A joint elastomer optimization design method based on a Gaussian filtering algorithm

Abstract

The application relates to the technical field of robot joint elastomer optimization, in particular to a joint elastomer optimization design method based on a Gaussian filtering algorithm, which establishes a finite element simulation model based on an Archimedes spiral line, constructs an optimization function with the maximum deformation and the minimum stress as targets, selects key design parameters of the elastomer to perform iterative optimization in stages, and finally performs smoothing processing on the edge curve of the H-bridge structure of the elastomer through the Gaussian filtering algorithm. The method can effectively reduce the stress concentration phenomenon of the joint elastomer and improve the thinness of the structure, realize the storage and release of impact energy, and thus significantly enhance the dynamic stability and load capacity of the joint while ensuring uniform stress and improving the stiffness coefficient.

Description

Technical Field

[0001] This invention relates to the field of robot joint elastomer optimization technology, and in particular to a joint elastomer optimization design method based on Gaussian filtering algorithm. Background Technology

[0002] In the field of modern robotics, the performance of joint elastomers plays a crucial role in the overall motion efficiency and stability of a robot. Thanks to the rapid development of modern information technologies such as computer science and artificial intelligence, intelligent robots are gradually replacing humans in complex and dangerous tasks such as disaster relief, terrain exploration, and material transportation. These tasks often require maintaining high dynamic stability in complex and changing environments. However, traditional joint elastomer design methods have failed to adequately consider the handling of impact energy by the joints during robot movement, resulting in performance limitations in practical applications. Furthermore, meeting high load requirements also increases the weight and volume of the robot structure, affecting its flexibility and response speed. Summary of the Invention

[0003] To address the aforementioned technical problems in existing technologies, this invention proposes a joint elastomer optimization design method based on a Gaussian filtering algorithm. During motion, this joint elastomer can effectively store and release impact energy, thereby significantly enhancing the dynamic stability of the robot system and improving its load-bearing capacity. The specific technical solution is as follows:

[0004] A joint elastomer optimization design method based on Gaussian filtering algorithm, comprising:

[0005] Step S1: Based on the Archimedes spiral parametric equation, establish a finite element simulation model of the joint elastic body;

[0006] Step S2: Construct an optimization evaluation function with the optimization objective of maximizing the deformation of the joint elastomer and minimizing its stress.

[0007] Step S3: Using the constructed optimization evaluation function as a constraint, select the key design parameters of the elastomer for iterative optimization. The selected parameters include the bridge depth parameter H, which represents the H-bridge structure depth of the elastomer. The threshold of the optimization region of the H-bridge structure of the elastomer is obtained through iterative optimization.

[0008] Step S4: Use a Gaussian filtering algorithm to smooth the H-bridge edge curve of the elastomer.

[0009] Furthermore, in step S1, the polar coordinate equation of the Archimedean spiral is:

[0010] r = a + b · θ

[0011] Where r is the distance from the origin to any point on the spiral, and a and b are both real numbers; a is the distance between the starting point and the center of the polar coordinates when θ = 0, b is used to control the distance between the spirals and represents the density of the spirals, and θ is the angle parameter in polar coordinates. The larger θ is, the larger the range of the spiral.

[0012] The polar coordinate equation is transformed into a planar Cartesian coordinate equation as follows:

[0013] x = (α + β·θ)·cos(θ)

[0014] y = (α + β·θ)·sin(θ)

[0015] Here, parameters α and β are constants.

[0016] Furthermore, in step S2, the expression for the optimization evaluation function is as follows:

[0017] J(X) = w1·ε max (X)-w2·σ max (X)

[0018] Where, ε max (X) is the maximum deformation of the elastic body under stress, representing the maximum degree of deformation that the material can achieve under a load of X; σ max (X) is the maximum stress value per unit area of ​​the elastic body when it is subjected to force, reflecting the maximum stress level that the material can withstand; w1 and w2 are coefficients used to balance the weights of the two optimization objectives.

[0019] Furthermore, in step S3, the deformation and stress of the elastomer increase with the increase of the bridge depth parameter H, affecting the local stiffness and load distribution of the elastomer; the key design parameters of the selected elastomer also include: the width parameter h, which represents the lateral dimension of the elastomer and directly affects its mechanical properties and space occupation; and the width variation parameter d. n This indicates the change in the width of the elastomer along the helical direction, used to adjust its elastic properties.

[0020] Furthermore, using the aforementioned optimization evaluation function as a constraint, the width parameter h and the width variation parameter d are... n The bridge depth parameter H is iteratively optimized in stages. At each stage, the current performance of the design parameters is evaluated through finite element analysis. Based on the results of the optimization evaluation function, the parameter search direction is guided by a real-time feedback mechanism, and the key design parameters are updated and iterated to obtain the optimal solution.

