Method for establishing a mechanical hand gripping model of a surface contact

Abstract

The application discloses a kind of face contact mechanical hand grabbing model establishing method, belong to mechanical hand grabbing contact modeling application field.Real contact area and normal contact load are determined by obtaining finger surface fractal parameter, combining Hertz contact theory and elastic-plastic contact theory;Deformation tangential contact load is obtained by superimposed microconvex model;Friction cone angle is determined according to real contact area, normal and tangential contact load, and grabbing stability coefficient is obtained based on the relationship between friction cone angle and the inner normal vector angle of contact point;According to the position of finger and object and grabbing stability coefficient, spiral balance condition is established, and then mechanical hand grabbing model is constructed.The application realizes accurate modeling and stability determination of mechanical hand face contact grabbing process by constructing rough surface model of superimposed microconvex structure, combining friction cone constraint and force closed double criterion, and is suitable for object grabbing of any shape and material.

Description

Technical Field

[0001] This invention belongs to the field of contact-stabilized grasping applications of robotic arms, specifically relating to a method for establishing a surface-contact grasping model of a robotic arm. Background Technology

[0002] Robotic gripping technology is one of the core research areas in robotics, and the establishment of its gripping model directly determines the stability and reliability of the gripping operation. Current robotic arms primarily rely on rigid contact, but in actual gripping scenarios, the contact between the robotic arm and the target object is mostly through flexible surface contact. While surface contact provides greater friction and a more stable gripping effect, the continuity and distribution characteristics of the contact area significantly increase the complexity of contact mechanics analysis.

[0003] Current robotic arm designs primarily utilize rigid grippers. These grippers have limited degrees of freedom, resulting in extremely high requirements for the gripping position and difficulty in precisely controlling the gripping force. Existing technologies typically treat both the robotic arm and the target object as equivalent rigid bodies, simplifying the complex contact relationship between them into point contact. For a two-dimensional plane, at least four contact points are required to achieve shape-closed gripping; for a three-dimensional object, at least seven contact points are needed. While this type of point contact model reduces computational complexity to some extent, it has significant limitations: firstly, the actual contact area is smaller than the theoretical contact area, leading to excessive local contact pressure; secondly, it ignores the influence of the geometric characteristics of the contact surface on the gripping effect, ultimately resulting in a significant deviation between the theoretical prediction of gripping stability and the actual application results. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for establishing a surface-contact robotic gripping model, comprising the following steps:

[0005] Step 1: Calculate the fractal parameters of the contact profile by obtaining the root mean square roughness and arithmetic mean roughness between the robotic hand finger and the object, and obtain the fractal parameters of the equivalent contact profile; Based on the fractal parameters of the equivalent contact profile, combine Hertz contact theory, elastoplastic contact theory and area distribution function to determine the true contact area and normal contact load.

[0006] Step 2: Input the current contact parameters between the robotic hand fingers and the object into the pre-built superimposed micro-convex body model to obtain the deformation tangential contact load;

[0007] Step 3: Determine the friction cone angle α during the gripping process based on the actual contact area, the deformed tangential contact load, and the normal contact load; obtain the gripping stability coefficient based on the relationship between the friction cone angle α and the angle β between the inner normal vectors of the contact point.

[0008] Step 4: Based on the obtained position between the finger and the object and the grasping stability coefficient, establish the helical balance condition; based on the helical balance condition and the deformation tangential contact load, establish the robotic arm grasping model.

[0009] Preferably, step 4, which establishes the spiral balance condition based on the obtained position between the finger and the object and the grasping stability coefficient, includes:

[0010] Based on the obtained position between the finger and the object and the grasping stability coefficient, a global coordinate system and a local coordinate system for a single finger are established during the grasping process.

[0011] Construct a grasping mapping matrix based on the global coordinate system and the local coordinate system of the single finger;

[0012] Based on the grasping mapping matrix, the force spiral of the finger acting on the object is determined;

[0013] Based on the spiral force exerted by the finger on the object, establish the spiral equilibrium condition.

[0014] Preferably, in step 1, the fractal parameters of the contact profile are calculated from the obtained root mean square roughness and arithmetic mean roughness between the robotic hand finger and the object to obtain the fractal parameters of the equivalent contact profile, including:

[0015] The feature scale parameters of the contour are determined based on the root mean square roughness between the robotic arm's fingers and the object; the fractal dimension of the contour is determined based on the arithmetic mean roughness between the robotic arm's fingers and the object; satisfying the following expression:

[0016]

[0017]

[0018] Where D represents the fractal dimension of the contour, G represents the feature scale parameter of the contour, Ra is the arithmetic mean roughness between the robotic hand finger and the object, and Rq is the root mean square roughness between the robotic hand finger and the object.

[0019] The fractal parameters of the synthetic rough surface at the contact point between the robotic hand's finger and the object are constructed, including the fractal dimension and the characteristic scale parameters of the synthetic rough surface, satisfying the following expression:

[0020]

[0021]

[0022] Where: D sLet G represent the fractal dimension of the synthesized rough surface, D1 represent the fractal dimension of the finger surface contour, D2 represent the fractal dimension of the grasped object surface contour, and G represent the fractal dimension of the grasped object surface contour. s G1 represents the feature scale parameter of the synthesized rough surface, G2 represents the feature scale parameter of the finger surface contour, and G2 represents the feature scale parameter of the grasped object surface contour.

[0023] Construct the 2D contour height of the contact point between the robotic hand's finger and the object, satisfying the following expression:

[0024]

[0025] Where: z(x) represents the height of the two-dimensional profile, π represents pi, and n represents the frequency level. max Indicates the maximum frequency level, n min Minimum frequency level, γ is the spatial frequency of the profile, and x represents the sampling position of the horizontal coordinate of the two-dimensional profile.

[0026] in:

[0027]

[0028]

[0029] Where γ is the spatial frequency of the contour; L is the length of the acquired contour; and Δx is the distance between two adjacent sampling points.

[0030] The feature scale parameter of the contour, the fractal dimension of the contour, the fractal dimension of the synthesized rough surface, the feature scale parameter of the synthesized rough surface, and the height of the two-dimensional contour are used as the fractal parameters of the equivalent contact contour.

