TWI775411B - Soft actuator, gripping jaws, method, computer program product and computer readable recording medium for designing such - Google Patents

Abstract

The invention provides soft actuator, gripping jaws, method, computer program product and computer readable recording medium for designing such. The method is to use the three-dimensional topology optimization based on solid isotropic material with penalization. The three-dimensional topology optimization involves an objective function comprising mutual potential energy to avoid discontinuity of the structure after topology optimization.

Description

Soft gripper and design method thereof, computer program product, computer readable recording medium

The present invention relates to a clamping tool, especially a soft clamping jaw and its design method, a computer program product, and a computer-readable recording medium.

Soft grippers are widely used because they can be applied to objects with different shapes and can reduce the probability of clamping damaged objects. Relevant cases include, for example, "Flexible Gripper and Its Design Method, Computer Program Product, and Computer-Readable Recording Media" of the Republic of China Invention Patent Publication No. I630499, which was approved by the present inventor.

Among the many different types of soft grippers on the market, the pneumatic soft gripper is the most widely used in the production line, mainly due to the high actuation speed, which can greatly increase the production line capacity. The structure is mainly composed of a plurality of soft actuators with a flange interface to form a jaw, and the air bag of the soft actuator can be inflated to push the jaw to bend and clamp the target object.

However, at present, the load weight of pneumatic grippers still has a lot of room for improvement compared with other types of soft grippers.

，其 中：K為包含輸入端及輸出端連接彈簧常數之全域剛性矩陣：K=K _s +

；U₁為僅輸入負載下之全域位移向量；U₂為僅輸出負載下之全域位移向量，

中的上標T為轉置矩陣之意，所述全域位移向量中的固定端位移設為0；K _s 為虛擬彈簧之剛性矩陣；K _e 為單一元素之剛性矩陣；Σ _e 為所有元素矩陣加總之意；

為經濾化後之元素密度，其下標i代表設計區間中第i個元素，其上標p為懲罰係數，x _i 為濾化前之元素密度，為介於0到1之間的連續正實數。 Therefore, in order to improve the practicability of soft actuators, the present inventor proposes a design method for soft actuators, including designing with a topology optimization method, and the objective function of the topology optimization method is: Mutual potential energy (MPE):

, where: K is the global stiffness matrix including the spring constants of the input and output connections: K = K _s +

; U ₁ is the global displacement vector under only the input load; U ₂ is the global displacement vector under only the output load,

The superscript T in is the meaning of the transposed matrix, and the fixed end displacement in the global displacement vector is set to 0; K _s is the rigidity matrix of the virtual spring; Ke is the rigidity matrix of a single element _; Σ _e is the matrix of all elements to sum up;

is the element density after filtering, the subscript i represents the ith element in the design interval, the superscript p is the penalty coefficient, and x _i is the element density before filtering, which is a continuous between 0 and 1 positive real number.

w _ij =max(0,r _min -r _ij )；其中，N _e,i 為第i個元素周遭濾化半徑內的元素集合；下標j則代表元素為N _e,i 中第j個元素；w _ij 為濾化權重函數；v _j 為元素的體積；r _min 為濾化半徑；r _ij 表示i元素與j元素間的中心距離。 Further, the topology optimization method is to update the design variables with an element density filtering algorithm, and the calculation formula of the element density filtering algorithm is as follows:

w _ij =max(0, r _min - r _ij ); where _Ne,i is the set of elements within the filtering radius around the i - th element; the subscript j represents the element is the j - th element in _Ne,i ; w _ij is the filtering weight function; v _j is the volume of the element; r _min is the filtering radius; r _ij is the center distance between the i element and the j element.

Further, the topology optimization method is to update the variables with the method of moving asymptotes (Method of Moving Asymptotes, MMA).

The design method of the above-mentioned soft actuator can be implemented as a program and stored in a computer program product or a computer-readable recording medium. After the computer loads the program and executes it, the design method of the soft actuator as described above can be completed.

The present invention is also a soft actuator, which is manufactured by using the above-mentioned design method of the soft actuator, and includes a clamping portion for clamping an object, and the clamping portion is provided with spacers along a length direction. a plurality of airbag parts, and a joint part is connected between each adjacent two airbag parts to form a curved surface opposite to the clamping part, the clamping part and each airbag part are connected with each other an inflatable channel.