[0021] Furthermore, step S4 specifically includes:

[0022] Step S4.1: Obtain the threshold of the optimized region of the elastic body H-bridge structure from step S3, perform edge detection on the model point cloud data that is less than the set threshold, identify potential edge points, and extract the edge curves;

[0023] Step S4.2: Establish a two-dimensional Gaussian function and initialize the Gaussian kernel;

[0024] Step S4.3: For each edge point in the edge curve, apply a two-dimensional Gaussian function for smoothing filtering to obtain a smooth edge curve.

[0025] Furthermore, in step S4.1, the method for identifying edge points is as follows:

[0026] Iterate through each point cloud dataset, for each point P in the point cloud dataset... i Check in P i With δ as the center, does there exist at least one point P in each of the four quadrants with a search radius of δ? j (j≠i), the expression for determining whether a point is an edge point is:

[0027]

[0028] Where isEdge = 1 indicates that point P i If isEdge = 0, then point P is an edge point. i These are non-edge points.

[0029] Furthermore, in step S4.2, the expression for the two-dimensional Gaussian function is:

[0030]

[0031] Where σ represents the standard deviation of the Gaussian kernel, which is used to control the width of the Gaussian distribution and the smoothness of the curve.

[0032] Furthermore, step S4.3 specifically involves applying a Gaussian kernel constructed using a two-dimensional Gaussian function to each edge point P in the point cloud data. i The point cloud coordinates P after Gaussian filtering are obtained by performing a weighted average. i The weighted average is calculated as follows:

[0033]

[0034] Where, x i 'and y i 'It is point P' i After Gaussian filtering, x and y; m and n are the offsets relative to the center. K is the size of the Gaussian kernel; It is the weight of the Gaussian kernel at offset (m,n).

[0035] This invention achieves comprehensive and systematic optimization of joint elastomer design through the establishment of a precise simulation model and the construction of a multi-objective optimization evaluation function; by using iterative optimization methods and Gaussian filtering algorithms, it ensures the optimal performance of the elastomer's width parameter h and width variation parameter d. n The optimal configuration of the three design parameters—bridge depth parameter H, bridge depth parameter H, and edge curve smoothing—significantly improves the quality of point cloud data processing and the reliability of robot joints, ensuring that the design meets performance standards in terms of dynamic stability and load capacity. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the joint elasticity optimization method according to an embodiment of the present invention;

[0037] Figure 2 This is a cross-sectional schematic diagram of the H-bridge structure according to an embodiment of the present invention;

[0038] Figure 3 These are comparison images of the edge curves before and after smoothing in an embodiment of the present invention;

[0039] Figure 4 This is a schematic diagram of the structure of the joint elastomer according to an embodiment of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and technical effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0041] like Figure 1 As shown, this invention discloses a joint elastomer optimization design method based on Gaussian filtering algorithm, the steps of which include:

[0042] Step S1, Design a joint elastomer based on the Archimedes spiral: Based on the Archimedes spiral parametric equation, establish a finite element simulation model of the joint elastomer.

[0043] Specifically, the polar equation of the Archimedes spiral is:

[0044] r = a + b · θ

[0045] Where a and b are both real numbers; a is the distance between the starting point and the center of the polar coordinates when θ = 0. The distance between the spirals is used to control the density of the spirals. θ is an angular parameter in polar coordinates. The larger θ is, the larger the range of the spirals.

[0046] The Cartesian coordinate equation of the Archimedean spiral is:

[0047] x = (α + β·θ)·cos(θ)

[0048] y = (α + β·θ)·sin(θ)

[0049] Here, parameters α and β are constants. Changes in parameters α and β will affect the shape and spacing of the helix. α changes the starting position of the helix, while β controls the distance between the helixes.

[0050] In this embodiment, the inner helix of the elastomer simulation model has α1 = 9.2 and β1 = 3; the outer helix has α2 = 16 and β2 = 3.

[0051] The material selected for the joint elastomer is maraging steel 300, and its performance parameters are shown in Table 1. The maximum load of the joint elastomer is T = 50 N·m, and under load:

[0052] stε max ≥3mm

[0053] σ max ≤1200Mpa.

[0054]

[0055] Table 1 Performance parameters of martensitic aging steel 300.

[0056] Step S2: Construct an elastic body optimization function with the goal of maximizing deformation and minimizing stress: Construct a multi-objective optimization evaluation function with the goal of maximizing the deformation of the joint elastic body and minimizing its stress, so as to ensure that impact energy can be effectively stored and released during motion.