[0031] Preferably, the pre-construction process of the superimposed micro-convexity model includes:

[0032] Based on the contact parameters between the robotic hand's fingers and the object, construct the radius of curvature function and the height function;

[0033] Based on the curvature radius function and the height function, a stacked micro-convex body model is obtained by a step-by-step stacking method;

[0034] The radius of curvature function satisfies the following expression:

[0035]

[0036] Where: R I Let π represent the radius of curvature of the I-th layer micro-convexity, π represent pi, G represent the characteristic scale parameter of the profile, and n minMinimum frequency level, n represents the frequency level, I represents the level of the I-th micro-protrusion from bottom to top in the superimposed micro-protrusions, γ is the profile spatial frequency, and D represents the fractal dimension;

[0037] Preferably, the actual contact area satisfies the following expression:

[0038]

[0039] Among them, A r A represents the actual contact area. re A represents the contact area of ​​the elastically deformed micro-protrusion. rep1 Indicates the contact area of ​​the first elastoplastic micro-protrusion, A rep2 A represents the contact area of ​​the micro-protrusion that undergoes the second elastoplastic deformation. rp The contact area of ​​the micro-protrusion undergoing plastic deformation is represented by 'i', which represents the layer level of the micro-protrusion in contact with the rigid plane, and 'N' represents the total number of layers of stacked micro-protrusions, where N = n. max -n min +1, n max Indicates the maximum frequency level, n min Minimum frequency level, a iec a represents the critical contact area for elastic deformation of the i-th layer of micro-protrusions. iepc a represents the critical contact area for the first elastic-plastic deformation of the i-th layer of micro-protrusions. ipc Let n(a) represent the critical plastic deformation of the i-th layer of micro-protrusions, n(a) represent the area distribution function, and a represent the contact area of ​​the micro-protrusions. i+1,i a represents the contact area produced by the rigid plane passing through the intersection surface of the i+1 and i micro-protrusions in the superimposed micro-protrusions. i,i-1 a represents the contact area produced by the rigid plane passing through the intersection surface of the i-1 micro-protrusion layers in the superimposed micro-protrusions. Ii The contact area represents the maximum downward pressure when the micro-protrusions come into contact, and I represents the I-th layer of micro-protrusions from bottom to top;

[0040] The normal contact load satisfies the following expression:

[0041]

[0042] Among them: F r F represents the normal contact load. re The normal contact load F of the elastically deformed micro-protrusion is represented by... rep1 F represents the normal contact load on the first elastoplastic micro-protrusion. rep2 F represents the normal contact load of the micro-protrusion undergoing the second elastoplastic deformation. rp f represents the normal contact load on the micro-protrusion undergoing plastic deformation.ie f represents the normal contact load of a single micro-protrusion during elastic deformation of the i-th layer of micro-protrusions. iep1 f represents the normal contact load of a single micro-protrusion during the first elastoplastic deformation of the i-th layer of micro-protrusions. iep2 f represents the normal contact load of a single micro-protrusion during the second elastoplastic deformation of the i-th layer of micro-protrusions. ip This represents the normal contact load of the i-th layer of micro-protrusions undergoing plastic deformation.

[0043] The height function satisfies the following expression:

[0044]

[0045] In the above formula, Δ I This indicates the height of the I-th layer of micro-protrusions.

[0046] Preferably, the deformable tangential contact load satisfies the following expression:

[0047]

[0048] Among them: T r T represents the tangential contact load during deformation. re T represents the tangential contact load on the elastically deformed micro-protrusion. rep1 Let n(a) represent the tangential contact load of the micro-protrusion undergoing the first elastoplastic deformation, n(a) represent the area distribution function, N represent the total number of layers of superimposed micro-protrusions, a represent the contact area of ​​the micro-protrusions, and i represent the layer level of the micro-protrusion in contact with the rigid plane. iec a represents the critical contact area for elastic deformation. iepc a represents the critical contact area for the first elastic-plastic deformation of the i-th layer. ie a represents the contact area when the i-th layer of micro-protrusions undergoes elastic deformation. iepc1 f represents the contact area during the first elastic-plastic deformation of the i-th layer. ie f represents the normal contact load of a single micro-protrusion during elastic deformation of the i-th layer of micro-protrusions. iep1 σ represents the normal contact load of a single micro-protrusion during the first elastoplastic deformation of the i-th layer of micro-protrusions. s denoted by , v represents the yield strength of the softer material, I represents the I-th micro-protrusion from bottom to top in the stacked micro-protrusions, and π represents pi.

[0049] Preferably, the friction cone angle α satisfies the following expression:

[0050]

[0051] Where μ represents the friction coefficient of the rough surface;

[0052] The included angle β of the inner normal vectors satisfies the following expression:

[0053]

[0054] Among them, f yej This represents the component of force along the y-tangential direction at the contact point of the j-th finger; f xej This represents the component of force along the x-tangential direction at the contact point of the j-th finger; f zej This represents the component of force along the z-direction at the contact point of the j-th finger; T r F represents the tangential contact load during deformation. r Indicates the normal contact load.

[0055] Preferably, the grasping stability coefficient satisfies the following expression:

[0056]

[0057] Where, k j Let α represent the grasping stability coefficient during the grasping process of the j-th finger, α be the friction cone angle, and β be the angle between the inner normal vectors at the contact point.

[0058] Preferably, the capture mapping matrix satisfies the following matrix expression:

[0059]

[0060] Among them, G j Let g represent the grasping mapping matrix of the j-th finger. j E represents the grasping Jacobian submatrix of the j-th finger. j The pose transformation matrix of the j-th finger, r zej r xej r yej Let φ be the position vector of the j-th finger's contact point in the object's coordinate system. j1 For x j y j Projection on the plane and x j The included angle of the axis, φ j2 For the inner normal vector n j With z j The included angle of the axis.

[0061] Preferably, the force spiral exerted by the finger on the object satisfies the following formula:

[0062]

[0063] Where F represents the force spiral applied by the finger in global coordinates, j represents the j-th finger, and m represents the number of grasping positions. zj F represents the force exerted by the j-th finger on the object in the global coordinate system.e This indicates the spiral force exerted by the finger on an object.

[0064] Compared with the prior art, the present invention has the following advantages and technical effects:

[0065] The method for establishing a surface contact manipulator grasping model of the present invention obtains the fractal parameters of the equivalent contact contour and, in combination with Hertz contact theory, elastoplastic contact theory, and area distribution function, accurately determines the actual contact area and normal contact load, overcoming the problem of local pressure misjudgment caused by contact area estimation deviation. By inputting the contact parameters into a superimposed micro-convex body model to obtain the deformable tangential contact load, it compensates for the deficiency of rigid point contact models in reflecting the deformation characteristics of the contact surface. By determining the friction cone angle α based on the actual contact area, deformable tangential contact load, and normal contact load, and obtaining the grasping stability coefficient based on the relationship between the friction cone angle α and the angle β between the inner normal vectors of the contact point, the qualitative stability judgment is transformed into a quantifiable index, effectively reducing the deviation between theoretical prediction and actual effect. Finally, by establishing the helical equilibrium condition based on the position between the fingers and the object and the grasping stability coefficient, and combining the deformable tangential contact load to establish a complete manipulator grasping model, the judgment conditions of the surface contact grasping model are revealed from a mechanistic perspective, providing a unified and quantifiable modeling method for grasping stability analysis of objects of arbitrary shape and material. Attached Figure Description

[0066] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0067] Figure 1 This is a flowchart illustrating a method for establishing a surface-contact robotic gripping model according to the present invention.