The present invention is also a soft actuator, comprising a clamping surface for clamping an object, a curved surface opposite to the clamping surface, and two side surfaces connecting the clamping surface and the curved surface, the curved surface along the A plurality of airbag parts are arranged at intervals in the longitudinal direction, and a joint part is connected between each two adjacent airbags. The joint part has a raised part at the center, and the raised part tapers to both sides to form a trapezoid. .

The present invention is also a clamping jaw comprising a plurality of the aforementioned soft actuators mounted on a flange interface.

With the above features, the following effects can be mainly achieved:

1. The objective function of the topology optimization method adopts the interactive potential energy to avoid the discontinuous structure in the topology optimization result.

2. The topology optimization method adopts the element density filtering method to improve the convergence of topology optimization.

3. The variable update of the topology optimization method adopts the MMA method, and rewrites the original topology optimization problem into the general optimization formula of MMA to obtain a better objective function.

4. The actuator designed with the above topology optimization has good bending performance compared with the commercially available actuator, and the gripper made by this can effectively increase the load weight.

(1): Clamping part

(2): Airbag part

(3): Joints

(31): uplift part

(4): Curved surface

(5): Inflatable runner

(6): Fingertip structure

(100): Soft Actuator

(200): Flange interface

(300): Flange interface

(400): Flange interface

(S01): Step 1

(S02): Step 2

(S03): Step 3

(S04): Step 4

(S05): Step 5

FIG. 1 is a flow chart of topology optimization according to an embodiment of the present invention.

FIG. 2 is a schematic diagram of a design interval according to an embodiment of the present invention.

FIG. 3 is a schematic diagram of a filtering radius according to an embodiment of the present invention.

4A is a schematic diagram of a design interval of a flexible mechanism according to an embodiment of the present invention.

FIG. 4B is a schematic diagram of a superposition principle according to an embodiment of the present invention.

FIG. 5 is a schematic plan view of a soft actuator according to an embodiment of the present invention.

FIG. 6A is a schematic diagram of the boundary condition of a single output terminal in an embodiment of the present invention.

FIG. 6B is a schematic diagram of the boundary conditions of dual output terminals in an embodiment of the present invention.

FIG. 7 is a graph showing the influence of volume ratio on the average displacement of end nodes per unit length according to an embodiment of the present invention.

FIG. 8 is a schematic diagram of design parameters of an airbag according to an embodiment of the present invention.

FIG. 9 is a graph showing the influence of the size of the airbag on the average displacement of the end node according to the embodiment of the present invention.

FIG. 10 is a graph showing the influence of the airbag spacing on the average displacement of the end nodes per unit length according to an embodiment of the present invention.

11 is a graph showing the influence of the thickness of the airbag on the average displacement of the end node per unit length according to an embodiment of the present invention.

FIG. 12 is a schematic three-dimensional appearance diagram of a soft actuator according to an embodiment of the present invention.

FIG. 13 is a schematic side sectional view of the soft actuator according to the embodiment of the present invention.

FIG. 14 is a partial three-dimensional cross-sectional schematic diagram of the soft actuator according to the embodiment of the present invention.

FIG. 15 is a schematic cross-sectional front view of a soft actuator according to an embodiment of the present invention.

FIG. 16 is a comparison diagram of the track of the gripper jaws of the embodiment of the present invention and the commercially available gripper.

FIG. 17 is a comparison diagram of the bending curvature of an embodiment of the present invention and a commercially available actuator.

FIG. 18 is a comparison diagram of the bending angle between the embodiment of the present invention and a commercially available actuator.

19 is a schematic three-dimensional appearance diagram of a two-finger gripper according to an embodiment of the present invention.

FIG. 20 is a graph showing the relationship between the input pressure and the maximum load of the two-finger gripper according to the embodiment of the present invention.

FIG. 21 is a schematic three-dimensional appearance diagram of a three-finger gripper according to an embodiment of the present invention.

Fig. 22 is a graph showing the relationship between the input pressure and the maximum load of the three-finger gripper according to the embodiment of the present invention

FIG. 23 is a schematic three-dimensional appearance diagram of a four-finger gripper according to an embodiment of the present invention.

In view of the above technical features, the main functions of the soft gripper and the design method thereof, the computer program product, and the computer-readable recording medium of the present invention can be clearly presented in the following embodiments with drawings. It should be noted that, for ease of understanding, in each figure, similar or identical reference numerals will be used for similar functional elements.