[0057] Specifically, the expression for the optimization evaluation function is as follows:

[0058] J(X) = w1·ε max (X)-w2·σ max (X)

[0059] Where, ε max (X) is the maximum deformation of the elastic body under stress, representing the maximum degree of deformation that the material can achieve under a load of X; σ max (X) is the maximum stress per unit area of ​​the elastic body under stress, reflecting the maximum stress level borne by the material; w1 and w2 are coefficients used to balance the weights of the two optimization objectives, and the values ​​of w1 and w2 are within... Under the condition that, satisfy And all are greater than zero.

[0060] Step S3: Select key design parameters of the elastomer for iterative optimization: Determine the design parameters to be optimized for the elastomer, use the constructed multi-objective optimization evaluation function as a constraint, and systematically adjust the design parameters through iterative optimization until the predetermined performance standard is reached, thereby achieving the optimal configuration of the parameters.

[0061] Specifically, the three main design parameters for optimizing the elastomer are determined: the width parameter, the width variation parameter, and the bridge depth parameter.

[0062] Width parameter h: determines the lateral dimension of the elastomer, directly affecting its mechanical properties and space occupation;

[0063] Width variation parameter d n This involves the variation of the width of the elastomer along the helical direction, used to adjust its elastic properties;

[0064] Bridge depth parameter H: This parameter relates to the depth of the H-bridge structure. The deformation and stress of the elastic body increase with increasing H, significantly affecting the local stiffness and load distribution of the elastic body. The H-bridge structure is as follows: Figure 2 As shown.

[0065] Using the evaluation function in step S2 as constraints, the three objective parameters are iteratively optimized in stages. At each step, finite element analysis is used to evaluate the current performance of the design parameters, and the parameters are updated based on the evaluation function results. The optimization method uses a real-time feedback mechanism to guide the parameter search direction, ensuring that each iteration moves closer to the global optimum. The final optimal parameter configuration is: h = 2. H = 1.2 mm.

[0066] Step S4: Smooth the edge curve of the H-bridge: Determine the threshold of the H-bridge edge, and use a Gaussian filtering algorithm to smooth the edge curve of the H-bridge. Select an appropriate Gaussian kernel size and standard deviation to achieve the best smoothing effect. Under the premise of satisfying the requirements of uniform force distribution, reduced stress concentration, and improved elastic body stiffness coefficient, the structural design is further optimized to achieve a thinner and lighter structure, thereby improving the dynamic stability and load capacity during joint movement. Specifically, this includes the following sub-steps:

[0067] Step S4.1: Perform edge detection on point cloud data that is less than a set threshold, identify potential edge points, and extract edge curves;

[0068] Based on step S3, the threshold σ of the elastomer H-bridge optimization region is determined. th =200 MPa, P i Let P be the i-th point in the point cloud data, δ be the preset search radius, and N be the total number of points in the point set. For each point P... i Check in P iDoes a point P exist in each of the four quadrants with center δ and radius δ? j (j≠i), the conditional expression is:

[0069]

[0070] Where isEdge = 1 indicates that point P i If isEdge = 0, then point P is an edge point. i These are non-edge points.

[0071] Step S4.2: Establish a two-dimensional Gaussian function and initialize the Gaussian kernel;

[0072] The expression for the two-dimensional Gaussian function is:

[0073]

[0074] The standard deviation of the Gaussian kernel, σ = 2, controls the width of the Gaussian distribution and the smoothness of the curve.

[0075] Step S4.3, for each edge point P in the edge curve obtained above i A two-dimensional Gaussian function is used for smoothing filtering to reduce noise and improve the continuity of edge curves;

[0076] A Gaussian kernel constructed using a two-dimensional Gaussian function is applied to each edge point P in the point cloud data. i A weighted average is performed to smooth the point cloud data. The point cloud coordinates P after Gaussian filtering are... i It is calculated using the following weighted average formula:

[0077]

[0078] Where, x i 'and y i 'It is point P' i After Gaussian filtering, x and y; m and n are the offsets relative to the center. K=5 is the size of the Gaussian kernel; The weights G of the Gaussian kernel at offset (m,n) are determined by the Gaussian function, ensuring that the contribution of neighboring points to the filtered coordinates is proportional to their distance P. i The weight is directly proportional to the distance; that is, the closer the distance, the greater the weight.

[0079] Through the above steps, the smoothed edge curve is finally obtained, as shown below. Figure 3 As shown. This process not only preserves the key features of the edge points but also improves the overall quality of the curve, ultimately optimizing the final joint elastomer, as shown. Figure 4As shown. Through this series of improvements, the stress distribution of the elastomer was optimized while ensuring an ideal mechanical response, thus improving the storage and release of impact energy. Ultimately, this not only enhanced the dynamic stability and load-bearing capacity of the robot joints but also optimized cost-effectiveness.