[0068] Figure 2 This is a schematic diagram of the contact between the robotic hand fingers during grasping according to an embodiment of the present invention;

[0069] Figure 3 This is a schematic diagram of a superimposed micro-protrusion according to an embodiment of the present invention. Wherein (a) is a schematic diagram of a superimposed micro-protrusion with non-coincident symmetry axes, and (b) is a schematic diagram of a superimposed micro-protrusion with coincident symmetry axes.

[0070] Figure 4 This image shows a comparison between the superimposed micro-protrusion at point (0,0) and the actual micro-protrusion contour in an embodiment of the present invention. Where (a) represents the fractal dimension D=1.3 and G=1×10⁻⁶. -11 n min =1、n max= 30, (b) represents the fractal dimensions D=1.3 and G=1×10. -11 n min=5、n max= 30.

[0071] Figure 5 This is a comparison between the three-dimensional superimposed micro-protrusion of the present invention and the actual micro-protrusion, where (a) represents the fractal dimension D=1.3 and n. min =1、n max= 30, (b) represents the fractal dimension D = 1.3, n min =5、n max= 30.

[0072] Figure 6 The friction cone α and the inner normal vector β generated when the finger grasps an object in an embodiment of the present invention.

[0073] Figure 7 This is a mechanical analysis of the finger grasping an object according to an embodiment of the present invention.

[0074] Figure 8 The mechanical properties of the robotic arm grasping the aluminum ball in this embodiment of the invention are shown. Among them, (a) is the area-normal load curve, and (b) is the area-tangential load curve.

[0075] Figure 9 The mechanical properties of the robotic arm grasping the steel ball in this embodiment of the invention are shown. Wherein (a) is the area-normal load curve, and (b) is the area-tangential load curve.

[0076] Figure 10 This is a schematic diagram illustrating the establishment of the object coordinate system for the robotic arm to grasp a small metal ball according to an embodiment of the present invention.

[0077] Figure 11 To assess the stability of a robotic arm grasping an aluminum ball. (a) shows the relationship between the angle β of the inner normal vector and the cone angle α of the friction cone during the grasping process, and (b) shows the change in grasping stability of the aluminum ball with respect to the actual contact area.

[0078] Figure 12 This study assesses the stability of a robotic arm grasping a steel ball. (a) shows the relationship between the internal normal angle β and the friction cone angle α during the grasping process, while (b) shows the change in grasping stability of an aluminum ball with respect to the actual contact area. Detailed Implementation

[0079] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0080] It should be noted that the example shown in the attached figure is a specific example of constructing the contact surface model and solving the grasping stability when a robotic arm grasps an object. This method is also applicable to surface morphology modeling of objects of any material and solving the grasping stability of objects of any shape. Furthermore, this method has good scalability; it is not only applicable to single surface morphology and shape, but can also be combined with parameters such as surface roughness Ra to adaptively adjust the fractal parameters of the WM function. Moreover, a grasping mapping matrix can be established according to different grasping positions, thereby achieving unified modeling and solving of the grasping stability of objects of different materials and shapes.

[0081] Example 1

[0082] like Figure 1 As shown, this embodiment provides a method for establishing a surface-contact robotic gripping model, including the following steps:

[0083] Step 1: Calculate the fractal parameters of the contact profile by obtaining the root mean square roughness and arithmetic mean roughness between the robotic hand finger and the object, and obtain the fractal parameters of the equivalent contact profile; Based on the fractal parameters of the equivalent contact profile, combine Hertz contact theory, elastoplastic contact theory and area distribution function to determine the true contact area and normal contact load.

[0084] Step 2: Input the current contact parameters between the robotic hand fingers and the object into the pre-built superimposed micro-convex body model to obtain the deformation tangential contact load;

[0085] Step 3: Determine the friction cone angle α during the gripping process based on the actual contact area, the deformed tangential contact load, and the normal contact load; obtain the gripping stability coefficient based on the relationship between the friction cone angle α and the angle β between the inner normal vectors of the contact point.

[0086] Step 4: Based on the obtained position between the finger and the object and the grasping stability coefficient, establish the helical balance condition; based on the helical balance condition and the deformation tangential contact load, establish the robotic arm grasping model.

[0087] like Figure 2 As shown, in step 1, the contact during the gripping process of the robot can be equivalent to the contact between a rigid plane and a rough surface contour. The contact process between the robot and the object being gripped is simulated by the downward pressure of the rigid plane. The actual contact area and normal contact load during the robot's contact process are calculated by the deformation of the micro-protrusions on the rigid plane.

[0088] Further, in step 1, the root mean square roughness and arithmetic mean roughness between the obtained robotic hand fingers and the object are used to calculate the fractal parameters of the contact profile, resulting in the fractal parameters of the equivalent contact profile, including:

[0089] The feature scale parameters of the contour are determined based on the root mean square roughness between the robotic arm's fingers and the object; the fractal dimension of the contour is determined based on the arithmetic mean roughness between the robotic arm's fingers and the object; satisfying the following expression:

[0090]

[0091]

[0092] Where D represents the fractal dimension of the contour, G represents the feature scale parameter of the contour, Ra is the arithmetic mean roughness between the robotic hand finger and the object, and Rq is the root mean square roughness between the robotic hand finger and the object.

[0093] The fractal parameters of the synthetic rough surface at the contact point between the robotic hand's finger and the object are constructed, including the fractal dimension and the characteristic scale parameters of the synthetic rough surface, satisfying the following expression:

[0094]

[0095]

[0096] Where: D s Let G represent the fractal dimension of the synthesized rough surface, D1 represent the fractal dimension of the finger surface contour, D2 represent the fractal dimension of the grasped object surface contour, and G represent the fractal dimension of the grasped object surface contour. s G1 represents the feature scale parameter of the synthesized rough surface, G2 represents the feature scale parameter of the finger surface contour, and G2 represents the feature scale parameter of the grasped object surface contour.