The design method of the soft actuator according to the embodiment of the present invention can be implemented as a program and stored in a computer program product or a computer-readable recording medium. After the computer loads the program and executes it, the design method of the soft actuator as described above can be completed.

The design method of the soft actuator includes designing with a topology optimization method, and the topology optimization is mainly based on the SIMP method (Solid Isotropic Material with Penalization), which has better computing Speed and mesh-free dependence, suitable for flexible mechanism design. In order to avoid the structural disconnection between the input end and the output end, in this embodiment, the objective function is maximized by mutual potential energy (MPE), and the design interval is decomposed into loads with only input power and only output power Then, the objective function is calculated according to the superposition principle, and the MMA method is used to update the design variables [Method of Moving Asymptotes (MMA)].

The following will introduce the process and theory of 3D topology optimization in sequence, including design interval, design variables, finite element analysis, filtering algorithm, MMA theory, convergence criterion, objective function and element sensitivity.

Please refer to FIG. 1 first, which discloses the flow of the topology optimization method in this embodiment, which is based on the SIMP method. A singular rigid matrix is generated when computing finite elements, and the topology optimization method includes:

Step 1 (S01): Define the design interval, boundary conditions, design parameters and initial values.

Step 2 ( S02 ): using the filtering algorithm to update the design variables, establishing a finite element model with the updated design variables and boundary conditions, and then performing finite element analysis.

Step 3 (S03): Calculate the objective function and the element sensitivity with the displacement obtained by the finite element method.

Step 4 (S04): Update the design variables by the MMA method.

Step 5 (S05): determine whether to converge, if the convergence condition is not met, go back to step 2 (S02) to continue execution, and if the convergence condition is met, end topology optimization.

The design interval, boundary conditions, and finite element analysis are described in further detail below:

In this embodiment, a three-dimensional topology optimization method is used to design its external structure. Taking the design interval of a cuboid as an example, the design interval is discretely divided into multiple cube elements, and the length, width and height of each element are the same. As shown in Figure 2, the element amount in the X direction in the design interval is nelx, and the element amount in the Y direction is nely, and the element amount in the Z direction is nelz. Each cube element has its independent element density ( x _i ), the element density is the optimized design variable, and its subscript i represents the i-th element in the design interval. The element density represents the presence or absence of the element, and all element densities are continuous positive real numbers between 0 and 1. When the element density is 1, it means that the element is a solid element and needs to be retained; when the element density is 0, it means that the element is a hollow element and needs to be removed. In the improved SIMP method, it is assumed that the design variable of each element has a linear relationship with the Young's coefficient ( E _i ), and the Young's coefficient has a linear relationship with the value of the stiffness matrix ( ki ₎ , and the relationship is as follows:

Formula (2-2): k _i = E _i k ₀

為經濾化後之元素密度；p為懲罰係數；k為元素剛性矩陣；k ₀為楊氏係數代入1之元素剛性矩陣。懲罰係數可以使設計變數更趨近於極值，可將其數值定義為3，透過此方法可以大幅減少程式運算達到收斂的時間。當

時，拓樸結果為黑色，代表該元素之楊氏係數為E ₀。當

時，拓樸結果為白色，代表 該元素之楊氏係數為0，在實際數值上則代入極小值E _min ，以避免拓樸運算時產生奇異之剛性矩陣而使結果無法收斂。當

介於0到1之間時，因其拓樸結果呈現灰色而稱之為灰階元素，此元素可提升收斂之穩定性但不具有實際上之物理意義，故使用上常以懲罰係數或投射方法使拓樸之元素密度趨向二值化。 Among them, E ₀ is the Young's coefficient of the material; E _min is a positive number approaching 0;

is the element density after filtering; p is the penalty coefficient; k is the element rigidity matrix; k ₀ is the element rigidity matrix with the Young's coefficient substituted into 1. Penalty coefficient can make the design variable more close to the extreme value, and its value can be defined as 3. Through this method, the time for the program operation to reach convergence can be greatly reduced. when

When , the topological result is black, representing that the Young's coefficient of the element is E ₀ . when

When , the topology result is white, which means that the Young's coefficient of the element is 0, and the minimum value E _min is substituted in the actual value to avoid generating a singular rigid matrix during the topology operation and the result cannot be converged. when

When it is between 0 and 1, it is called a gray-scale element because its topology result is gray. This element can improve the stability of convergence but has no actual physical meaning, so it is often used with penalty coefficient or projection. The method makes the element density of topology tend to be binarized.

