includes: The module includes an initial design module, an isogeometric analysis module, a topology optimization module, and an array generation module. Initial design module: Receives the geometric dimensions and material parameters of the humanoid robot's leg structure, establishes the control points and node parameters of the mechanical metamaterial microstructure through non-uniform rational B-spline basis functions, including chiral microstructures or concave microstructures, and outputs a parameterized geometric model file; Iso-geometric analysis module: Receives parameterized geometric model files, uses an energy-based homogenization method to calculate the equivalent elastic properties of the microstructure at the macroscale, and outputs homogenized elastic tensor data; Topology optimization module: Receives homogenized elastic tensor data, constructs an isogeometric topology optimization model through the node density distribution function, adopts a multi-objective optimization strategy of minimizing strain energy and maximizing negative Poisson's ratio effect, and outputs optimized microstructure configuration data; Array generation module: Receives optimized microstructure configuration data, performs periodic arrangement of microstructures and cylindrical surface curling operations according to the size of the humanoid robot's feet and the installation space requirements of the series elastic actuators, and outputs three-dimensional model data of the mechanical metamaterial infill structure.

2. The humanoid robot flexible interactive metamaterial topology optimization system according to claim 1, characterized in that: The construction process of the non-uniform rational B-spline basis functions in the initial design module is as follows: First, the CAD geometric file of the humanoid robot's leg structure is read, and the contour curve data of the foot contact surface and ankle joint connection are extracted. The number and position of control points are set according to the contour curvature characteristics. The node vector values ​​are calculated using the chord length parameterization method. The boundary curve of the mechanical metamaterial unit cell is fitted by the back calculation control point technology. The mapping relationship from the two-dimensional parameterized space to the three-dimensional physical space is established. Finally, a parameterized geometric model file containing control point coordinates, node vector sequence and basis function order is generated. This file is transferred to the isogeometric analysis module for finite element mesh generation. The number of control points is dynamically adjusted according to the rate of change of contour curvature. The node vector sequence is generated using the uniform parameterization method. The order of the basis function is set to quadratic or cubic to achieve curve smoothness. The entire construction process iteratively optimizes the position of control points to reduce fitting error and achieves high-precision representation of the geometric model.

3. The humanoid robot flexible interactive metamaterial topology optimization system according to claim 2, characterized in that: The execution process of the energy-based homogenization method in the isogeometric analysis module is as follows: The non-uniform rational spline basis function information is read from the parametric geometric model file. Gaussian integration points and weight coefficients are generated in the parameter space. The derivatives and Jacobian matrix determinants of the basis functions at each integration point are calculated. The micro-stiffness matrix is ​​obtained by integrating the product of the constitutive relation matrix and the strain-displacement matrix. The micro-displacement response under the unit test strain field is solved. The values ​​of each component of the macro-equivalent elastic tensor, including Young's modulus, shear modulus and Poisson's ratio, are calculated according to the mean stress-strain relationship. These parameters are transmitted to the topology optimization module as homogenized elastic tensor data. The number of Gaussian integration points is automatically selected based on the order of the basis functions, the determinant of the Jacobian matrix is ​​used to achieve integration accuracy, the micro-displacement response is solved using the conjugate gradient method, and the mean stress-strain relationship is obtained through volume averaging.

4. The humanoid robot flexible interactive metamaterial topology optimization system according to claim 3, characterized in that: The process of establishing the node density distribution function in the topology optimization module is as follows: A density variable allocation scheme corresponding to control points is adopted, with each control point associated with a density value between zero and one. A continuous mapping from control point density to field point density is achieved through radial basis function interpolation. A penalty factor is introduced to suppress intermediate density values. Sensitivity analysis is used to calculate the derivative of the objective function with respect to the density variable. The density variable values ​​are updated using the optimization criterion method. The optimization process that satisfies volume constraints is completed by using the moving asymptote algorithm. After iterative calculation, the optimal density distribution field is output. The initial value of the density variable is set to 0.5, the radial basis function kernel radius is adaptively adjusted according to the control point spacing, the penalty factor is between two and four, the sensitivity analysis adopts the adjoint variable method, the volume constraint is implemented by the Lagrange multiplier method, and the iterative calculation is performed until the density change is less than the threshold.

5. The humanoid robot flexible interactive metamaterial topology optimization system according to claim 4, characterized in that: The specific construction method of the geometric topology optimization model in the topology optimization module is as follows: Using the minimization of the compliance of the micro-unit cell and the maximization of the negative Poisson's ratio effect as dual objective functions, the multi-objective process is transformed into a single-objective optimization process through the weighted summation method. The macroscopic equivalent performance parameters are calculated using an energy-based homogenization method, and the amount of material used is limited by the volume fraction constraint. The constraint optimization process is realized through the Lagrange multiplier method, and the sensitivity of the objective function to the design variables is calculated using the adjoint variable method. The gradient-based optimization algorithm is used for iterative solution. Each iteration requires recalculation of the homogenization elastic tensor and sensitivity information, and finally, microstructure configuration data with negative Poisson's ratio properties are obtained. Among them, compliance is defined as the strain energy density integral, the negative Poisson's ratio effect is quantified by the principal Poisson's ratio, the weight coefficients of the weighted summation method are adjusted according to the application requirements, the upper limit of the volume fraction constraint is set to 0.3 of the material volume fraction, and the gradient-based algorithm adopts the MMA method.