[0097] Construct the 2D contour height of the contact point between the robotic hand's finger and the object, satisfying the following expression:

[0098]

[0099] Where: z(x) represents the height of the two-dimensional profile, π represents pi, and n represents the frequency level. max Indicates the maximum frequency level, n min Minimum frequency level, γ is the spatial frequency of the profile, and x represents the sampling position of the horizontal coordinate of the two-dimensional profile.

[0100] in:

[0101]

[0102]

[0103] Where γ is the spatial frequency of the contour; L is the length of the acquired contour; and Δx is the distance between two adjacent sampling points.

[0104] The feature scale parameter of the contour, the fractal dimension of the contour, the fractal dimension of the synthesized rough surface, the feature scale parameter of the synthesized rough surface, and the height of the two-dimensional contour are used as the fractal parameters of the equivalent contact contour.

[0105] For rough surface profiles exhibiting fractal characteristics, the WM function in the above equation can be used for construction. Based on the properties of the WM function, the rough surface profile can be considered as a superposition of cosine waves of different frequency levels, where each cosine wave can be equivalent to a hemispherical micro-protrusion with a specific radius of curvature. The radius of curvature and height of each micro-protrusion can be calculated using the above equation.

[0106]

[0107]

[0108] Where n1 represents the frequency level of the micro-convexity. This represents the radius of curvature of a micro-convexity with a frequency level of n1. This indicates the height of the micro-protrusion with a frequency level of n1.

[0109] The above formula shows that the radius of curvature of the micro-convexity gradually decreases as the frequency level increases. Therefore, in the process of building a single stacked micro-convexity model, the hemispherical micro-convexity with a smaller frequency level is placed at the bottom layer, and the hemispherical micro-convexity with a larger frequency level is placed at the top layer. However, the axes of symmetry of hemispherical micro-convexities at adjacent frequency levels do not coincide during the stacking process. At this time, the axes of symmetry for micro-convexities at frequency levels n and n-1 are respectively:

[0110]

[0111]

[0112] Where x n The axis of symmetry of a hemispherical micro-convexity with frequency level n is x. n-1 k represents the axis of symmetry of a hemispherical micro-convex body with frequency level n-1. n k represents a micro-convexity at different locations representing a cosine function of frequency order n. n-1 This represents a micro-convexity representing a cosine function with frequency order n-1 at different locations. For example... Figure 3 As shown in (a), when the axes of symmetry of two adjacent hemispherical micro-protrusions do not coincide, the resulting superimposed micro-protrusions exhibit diverse geometric shapes. To ensure a unique geometric shape for the superimposed micro-protrusions, it is crucial to guarantee that their axes of symmetry coincide during the superposition process, such as... Figure 3 As shown in (b).

[0113] Figure 4 and Figure 5This paper presents a comparison between the superimposed micro-protrusion model constructed in this paper and the actual superimposed micro-protrusion contour. Figure 4 (a) and Figure 5 (a) Its fractal parameters D=1.3, n min =1、n max =30, G=1×10 -11 , Figure 4 (b) and Figure 5 (b) Its fractal parameters D=1.3, n min =5、n max =30, G=1×10 -11 By comparison, it was found that the area of ​​the superimposed micro-convex body contour constructed in this paper that coincides with the actual contour and the x-axis is less than 10%. This verifies the rationality of the superimposed micro-convex body model constructed in this paper.

[0114] In step 2 above, the pre-construction process of the superimposed micro-convexity model may include the following process:

[0115] Step 2.1: Construct the radius of curvature function and height function based on the contact parameters between the robotic hand's fingers and the object;

[0116] Step 2.2: Based on the radius of curvature function and the height function, a stacked micro-convex body model is obtained by using a step-by-step stacking method;

[0117] The radius of curvature function satisfies the following expression:

[0118]

[0119] Where: R I denoted by the radius of curvature of the I-th layer of micro-protrusions, where I represents the layer of the I-th micro-protrusion from bottom to top in the stacked micro-protrusions;

[0120] The height function satisfies the following expression:

[0121]

[0122] In the above formula, Δ I This indicates the height of the I-th layer of micro-protrusions.

[0123] When the surface of a robotic hand's finger deforms, the deformation state of the first layer of micro-protrusions superimposed on its contact surface, according to Hertz's theory and elastoplastic theory, can be classified into four types: elastic deformation, first elastoplastic deformation, second elastoplastic deformation, and plastic deformation. The deformation state of the first layer of micro-protrusions depends on the deformation amount ω of the micro-protrusions. I The four deformation states of the micro-protrusion are shown in Table 1:

[0124] Table 1. Criteria for Judging the Contact State of the First Layer of Superimposed Micro-protrusions

[0125]

[0126] For a given two-dimensional fractal profile surface, the area density distribution function of the micro-convexity is:

[0127]

[0128] n(a) represents the number density of microconvexities of size a per unit area, a I This represents the maximum contact area of ​​a single micro-protrusion, where 'a' represents the area of ​​the micro-protrusion.

[0129] The actual contact area A of the rough surface r :

[0130]

[0131] Assuming the rigid plane comes into contact with the I-th (1≤I≤N) layer of the stacked micro-protrusions, when the maximum contact area of ​​the micro-protrusions is a I1 The actual contact area then satisfies the following expression:

[0132]

[0133] Among them, A r A represents the actual contact area. re A represents the contact area of ​​the elastically deformed micro-protrusion. rep1 Indicates the contact area of ​​the first elastoplastic micro-protrusion, A rep2 A represents the contact area of ​​the micro-protrusion that undergoes the second elastoplastic deformation. rp The contact area of ​​the micro-protrusion undergoing plastic deformation is represented by i, which represents the layer level of the micro-protrusion in contact with the rigid plane, and N represents the total number of layers of stacked micro-protrusions. iec a represents the critical contact area for elastic deformation of the i-th layer of micro-protrusions. iepc a represents the critical contact area for the first elastic-plastic deformation of the i-th layer of micro-protrusions. ipc Let n(a) represent the critical plastic deformation of the i-th layer of micro-protrusions, n(a) represent the area distribution function, and a represent the contact area of ​​the micro-protrusions. i+1,i a represents the contact area produced by the rigid plane passing through the intersection surface of the i+1 and i micro-protrusions in the superimposed micro-protrusions. i,i-1 a represents the contact area produced by the rigid plane passing through the intersection surface of the i-1 micro-protrusion layers in the superimposed micro-protrusions. Ii This represents the contact area at which the downward pressure is at its maximum when the micro-protrusions come into contact.