In this embodiment, static finite element analysis is used, and boundary conditions (including fixed end, input force and output force) are given in the set design interval, the displacement of each element node is obtained according to Hooke's law, and then the target is calculated according to the displacement result. Function ( f ) and element sensitivity ( α _i ), the relationship is as follows: Formula (2-3): KU=F

Among them, K is the global rigidity matrix, U is the global displacement vector, and F is the global force vector.

式(2-6)：w _ij =max(0,r _min -r _ij )；其中，N _e,i 為第i個元素周遭濾化半徑內的元素集合；下標j則代表元素為N _e,i 中第j個元素；w _ij 為濾化權重函數；v _j 為元素的體積；r _min 為濾化半徑；r _ij 表示i元素與j元素間的中心距離。 Filtering algorithm: The element density filtering algorithm used in this embodiment solves the problem of checkerboard grids and grid dependencies. The calculation formula of the element density filtering algorithm is as follows:

Formula (2-6): w _ij =max(0, r _min - r _ij ); among them, _Ne,i is the set of elements within the filtering radius around the _i - th element; the subscript j represents that the element is Ne _{, the jth element in i} ; w _ij is the filtering weight function; v _j is the volume of the element; r _min is the filtering radius; r _ij represents the center distance between the i element and the j element.

The concept of the element density filtering algorithm is shown in Figure 3. The black circle on the central element is used as the center, and the elements within the radius of r _min are regarded as surrounding elements. Calculate its linear weight according to the distance between each surrounding element and the central element. The closer the element within the radius is to the central element, the greater the weight, and vice versa, the smaller the weight, while the weight outside the radius is 0. to obtain the elemental density after filtering.

Method of Moving Asymptotes (MMA), hereinafter referred to as MMA method: MMA method belongs to a non-linear programming method of structural optimization, which can be applied to deal with multiple variables and multiple constraints The general optimization method of the conditions, this embodiment uses the MMA method to update the variables, which helps to obtain better convergence results when facing the problem of large displacement deformation. The general formula of the optimization problem is as follows:

0、c _i

0、d _i

0且c _i +d _i >0，當a _i >0時a _i c _i >a ₀；x _j 是設計變數；y _i 及z是人工變數(Artificial variable)；而

與

為設計變數x _j 的上下界限。 Among them, f ₀ is the original objective function; f ₁ ,..., f _m is a restriction formula and f ₀ , f ₁ ... ,f _m is a continuous differentiable function; a ₀ , a _i , c _i and d _i is a given constant, must satisfy a ₀ , a _i

0. c _i

0. d _i

0 and c _i + d _i >0, a _i c _i > a 0 when a _i >₀; x _j are design variables; y _i and z are artificial variables; and

and

are the upper and lower bounds of the design variable x _j .

The solution flow of the MMA method is as follows:

Step 1: Set the MMA parameters, give an initial value x ⁽⁰⁾ , and assume the initial number of iterations iter=0.

。 Step 2: Calculate f _i ( x ^iter ) and gradient value ▽ f _i ( x ^iter ) with the iterative point x ^iter , and then convert the function f _i into a convex function approximation to generate an approximate function

.

產生一個子問題P^iter取代初始最佳化問題P，並以對偶法求解子問題。 Step 3: Approximate the function with

A subproblem P ^iter is generated to replace the initial optimization problem P, and the subproblem is solved by the dual method.

Step 4: Take the best solution of the sub-problem P ^iter as the next iteration point x ^{( iter +1)} , and set iter=iter+1. Among them, the sub-problem of the MMA initial optimization problem is as follows:

及

分別為下移動限制及上移動限制。 in,

and

They are the lower movement limit and the upper movement limit, respectively.

如下：

Among them, the approximate function in formula (2-8)

as follows:

in,

in,

及

計算方式如下：

upper movement restriction

and

It is calculated as follows:

為下漸進線(Lower asymptotes)，

為上漸進線(Upper asymptotes)。 in,

is the lower asymptotes,

For the upper asymptotes (Upper asymptotes).

When iter=1 and iter=2,

3時，

when iter

3 o'clock,

為移動漸進線之調整參數，

in,

is the adjustment parameter for the moving asymptote,

In order to solve the topology optimization of the soft actuator by the MMA method, in this embodiment, the optimization problem is transformed into the general problem of MMA, and the general formula is as the aforementioned formula (2-8). In order to make the general formula of MMA equivalent to the original formula, the parameters are substituted into the general formula of MMA according to the settings in Table 1. In addition, in this embodiment, some parameters in the original MMA sub-problem are modified, and the modified parameters are shown in Table 2.