6. The humanoid robot flexible interactive metamaterial topology optimization system according to claim 5, characterized in that: The implementation process of periodic arrangement of microstructures in the array generation module is as follows: The array layout area is determined based on the shape of the foot sole of the humanoid robot. The microstructure units are arranged in a hexagonal close-packing manner. Boolean operations are used to realize the connection relationship between adjacent microstructures to maintain the continuity of the force flow path. Incomplete units at the edge are trimmed and transitioned. A radial arrangement is used in the ankle joint mounting area to adapt to the cylindrical space constraint. Finally, parameterized array data containing unit position coordinates, rotation angles and scaling ratios are generated. The array arrangement area is obtained by discretizing the foot surface, the hexagonal stacking spacing is calculated based on the microstructure unit size, Boolean operation uses union operation to achieve structural connectivity, edge trimming uses adaptive mesh refinement technology, and the radial arrangement angle is evenly distributed according to the installation space.

7. The humanoid robot flexible interactive metamaterial topology optimization system according to claim 6, characterized in that: The specific steps of the cylindrical surface curling operation in the array generation module are as follows: First, the radius and height parameters of the target cylindrical surface of the series elastic actuator are determined. A mapping function from the planar coordinate system to the cylindrical surface coordinate system is established. The geometric properties of the microstructure unit are kept unchanged by conformal transformation technology. The mesh distortion adjustment during the curling process is achieved by piecewise linear interpolation. The connection area is smoothly transitioned to achieve structural continuity. Finally, STL format surface model data that can be used for 3D printing manufacturing is generated. The cylindrical radius is set according to the ankle joint size, the height parameter is matched with the foot length, the mapping function uses polar coordinate transformation, the conformal transformation maintains the angle and length ratio unchanged, the piecewise linear interpolation is adjusted based on the grid node position, and the smooth transition uses B-spline curve fitting.

8. The humanoid robot flexible interactive metamaterial topology optimization system according to claim 7, characterized in that: The optimization design process for the chiral microstructure mechanical metamaterial is as follows: An initial design configuration with central symmetry was adopted. Anisotropy control was achieved by adjusting the beam element width and connection angle. During the optimization process, the numerical changes of the main and secondary Poisson ratios were monitored. The design variables that contribute the most to the negative Poisson ratio were identified through sensitivity analysis. The structural connectivity and manufacturability were achieved by using a constrained optimization algorithm. Finally, chiral-type microstructure configuration data that exhibits a rotational deformation mechanism under axial load were obtained. The initial design configuration is a hexagonal honeycomb structure. The beam element width ranges from 0.1 to 1 millimeter, the connection angle ranges from 30 to 60 degrees, the main Poisson's ratio is calculated using the homogenization method, the sensitivity analysis uses the finite difference method, and the constraint optimization algorithm includes stress constraints and geometric constraints.

9. A humanoid robot flexible interactive metamaterial topology optimization system according to claim 8, characterized in that: The optimization design process for the concave microstructure mechanical metamaterial is as follows: The initial design configuration using rectangular holes was adopted. Negative Poisson's ratio characteristics were achieved by controlling the rib thickness and inclination angle. During the optimization process, the off-diagonal element values ​​of the macroscopic elastic tensor were monitored. The orthogonal anisotropy of the structure was maintained by symmetry constraints. Stress constraints were used to reduce the stress concentration. Finally, re-entrant microstructure configuration data that exhibits an inward contraction deformation mechanism under compressive load were obtained. The initial design configuration is a square grid, the rib thickness ranges from 0.2 to 2 mm, the tilt angle ranges from 10 to 45 degrees, the off-diagonal elements of the macroscopic elastic tensor are obtained through homogenization, symmetry constraints are applied to the design variables, and stress constraints are based on the Von Mises stress criterion.

10. A topology optimization method for a humanoid robot flexible interactive metamaterial is applied to a topology optimization system for a humanoid robot flexible interactive metamaterial as described in any one of claims 1-9, characterized in that: Specifically, the following steps are included: Step S1: Receive the geometric dimension parameters and material property parameters of the humanoid robot's leg structure, and use non-uniform rational B-spline basis functions to construct a mechanical metamaterial microstructure geometric model containing control point coordinates and node vector sequences, generating a parameterized geometric model file; Step S2: Read the basis function information and control point data in the parameterized geometric model file, perform an energy-based homogenization calculation process to obtain the equivalent elastic parameters of the microstructure at the macro scale, and output a homogenized elastic tensor dataset containing Young's modulus, shear modulus and Poisson's ratio parameters. Step S3: Obtain the homogenized elastic tensor dataset, establish the mapping relationship between the node density distribution function and the isogeometric topology optimization model, implement the optimization calculation process with the goal of minimizing strain energy density and maximizing negative Poisson's ratio effect, and generate the optimized microstructure configuration data file; Step S4: Receive the optimized microstructure configuration data file, and based on the contour dimensions of the humanoid robot's foot surface and the spatial constraints of the series elastic actuator installation, complete the periodic array arrangement of the microstructure units and the cylindrical surface curling transformation operation to generate a three-dimensional model data of a mechanical metamaterial filling structure that can be used for additive manufacturing.

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