[0134] The normal contact load satisfies the following expression:

[0135]

[0136] Among them: F r F represents the normal contact load. re The normal contact load F of the elastically deformed micro-protrusion is represented by... rep1 F represents the normal contact load on the first elastoplastic micro-protrusion. rep2 F represents the normal contact load of the micro-protrusion undergoing the second elastoplastic deformation. rp f represents the normal contact load on the micro-protrusion undergoing plastic deformation. ie f represents the normal contact load of a single micro-protrusion during elastic deformation of the i-th layer of micro-protrusions. iep1 f represents the normal contact load of a single micro-protrusion during the first elastoplastic deformation of the i-th layer of micro-protrusions. iep2 f represents the normal contact load of a single micro-protrusion during the second elastoplastic deformation of the i-th layer of micro-protrusions. ip This represents the normal contact load of the i-th layer of micro-protrusions undergoing plastic deformation.

[0137] If we calculate the contact mechanical properties at the intersection of the I-th layer micro-protrusion and the (I-1)-th layer micro-protrusion, then a I,I-1 When the intersecting surfaces of two adjacent micro-protrusions belonging to the I-th layer come into contact, and the superimposed micro-protrusions of the I-th layer undergo elastic deformation:

[0138]

[0139] When the first layer of stacked micro-protrusions undergoes its first elastoplastic deformation:

[0140]

[0141] When the first layer of stacked micro-protrusions undergoes the second elastoplastic deformation:

[0142]

[0143] When the first layer of stacked micro-protrusions undergoes plastic deformation:

[0144]

[0145] Where: a I,I-1 a represents the intersection area of ​​layer I and layer I-1 under deformation. Iec ax represents the critical contact area for elastic deformation of the I-th layer of micro-protrusions. I,I-1 Let φ1 = 0.5, φ2 = 0.465, φ3 = 0.47, ε1 = -0.136, ε2 = -0.146.

[0146] In step 2 above, when the micro-protrusions are compressed, only those in the elastic stage and the first elastoplastic deformation stage can withstand the tangential load. Therefore, when calculating the tangential contact load, only these two types of deformation need to be considered. Assuming that when the rigid plane comes into contact with the I-th layer of the stacked micro-protrusions, the yielding of the contact-deformed plane occurs at the edge of the contact point, and the stress at the edge of the I-th layer is:

[0147]

[0148]

[0149]

[0150] Where, σ x σ is the stress direction that is the same as the direction of the normal contact load. y For the stress direction that is the same as the direction of friction, σ z f is the force perpendicular to the plane containing the normal load direction. I Let v represent the normal contact load acting on the I-th layer of the superimposed micro-convex body, T represent the tangential contact load, and τ represent the normal contact load acting on the superimposed micro-convex body. xy For the shear stress in the xy plane, τ xz For the shear stress in the xz plane, τ yz This represents the shear stress in the yz plane. According to the Treaca yield criterion...

[0151]

[0152] Based on this, the maximum tangential load that a single micro-assurance layer I can withstand can be calculated:

[0153]

[0154] Where, σ s It is the yield strength of a relatively soft material, therefore the maximum tangential load that a single stacked micro-protrusion can withstand is:

[0155]

[0156] Where T d a represents the maximum tangential load that a single stacked micro-convexity can withstand. i f represents the contact area of ​​the i-th layer. i This represents the normal contact load of the i-th layer.

[0157] In step 2, the deformation tangential contact load satisfies the following expression:

[0158]

[0159] Among them: T rT represents the tangential contact load during deformation. re T represents the tangential contact load on the elastically deformed micro-protrusion. rep1 Let n(a) represent the tangential contact load of the micro-protrusion undergoing the first elastoplastic deformation, n(a) represent the area distribution function, N represent the total number of layers of superimposed micro-protrusions, a represent the contact area of ​​the micro-protrusions, and i represent the layer level of the micro-protrusion in contact with the rigid plane. iec a represents the critical contact area for elastic deformation. iepc a represents the critical contact area for the first elastic-plastic deformation of the i-th layer. ie a represents the contact area when the i-th layer of micro-protrusions undergoes elastic deformation. iepc1 f represents the contact area during the first elastic-plastic deformation of the i-th layer. ie f represents the normal contact load of a single micro-protrusion during elastic deformation of the i-th layer of micro-protrusions. iep1 σ represents the normal contact load of a single micro-protrusion during the first elastoplastic deformation of the i-th layer of micro-protrusions. s denoted by , v represents the yield strength of the softer material, I represents the I-th micro-protrusion from bottom to top in the stacked micro-protrusions, and π represents pi.

[0160] In step 3 above, the friction cone angle α satisfies the following expression:

[0161]

[0162] Where μ represents the coefficient of friction of the rough surface; the friction cone α and the inner normal vector β generated when the finger grasps the object are as follows: Figure 6 As shown.

[0163] When gripping an object, the normal contact load should be used to fix the object, and its normal contact load should satisfy the following:

[0164]

[0165] The two components of its tangential contact load are used to prevent the object from slipping during the grasping process, therefore f must also satisfy the following condition:

[0166]

[0167] Where u 扭 f represents the torsional coefficient. xej This represents the component of force along the x-tangential direction at the contact point of the j-th finger; f yej This represents the component of force along the y-tangential direction at the contact point of the j-th finger; f zej This represents the component force f along the z-direction at the contact point of the j-th finger. wejLet be the tangential torsional component at the j-th contact point. Since the object being grasped is stationary, there is no torsion, so the equation simplifies to:

[0168]

[0169] Furthermore, the included angle β of the inner normal vectors satisfies the following expression:

[0170]

[0171] Among them, f yej This represents the component of force along the y-tangential direction at the contact point of the j-th finger; f xej This represents the component of force along the x-tangential direction at the contact point of the j-th finger; f zej This represents the component of force along the z-direction at the contact point of the j-th finger; T r F represents the tangential contact load during deformation. r Indicates the normal contact load.

[0172] Furthermore, in step 3 above, the grasping stability coefficient satisfies the following expression:

[0173]

[0174] Where, k j Let α represent the grasping stability coefficient during the grasping process of the j-th finger, α be the friction cone angle, and β be the angle between the inner normal vectors at the contact point.

[0175] The closer the grasping stability coefficient is to 1, the better the grasping stability. When a robotic arm grasps an object, its grasping stability coefficient k satisfies the following formula:

[0176]

[0177] When the grasping stability coefficient is closer to 1, the angle between the friction cone angle and the inner normal vector is closer, and the grasping tends to be in a critical stable state. When the grasping stability coefficient is less than 1, it indicates that the current grasping state meets the friction cone constraint condition and stable grasping can be performed. When the grasping stability coefficient is greater than 1, it indicates that the grasping is unstable. By calculating the grasping stability coefficient of each finger, the overall grasping stability can be comprehensively evaluated.