Convergence criterion:

The general convergence criterion is whether the difference between the target value of the current iteration and the target value of the previous iteration is less than the set tolerance error. Generation update process. This embodiment adopts the same criterion in the objective function value part, and its calculation method is shown in the following formula (2-22), dividing the difference between the objective function of the current iteration and the previous iteration by the objective function value of the previous iteration to obtain the percentage of difference, This improves the convergence stability.

Wherein, cn and cn _{-1 are} the current objective function and the previous objective function, err is the objective function tolerance error, and in this embodiment, the objective function tolerance error err is set to 0.0001.

For the volume rate part, the difference between the current iteration volume rate and the target volume rate is used. process.

為當次疊代之元素密度，

為目標體積率，voltol為體積率容忍誤差，本實施例將體積率容忍誤差設定為0.001。 in,

is the element density of the current iteration,

is the target volume rate, and voltol is the volume rate tolerance error. In this embodiment, the volume rate tolerance error is set to 0.001.

Objective function:

The initial design interval for topology optimization of the flexible mechanism is shown in Figure 4A. The left side is the input end with the input force F _in , and its force can be divided into two direction components, F _{in, x} and F _{in, y} . The end and the design interval have a connecting spring kin , which can be divided into two directional components _kin,x and _{kin ,y} . The bottom is the fixed end, and the right side is the output end with the output force F _out . The force can be divided into two directions: F _{out, x} and F _{out, y} . There is a connecting spring k _out at the output end and the design interval, which can be divided into two directions. are two direction components of k _{out, x} and k _{out, y} .

The objective function adopted in this embodiment is mutual potential energy (MPE), which is used to describe the flexibility of the structure under the action of two external forces. Flexible mechanisms are often designed to transmit force or displacement by applying force to one end, and the mechanism deforms to cause force or displacement at the other end. In order to carry out the topological analysis, the end that exerts the force is defined as the input end, and the end that generates the force or displacement is defined as the output end, and the input and output forces are applied to the two external forces of the interaction potential energy, and according to the principle of superposition (Principle of superposition) disassembles the original design interval into two boundary conditions of only input force and only output force, as shown in Figure 4B.

Because the boundary conditions are disassembled into two different design intervals, the finite element analysis of the two boundary conditions is carried out to obtain the displacement results, and the following two sets of static equilibrium equations are obtained according to Hooke's law:

Among them, K is the global stiffness matrix including the spring constants of the input and output connections, as shown in Equation (2-25).

其中U₁及F₁分別為僅輸入負載下之全域位移向量及全域力量向量；U₂及F₂為僅輸出負載下之全域位移向量及全域力量向量，而所述全域位移向量中的固定端位移設為0；K _s 為虛擬彈簧之剛性矩陣；K _e 為單一元素之剛性矩陣；Σ _e 為所有元素矩陣加總之意；

為經濾化後之元素密度，其下標i代表設計區間中第i個元素，其上標p為懲罰係數，x _i為濾化前之元素密度，為介於0到1之間的連續正實數。

Wherein U ₁ and F ₁ are the global displacement vector and the global force vector under only the input load, respectively; U ₂ and F ₂ are the global displacement vector and the global force vector under only the output load, and the fixed end of the global displacement vector The displacement is set to 0; K _s is the rigidity matrix of the virtual spring; Ke is the rigidity matrix of a single element _; Σ _e is the sum of all element matrices;

is the element density after filtering, the subscript i represents the ith element in the design interval, the superscript p is the penalty coefficient, and x _i is the element density before filtering, which is a continuous between 0 and 1 positive real number.

The two global displacement vectors obtained are calculated according to formula, and the objective function of interaction potential energy (MPE) can be obtained as formula (2-26).

中的上標T為轉置矩陣之意。在本實施例中，以負值之交互位能最小化為目標。 in,

The superscript T in it means to transpose the matrix. In this embodiment, the goal is to minimize the interaction potential energy of negative values.

Elemental Sensitivity:

Element sensitivity is a judgment index for the degree of influence of a design variable as a single element on the objective function, which is defined as the partial differential of the objective function to the design variable, which is derived as follows (2-27).