[0080] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any way. Although the implementation process of the present invention has been described in detail above, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A joint elastomer optimization design method based on Gaussian filtering algorithm, characterized in that, include: Step S1: Based on the Archimedes spiral parametric equation, establish a finite element simulation model of the joint elastic body; Step S2: Construct an optimization evaluation function, which aims to maximize the deformation of the joint elastomer and minimize its stress; the expression of the optimization evaluation function is as follows: J(X)=w1·ε max (X)-w2·σ max (X) Where, ε max (X) is the maximum deformation of the elastic body under stress, representing the maximum degree of deformation that the material can achieve under a load of X; σ max (X) is the maximum stress value per unit area of ​​the elastic body when it is subjected to force, reflecting the maximum stress level that the material can withstand; w1 and w2 are coefficients used to balance the weights of the two optimization objectives; Step S3: Using the constructed optimization evaluation function as a constraint, select the key design parameters of the elastomer for iterative optimization. The selected parameters include the bridge depth parameter H, which represents the H-bridge structure depth of the elastomer. The threshold of the optimization region of the H-bridge structure of the elastomer is obtained through iterative optimization. Step S4 involves smoothing the H-bridge edge curve of the elastomer using a Gaussian filtering algorithm, specifically including: Step S4.1: Obtain the threshold of the optimized region of the elastic body H-bridge structure from step S3, perform edge detection on the model point cloud data that is less than the set threshold, identify potential edge points, and extract the edge curves; Step S4.2: Establish a two-dimensional Gaussian function and initialize the Gaussian kernel; Step S4.3: For each edge point in the edge curve, apply a two-dimensional Gaussian function for smoothing filtering to obtain a smooth edge curve.

2. The joint elastomer optimization design method according to claim 1, characterized in that, In step S1, the polar equation of the Archimedean spiral is: r = a + b · θ Where r is the distance from the origin to any point on the spiral, and a and b are both real numbers; a is the distance between the starting point and the center of the polar coordinates when θ = 0, b is used to control the distance between the spirals and represents the density of the spirals, and θ is the angle parameter in polar coordinates. The larger θ is, the larger the range of the spiral. The polar coordinate equation is transformed into a planar Cartesian coordinate equation as follows: x = (α + β·θ)·cos(θ) y = (α + β·θ)·sin(θ) Here, parameters α and β are constants.

3. The joint elastomer optimization design method according to claim 1, characterized in that, In step S3, the deformation and stress of the elastomer increase with the increase of the bridge depth parameter H, affecting the local stiffness and load distribution of the elastomer. The key design parameters selected for the elastomer also include: the width parameter h, which represents the lateral dimension of the elastomer and directly affects its mechanical properties and space occupation; and the width variation parameter d. n This indicates the change in the width of the elastomer along the helical direction, used to adjust its elastic properties.

4. The joint elastomer optimization design method according to claim 3, characterized in that, Using the aforementioned optimization evaluation function as a constraint, the width parameter h and the width variation parameter d are... n The bridge depth parameter H is iteratively optimized in stages. At each stage, the current performance of the design parameters is evaluated through finite element analysis. Based on the results of the optimization evaluation function, the parameter search direction is guided by a real-time feedback mechanism, and the key design parameters are updated and iterated to obtain the optimal solution.

5. The joint elastomer optimization design method according to claim 1, characterized in that, In step S4.1, the method for identifying edge points is as follows: Iterate through each point cloud dataset, for each point P in the point cloud dataset... i Check in P i With δ as the center, does there exist at least one point P in each of the four quadrants with a search radius of δ? j (j≠i), the expression for determining whether a point is an edge point is: Where isEdge = 1 indicates that point P i If isEdge = 0, then point P is an edge point. i These are non-edge points.

6. The joint elastomer optimization design method according to claim 5, characterized in that, In step S4.2, the expression for the two-dimensional Gaussian function is: Where σ represents the standard deviation of the Gaussian kernel, which is used to control the width of the Gaussian distribution and the smoothness of the curve.

7. The joint elastomer optimization design method according to claim 6, characterized in that, Step S4.3 specifically involves applying a Gaussian kernel constructed using a two-dimensional Gaussian function to each edge point P in the point cloud data. i The point cloud coordinates P after Gaussian filtering are obtained by performing a weighted average. i The weighted average is calculated as follows: Where, x i 'and y i 'It is point P' i After Gaussian filtering, x and y; m and n are the offsets relative to the center. K is the size of the Gaussian kernel; It is the weight of the Gaussian kernel at offset (m,n).

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