[0178] Further, in step 4, establishing the spiral balance condition based on the obtained position between the finger and the object and the grasping stability coefficient includes the following steps:

[0179] Step 4.1: Based on the obtained position between the finger and the object and the grasping stability coefficient, establish a global coordinate system and a local coordinate system for a single finger during the grasping process;

[0180] Step 4.2: Construct a grasping mapping matrix based on the global coordinate system and the local coordinate system of a single finger;

[0181] Step 4.3: Determine the force screw exerted by the finger on the object according to the grasping mapping matrix;

[0182] Step 4.4: Establish a screw balance condition according to the force screw exerted by the finger on the object.

[0183] Furthermore, in the above step 4.3, the grasping mapping matrix G j , satisfies the following matrix expression:

[0184]

[0185] where G j represents the grasping mapping matrix of the j-th finger, g j represents the grasping Jacobian submatrix of the j-th finger, E j is the attitude transformation matrix of the j-th finger, r zej r xej r[[ID=2,8]] yej is the position vector of the contact point of the j-th finger in the object coordinate system, φ j1 is the angle between the projection on the x j y j plane and the x j axis, φ j2 is the angle between the inner normal vector n j and the z j axis. During the grasping process, the force screw of the resultant force and resultant torque exerted by the j-th finger on the object is F hj :, then there is:

[0186]

[0187] where F hj is the force screw of the resultant force and resultant torque exerted by the j-th finger on the object in the local coordinate system, A is the contact matrix, f hj =( f xej , f yej , f zej , m xej , m yej , m zej ) represents the force and torque components exerted on the object at the contact point i. To determine the influence of the contact forces of each finger on the force state of the object, it is necessary to convert the contact forces from the contact coordinate system to the object coordinate system. Then, in the object coordinate system, the force screw F zj exerted by the j-th (1 < j < m) finger on the object can be expressed as:

[0188]

[0189] F zj The force screw F of the jth (1 < j < m) finger acting on the object in the object coordinates represents the force and torque applied to the object zj

[0190] Furthermore, in the above step 4.4, the force screw of the finger acting on the object satisfies the following formula:

[0191]

[0192] where F represents the force screw applied by the finger in the global coordinates, j represents the jth finger, m represents the number of grasping positions, and F zj represents the force applied by the jth finger to the object in the global coordinate system, and F e represents the force screw of the finger acting on the object

[0193] Compared with the prior art modeling method that simplifies the manipulator and the target object into rigid bodies and simplifies the complex contact relationship into point contact, the present invention also has the following remarkable technical effects:

[0194] First, accurate calculation of the real contact area is achieved. Aiming at the problem in the background technology that "the actual contact area is smaller than the theoretical contact area, resulting in excessive local contact pressure", by obtaining the fractal parameters of the equivalent contact profile and then combining with the Hertz contact theory, the elastic-plastic contact theory and the area distribution function, the real contact area can be accurately determined, providing an accurate area data basis for the judgment of grasping stability and avoiding misjudgment of local pressure caused by estimation deviation of the contact area

[0195] Second, the tangential contact load is accurately obtained. Aiming at the defect that the rigid point contact model in the background technology cannot reflect the deformation characteristics of the contact surface, in step 2 of the present invention, by inputting the contact parameters into the pre-constructed superimposed microconvex body model, the deformed tangential contact load can be obtained, making the calculation of the tangential load more in line with the surface contact deformation characteristics in the actual grasping process

[0196] Third, quantitative judgment of grasping stability is achieved. Aiming at the problem in the background technology that "there is a large deviation between the theoretical prediction result of grasping stability and the actual application effect", in step 3 of the present invention, the friction cone angle α is determined according to the real contact area, the deformed tangential contact load and the normal contact load, and then the grasping stability coefficient is obtained according to the relationship between the friction cone angle α and the included angle β between the inner normal vector of the contact point, converting the original qualitative stability judgment into a quantifiable index, effectively reducing the deviation between the theoretical prediction and the actual effect

[0197] Fourth, a complete surface contact grasping model was constructed. Step 4 of this invention establishes helical balance conditions based on the position between the finger and the object and the grasping stability coefficient. Then, by combining the helical balance conditions and the deformation tangential contact load, a robotic hand grasping model suitable for surface contact was finally established, overcoming the limitation of the prior art that "ignores the influence of the geometric characteristics of the contact surface on the grasping effect".

[0198] Example 2

[0199] To illustrate the method of this invention, an example of a process for solving a capture instance is provided below:

[0200] The specific steps for calculating the robotic arm's grasping example are as follows:

[0201] (1) Based on the fractal parameters of the equivalent contact profile, combined with Hertz contact theory, elastoplastic contact theory and area distribution function, determine the expressions for the real contact area, normal contact load and tangential contact load;

[0202] (2) Based on the established contact mechanics model expression, draw and analyze the relationship between the actual contact area, normal contact load and tangential contact load during the contact process;

[0203] (3) Based on the location information of the contact point, establish a global coordinate system and a local contact coordinate system, and construct a capture mapping matrix on this basis;

[0204] (4) Combining the contact load obtained in step (2), derive the relationship between the friction cone angle α and the contact point normal angle β, obtain the position between the finger and the object and the grasping stability coefficient, and establish the spiral balance condition; based on the spiral balance condition and the deformation tangential contact load, establish the manipulator grasping model.

[0205] This invention uses two common materials and a 60mm metal sphere as examples to establish a gripping stability model:

[0206] Table 3 Properties of common metallic materials

[0207]

[0208] Based on the root mean square roughness of the mechanical finger and the object's surface profile and the instrument resolution, the equivalent surface fractal parameters are obtained as follows: ① Fractal parameters of the equivalent surface profile of the mechanical finger and the aluminum ball: D=1.486, G=2.12×10 -11 m、n min =5、n max= 30, ② Fractal parameters of the equivalent surface profile of the robot and the steel ball: D=1.502, G=1.84×10 -11 m、n min =5、n max=30.

[0209] The actual contact area, normal contact load, and tangential contact load described in step (2) can be solved using the corresponding expressions, as shown in the figure. Figure 8 , Figure 9 As shown.

[0210] According to the mapping matrix described in step (3), based on Figure 10 Establish the coordinate system of the object being captured, where Figure 10 Figures (a) and (b) show how the gripping position of the fingers on the metal sphere is determined. An oxyz coordinate system is established with the origin of the sphere's center. For the fingers e1, e2, and e3, a local coordinate system is established according to the right-hand rule, as shown below. Figure 10 As shown in (c), based on the position coordinates of the sphere, we can know that the sphere has coordinates e1(r, 0, 0) and e2(-r / 2, ,0), e3(-r / 2,- The coordinates of (0, 0) are given by the following capture matrix:

[0211] Its e1, e 2、 The direction matrix of e3:

[0212]

[0213] Its e1, e2, and e3 capture matrices:

[0214]

[0215] By capturing the mapping matrix rank(G) = 6, the force closure condition is satisfied.