，重新整理上式可得下列式(2-28)。 Because K is a symmetric matrix, according to the commutative law of matrix multiplication, we can get:

, rearrange the above formula to get the following formula (2-28).

In order to replace the partial differential of the global displacement vector to the design variables in the above formula, formula (2-24) is partially differentiated to the design variables, and the result is shown in the following formula (2-29), where the global force vector is constant, so after the partial differentiation is 0:

In order to substitute into Equation (2-28), Equation (2-29) can be obtained by shifting the terms and finishing Equation (2-30).

Substitute the above formula (2-30) into the formula (2-28) to obtain the formula (2-31).

Rewrite global element sensitivity to single element sensitivity:

Among them, u _1,j and u _2,j are the displacement vectors of a single element, and k _j is the rigidity matrix of all nodes on a single element. Substitute equations (2-1) and (2-2) for the partial differential of the rigid matrix to the design variables in equation (2-32):

Substitute equation (2-33) back into equation (2-32) to obtain the partial differential of the interaction potential energy with respect to the design variables:

In order to design the soft actuator knuckle by further applying the boundary conditions of the actuator to the flow of the above topology optimization method, the following will introduce the setting of the boundary conditions applicable to the actuator in sequence.

"Silicone material model": In this example, Dragon skin 30 silicone from Smooth-on Company is used as the material for making the pneumatic soft gripper. Its material hardness is 30A. The tensile strength is 3.87MPa and the elongation at break is 353. %. In this example, the assumption of a linear elastic material model is used to carry out topology optimization design, no-load simulation and clamping simulation. The equivalent density is about 1096kg/m ³ , and the Poisson's ratio is 0.49.

"Boundary condition setting of actuator knuckle structure":

In this embodiment, the actuator is defined as a knuckle-like structure with airbags, and three airbag knuckles with the maximum bending ability are designed through the above topology optimization method, and then the knuckle structures are linearly arranged to form a complete actuator . In order to compare the bending capacity and load weight with the commercially available Meristic Adjustable Gripper-SFG-FMA2 series pneumatic soft gripper from SRT Company, the actuator is designed with reference to the size of the gripper finger (length 86×width 50×height 26mm) , take one end as the fixed end and the other end as the output end. The fixed end is provided with an air pressure input hole and is connected to the air bag with a communication hole. The air bag is inflated to push the jaws to bend to achieve the function of gripping the target, as shown in Figure 5.

In this embodiment, the design interval is modified from a complete actuator to a knuckle with three airbags, and then the knuckle structures are linearly arranged and combined to form a complete actuator. The length of the knuckles is determined by the linear arrangement of the three airbags. The actual length is 16~28mm. The width and height are set to 50mm and 26mm according to the size of the commercially available SRT jaws. The airbags are arranged at equal intervals in the x direction, and the y direction is away from the bottom. 2mm, the outer layer is the solid non-design domain (Solid non-design domain), the thickness is 1~2mm, and the inner layer is the void non-design domain (Void non-design domain).

(nelz為設計區間z方向元素量)處平面加入z方向之自由度拘束，避免拓樸最佳化結果產生不對稱結構。 In addition to the above boundary conditions, because this embodiment adopts a three-dimensional topology optimization method to design the actuator, compared with the two-dimensional topology optimization design, the degree of freedom in the z-direction must be considered again, and when the gripper actually grips the object The clamping surface will not produce relative displacement in the z direction, so the

(nelz is the element quantity in the z-direction of the design interval), a degree of freedom constraint in the z-direction is added to the plane to avoid an asymmetric structure in the topology optimization result.

There are two kinds of "boundary condition settings", please refer to Figure 6A and Figure 6B:

The first one defines the objective function as formula (3-1), there are only two forces of f _in and f _out , and U ₁ is the global displacement vector obtained under the action of f _in , and U ₂ is obtained under the action of f _out the global displacement vector.

The second type of objective function is defined as formula (3-3), there are three forces _fin , f _out,1 and f _out,2 , and U ₁ is the global displacement vector obtained under the action of f _in , U ₂ is the global displacement vector obtained under the simultaneous action of f _out,1 and f _out,2 , both of which are maximized by the interaction potential energy (MPE) instead of displacement, and the goal is to minimize the negative interaction potential energy.

Here, the indexes of the bending ability of the soft actuator are defined as the average displacement of the end nodes and the average displacement of the end nodes per unit length. The former applies to the case where the size of the design interval is the same, and the latter applies to the case where the size of the design interval is different. When the length of the design interval in the x-direction is different, it must be divided by the length in the x-direction (nelx). The x-direction length under the single-output boundary condition can be defined as 28mm, which is the same as the full length of the design interval, and the average displacement of 51 nodes at the output end is calculated for the displacement change, as shown in Figure 6A; under the dual-output boundary condition, the The length in the x-direction is defined as half of the full length of the design interval, 14 mm, and the displacement change is calculated by calculating the average displacement of 102 nodes at the two output ends, as shown in Figure 6B.

The topology optimization design parameters of the above two boundary conditions are all set with the same settings, as shown in Table 3 below. The design interval is 28mm long x 50mm wide x 26mm high, consisting of a cube grid with a side length of 1mm; each node on the pressure surface of the inner wall of the airbag is given an input of the same size and a direction perpendicular to the pressure surface In the same way, the output end is given an output force with the same magnitude and the direction perpendicular to the pressure surface; each node on the input end and the output end is given an output force with the same spring constant and the direction perpendicular to the pressure surface The virtual spring, in which the sum of the spring constants of the input end and the sum of the spring constants of the output end are both set to 1N/m; the target volume rate is set according to Table 3, and the allowable error of the volume rate is set to ±0.001.

Table 4 shows the topologically optimized displacement results for the boundary conditions of the single-output terminal and the dual-output terminal. The displacement of the output terminal decreases with the increase of the volume rate, that is, the displacement change increases with the increase of the volume rate. As shown in Figure 7. When the volume ratio is 0.6, the average displacement of the end nodes per unit length of the double-output boundary is 0.5 mm, and the single-output boundary is 0.25 mm, and the difference between the two is 100%. In addition to the average displacement of the end nodes per unit length, considering the feasibility of manufacturing, the boundary conditions of the single output end are not concentrated on the same side of the communication structure between the airbags. The way is to use the design of double-outlet boundary conditions.

By observing Fig. 7, it can be seen that no matter in the boundary condition of single output terminal or double output terminal and the volume rate is lower than 0.6, the average displacement of the end node per unit length will increase with the increase of the volume rate. When the volume rate When it is close to 0.6 and above 0.6, it will tend to be stable, and the shape of the topology-optimized structure will gradually stabilize with the increase of the volume ratio. Therefore, in this embodiment, the target volume ratio of the topology-optimized design is defined as 0.6 or more.

"External spring design": In order to obtain a better objective function and fewer iterations of topology optimization, this embodiment defines the sum of the spring constants at the input end as 1N/m and the sum of the spring constants at the output end as 1N/m.

"Airbag parameter design": The airbag is defined as the non-design interval of topology optimization. Thickness) and spacing (Spacing) to optimize the topology of the airbag knuckles. The design parameters of the airbag are shown in Figure 8, and the design parameters of the airbag are set as shown in Table 5. The topology optimization parameters are set as described above. shown in Table 3.

The comparison index of the bending capacity of the soft actuator is defined as the average displacement of the end nodes at the output end. Figure 9 shows that the average displacement of the end nodes is proportional to the height and width of the airbag. When the airbag height increases by 1mm, the average displacement of the end nodes increases by 35.9%; when the airbag width increases by 1mm, the average displacement of the end nodes increases by 35.9%. will increase by 15.4%, so the airbag height has a higher influence on the displacement. In order to achieve the best degree of bending and avoid voids Structure, in this embodiment, the height and width of the airbag are defined as 24mm and 50mm, and the airbag spacing is analyzed with these settings.

The airbag spacing will change the x-direction length (nelx) of the design interval, so the comparison index is defined as the average displacement of the end nodes per unit length. The results are shown in Figure 10. The average displacement of the end nodes per unit length is negatively correlated with the airbag spacing. When the airbag spacing increases by 1mm, the average displacement of the end nodes per unit length will decrease by 9.3%.

When the thickness of the airbag increases, the pressure resistance of the soft actuator will increase, and the bending ability of the soft actuator will decrease due to the increase of the rigidity of the airbag. In this embodiment, the thickness of the airbag is respectively set to 1mm, 2mm, and 3mm for topology optimization design, and then the most suitable conditions are selected according to the result of the average displacement per unit length and the degree of pressure resistance.