[0216] Based on step (4) and the contact load obtained in step (2), the relationship between the friction cone angle α and the contact point normal angle β is derived, as follows: Figure 10 (a) and Figure 11 As shown in (a); furthermore, a criterion model for the contact stability of the robotic arm's grasping is established, as follows: Figure 10 (b) and Figure 11 As shown in (b), the final contact stability model of the robotic arm is obtained.

[0217] When grasping the aluminum ball, the actual contact area reaches 7mm. 2 At this point, the gripping state simultaneously satisfies the friction cone constraint condition and the force-closed gripping criterion. Further observation revealed that as the gripping load increases, the gripping stability coefficient consistently fluctuates slightly around 0.71 without showing a significant decreasing trend, indicating that the gripping system possesses good resistance to load disturbances at this state. Therefore, when the actual contact area is greater than 7mm... 2 During this process, the robotic arm can maintain stability in grasping the aluminum ball.

[0218] When grasping the steel ball, the actual contact area reaches 8.14 mm. 2 At this point, the gripping state simultaneously satisfies the friction cone constraint condition and the force-closed gripping criterion. Further observation revealed that as the gripping load increases, the gripping stability coefficient consistently fluctuates slightly around 0.43, without showing a significant decreasing trend, indicating that the gripping system possesses good resistance to load disturbances at this state. Therefore, when the actual contact area is greater than 8.14 mm²... 2 At that time, the robotic arm can maintain stability during the gripping process of the steel ball.

[0219] This invention establishes a model for a robotic hand to grasp a target object through surface contact. The surface morphology of the robotic hand finger is constructed using the superposition properties of the WM function. The surface micro-protrusions of the robotic hand are composed of superimposed micro-protrusions. Based on Hertz theory, the normal and tangential contact loads generated on the surface during grasping are calculated. A force-closed contact model is used for calculation, and a friction cone is used to determine the contact stability.

[0220] Considering the non-rigid characteristics of objects, surface contact forms, and complex morphologies of rough surfaces in real-world contact scenarios, this paper innovatively constructs a contact surface model for a robotic arm containing a superimposed micro-protrusion structure. This model determines the WM function characterization parameters based on the root mean square roughness of the grasped object's surface, thereby generating a superimposed micro-protrusion model for rough surface contact. Furthermore, by calculating the normal and tangential contact loads during the grasping process, and combining the friction cone constraint condition and the force-closed grasping matrix as dual criteria, the feasibility and stability of the robotic arm's grasping action are accurately determined.

[0221] The present invention can be applied in the following scenarios: (1) Precision electronic assembly: for fragile devices with rough surfaces such as chips and micro sensors, it can achieve non-destructive and high-precision gripping and assembly. (2) Flexible irregular workpiece processing: adapting to the non-rigid rough surfaces of composite material parts to ensure no deformation or slippage during the transfer process. (3) Aerospace precision operation: for high-value rough surface parts such as engine blades and satellite components, it can verify the reliability of gripping and avoid damage. (4) Special extreme environment operation: used for rough material transfer in scenarios such as nuclear industry, deep sea, and polar regions, improving the gripping stability in harsh environments. (5) Gripping theory scientific research experiment: as a simulation tool, it can support research and verification in the fields of contact mechanics and end effector design of robotic arms.

[0222] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for establishing a gripping model of a surface-contact robotic arm, characterized in that, Includes the following steps: Step 1: Calculate the fractal parameters of the contact profile by obtaining the root mean square roughness and arithmetic mean roughness between the robotic hand finger and the object, and obtain the fractal parameters of the equivalent contact profile; Based on the fractal parameters of the equivalent contact profile, combine Hertz contact theory, elastoplastic contact theory and area distribution function to determine the true contact area and normal contact load. Step 2: Input the current contact parameters between the robotic hand fingers and the object into the pre-built superimposed micro-convex body model to obtain the deformation tangential contact load; Step 3: Determine the friction cone angle α during the gripping process based on the actual contact area, the deformed tangential contact load, and the normal contact load; obtain the gripping stability coefficient based on the relationship between the friction cone angle α and the angle β between the inner normal vectors of the contact point. Step 4: Based on the obtained position between the finger and the object and the grasping stability coefficient, establish the helical balance condition; based on the helical balance condition and the deformation tangential contact load, establish the robotic arm grasping model.

2. The method according to claim 1, characterized in that, Step 4, which establishes the spiral balance condition based on the obtained position between the finger and the object and the grasping stability coefficient, includes: Based on the obtained position between the finger and the object and the grasping stability coefficient, a global coordinate system and a local coordinate system for a single finger are established during the grasping process. Construct a grasping mapping matrix based on the global coordinate system and the local coordinate system of the single finger; Based on the grasping mapping matrix, the force spiral of the finger acting on the object is determined; Based on the spiral force exerted by the finger on the object, establish the spiral equilibrium condition.

3. The method according to claim 1, characterized in that, Step 1 involves obtaining the root mean square roughness and arithmetic mean roughness between the robotic hand finger and the object, calculating the fractal parameters of the contact profile, and obtaining the fractal parameters of the equivalent contact profile, including: The feature scale parameters of the contour are determined based on the root mean square roughness between the robotic arm's fingers and the object; the fractal dimension of the contour is determined based on the arithmetic mean roughness between the robotic arm's fingers and the object; satisfying the following expression: ； ； Where D represents the fractal dimension of the contour, G represents the feature scale parameter of the contour, Ra is the arithmetic mean roughness between the robotic hand finger and the object, and Rq is the root mean square roughness between the robotic hand finger and the object. The fractal parameters of the synthetic rough surface at the contact point between the robotic hand's finger and the object are constructed, including the fractal dimension and the characteristic scale parameters of the synthetic rough surface, satisfying the following expression: ； ； Where: D s Let G represent the fractal dimension of the synthesized rough surface, D1 represent the fractal dimension of the finger surface contour, D2 represent the fractal dimension of the grasped object surface contour, and G represent the fractal dimension of the grasped object surface contour. s G1 represents the feature scale parameter of the synthesized rough surface, G2 represents the feature scale parameter of the finger surface contour, and G2 represents the feature scale parameter of the grasped object surface contour. Construct the 2D contour height of the contact point between the robotic hand's finger and the object, satisfying the following expression: ； Where: z(x) represents the height of the two-dimensional profile, π represents pi, and n represents the frequency level. max Indicates the maximum frequency level, n min Minimum frequency level, γ is the spatial frequency of the profile, and x represents the sampling position of the horizontal coordinate of the two-dimensional profile. in: ； ； Where γ is the spatial frequency of the contour; L is the length of the acquired contour; and Δx is the distance between two adjacent sampling points. The feature scale parameter of the contour, the fractal dimension of the contour, the fractal dimension of the synthesized rough surface, the feature scale parameter of the synthesized rough surface, and the height of the two-dimensional contour are used as the fractal parameters of the equivalent contact contour.

4. The method according to claim 1, characterized in that, The pre-construction process of the superimposed micro-convexity model includes: Based on the contact parameters between the robotic hand's fingers and the object, construct the radius of curvature function and the height function; Based on the curvature radius function and the height function, a stacked micro-convex body model is obtained by a step-by-step stacking method; The radius of curvature function satisfies the following expression: ； Where: R I Let π represent the radius of curvature of the I-th layer micro-convexity, π represent pi, G represent the characteristic scale parameter of the profile, and n min Minimum frequency level, n represents the frequency level, I represents the level of the I-th micro-protrusion from bottom to top in the superimposed micro-protrusions, γ is the profile spatial frequency, and D represents the fractal dimension; The height function satisfies the following expression: ； In the above formula, Δ I This indicates the height of the I-th layer of micro-protrusions.

5. The method according to claim 1, characterized in that, The actual contact area satisfies the following expression: ； Among them, A r A represents the actual contact area. re A represents the contact area of ​​the elastically deformed micro-protrusion. rep1 Indicates the contact area of ​​the first elastoplastic micro-protrusion, A rep2 A represents the contact area of ​​the micro-protrusion that undergoes the second elastoplastic deformation. rp The contact area of ​​the micro-protrusion undergoing plastic deformation is represented by 'i', which represents the layer level of the micro-protrusion in contact with the rigid plane, and 'N' represents the total number of layers of stacked micro-protrusions, where N = n. max -n min +1, n max Indicates the maximum frequency level, n min Minimum frequency level, a iec a represents the critical contact area for elastic deformation of the i-th layer of micro-protrusions. iepc a represents the critical contact area for the first elastic-plastic deformation of the i-th layer of micro-protrusions. ipc Let n(a) represent the critical plastic deformation of the i-th layer of micro-protrusions, n(a) represent the area distribution function, and a represent the contact area of ​​the micro-protrusions. i+1,i a represents the contact area produced by the rigid plane passing through the intersection surface of the i+1 and i micro-protrusions in the superimposed micro-protrusions. i,i-1 a represents the contact area produced by the rigid plane passing through the intersection surface of the i-1 micro-protrusion layers in the superimposed micro-protrusions. Ii The contact area represents the maximum downward pressure when the micro-protrusions come into contact, and I represents the I-th layer of micro-protrusions from bottom to top; The normal contact load satisfies the following expression: ； Among them: F r F represents the normal contact load. re The normal contact load F of the elastically deformed micro-protrusion is represented by... rep1 F represents the normal contact load on the first elastoplastic micro-protrusion. rep2 F represents the normal contact load of the micro-protrusion undergoing the second elastoplastic deformation. rp f represents the normal contact load on the micro-protrusion undergoing plastic deformation. ie f represents the normal contact load of a single micro-protrusion during elastic deformation of the i-th layer of micro-protrusions. iep1 f represents the normal contact load of a single micro-protrusion during the first elastoplastic deformation of the i-th layer of micro-protrusions. iep2 f represents the normal contact load of a single micro-protrusion during the second elastoplastic deformation of the i-th layer of micro-protrusions. ip This represents the normal contact load of the i-th layer of micro-protrusions undergoing plastic deformation.

6. The method according to claim 1, characterized in that, The deformable tangential contact load satisfies the following expression: ； Among them: T r T represents the tangential contact load during deformation. re T represents the tangential contact load on the elastically deformed micro-protrusion. rep1 Let n(a) represent the tangential contact load of the micro-protrusion undergoing the first elastoplastic deformation, n(a) represent the area distribution function, N represent the total number of layers of superimposed micro-protrusions, a represent the contact area of ​​the micro-protrusions, and i represent the layer level of the micro-protrusion in contact with the rigid plane. iec a represents the critical contact area for elastic deformation. iepc a represents the critical contact area for the first elastic-plastic deformation of the i-th layer. ie a represents the contact area when the i-th layer of micro-protrusions undergoes elastic deformation. iepc1 f represents the contact area during the first elastic-plastic deformation of the i-th layer. ie f represents the normal contact load of a single micro-protrusion during elastic deformation of the i-th layer of micro-protrusions. iep1 σ represents the normal contact load of a single micro-protrusion during the first elastoplastic deformation of the i-th layer of micro-protrusions. s denoted by , v represents the yield strength of the softer material, I represents the I-th micro-protrusion from bottom to top in the stacked micro-protrusions, and π represents pi.

7. The method according to claim 1, characterized in that, The friction cone angle α satisfies the following expression: ； Where μ represents the friction coefficient of the rough surface; The included angle β of the inner normal vectors satisfies the following expression: ； Among them, f yej This represents the component of force along the y-tangential direction at the contact point of the j-th finger; f xej This represents the component of force along the x-tangential direction at the contact point of the j-th finger; f zej This represents the component of force along the z-direction at the contact point of the j-th finger; T r F represents the tangential contact load during deformation. r Indicates the normal contact load.

8. The method according to claim 5, characterized in that, The capture stability coefficient satisfies the following expression: ； Where, k j Let α represent the grasping stability coefficient during the grasping process of the j-th finger, α be the friction cone angle, and β be the angle between the inner normal vectors at the contact point.

9. The method according to claim 1, characterized in that, The crawling mapping matrix satisfies the following matrix expression: ； Among them, G j Let g represent the grasping mapping matrix of the j-th finger. j E represents the grasping Jacobian submatrix of the j-th finger. j The pose transformation matrix of the j-th finger, r zej r xej r yej Let φ be the position vector of the j-th finger's contact point in the object's coordinate system. j1 For x j y j Projection on the plane and x j The included angle of the axis, φ j2 For the inner normal vector n j With z j The included angle of the axis.

10. The method according to claim 2, characterized in that, The force spiral exerted by the finger on the object satisfies the following formula: ； Where F represents the force spiral applied by the finger in global coordinates, j represents the j-th finger, and m represents the number of grasping positions. zj F represents the force exerted by the j-th finger on the object in the global coordinate system. e This indicates the spiral force exerted by the finger on an object.

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