As shown in Figure 11. When the thickness of the airbag increases from 1mm to 2mm, the average displacement of the end nodes per unit length decreases from 1.3mm to 0.6mm, a decrease of about 56%; when the thickness of the airbag increases from 1mm to 3mm, the average displacement of the end nodes per unit length decreases from 1.3mm to 0.6mm. 1.3mm dropped to 0.3mm, a reduction of about 76%. In order to make the pressure resistance level above 60kPa and maintain a high bending ability, the thickness of the airbag is set to 2mm in this embodiment.

Please refer to FIG. 12 and FIG. 13 . Further description will be given below. The soft actuator of the embodiment of the present invention formed according to the above topology optimization and condition setting mainly includes a clamping portion ( 1), a plurality of airbag parts (2) are arranged at intervals along a length direction on the clamping part (1), and a joint part (3) is connected between every two adjacent airbags (2), so as to A curved surface (4) relative to the clamping part (1) is formed, wherein the maximum width of the airbag part (2) in the longitudinal direction is approximately twice that of the joint part (3). In addition, the clamping part (1) and each of the airbag parts (2) have an inflation flow channel (5) communicating with each other, and the inflation flow channel (5) is in the shape of a circular tube and its diameter is along the length direction Tapered extension.

In detail, the knuckle structures of the above design are arranged in parallel to the maximum number of airbags allowed by the length of the commercially available pneumatic gripper (86mm); then the knuckle structures near the front end are extended to the front end. stretch to form a triangular column-shaped fingertip structure (6); finally, in order to increase the rigidity of the lower part of the soft actuator during clamping to improve the load capacity, the clamping part (1) is thickened and a 4mm solid structure is added. .

14 and 15, the joint portion (3) has a raised portion (31) at the center, the raised portion (31), the raised portion (31) is tapered to both sides and is approximately a trapezoid. The height of the raised portion (31) is about half of the height of the airbag portion (2).

In the following, the designed soft actuator is further fabricated with silicone rubber, and the bending ability of the soft actuator designed by the above topology optimization design method is confirmed and compared with the performance of the commercially available SRT gripper.

In order to compare the bending ability of the soft actuator of this embodiment and the commercially available SRT jaws, the soft actuator of this embodiment was set on a test platform. Use the air compressor as the pressure input source, connect the pressure regulating valve and the air pressure gauge with the air conduit, and introduce the air pressure into the soft actuator. Then fix the soft actuator with the fixed end facing up and the output end facing down, input the air pressure from the fixed end, the pressure starts from 0kPa, increases by 10kPa each time, and records the bending change, according to the experimental results into ImageJ and Draw its gripping surface track. In addition, the commercially available SRT gripper was tested in the same way and its gripping surface trajectory was drawn, and the comparison chart between the two is shown in Figure 16.

It can be seen from FIG. 16 that when the pressure of the soft actuator of this embodiment is 20 kPa, the bending curvature and the bending angle of the fingertip point have reached the performance of the commercially available soft actuator under the pressure of 80-90 kPa; Under the maximum allowable pressure of 100 kPa, the bending amplitude of the actuator is still far lower than that of the soft actuator of this embodiment under 30 kPa. From the above results, it can be shown that the bending ability of the soft actuator of the present embodiment is obviously better than that of the commercially available ones.

The average bending curvature and bending angle of the clamping surface of commercially available SRT actuators are shown in Figures 17 and 18. Within the pressure range of 0~60kPa, the average bending curvature of the soft actuator of this embodiment is better than The commercial soft actuator is more than 112%, and the bending angle is more than 150% better than the commercial soft actuator, and its effect is very obvious.

In order to test the actual gripping ability of the soft actuator of this embodiment, two soft actuators (100) of this embodiment are composed of a flange interface (200) to form a clamping jaw, as shown in FIG. 19, through the clamp The jaws were tested for maximum load and range of grip and compared to commercially available SRT two-finger grippers.

The experimental result record is shown in Figure 20. The input pressure is positively correlated with the maximum load weight. When the maximum input pressure is 80kPa, the maximum load weight of the gripper is 2665g, which is compared with the maximum load of the commercially available SRT gripper under the same pressure. 1590g, its maximum load weight is 67.6% higher, while the average load weight is 43.82% higher.

In the following, three soft actuators (100) of the present embodiment are further composed of a clamping jaw with a flange interface (300), as shown in FIG. 21 . The gripper jaw maximum load test and gripping range test were performed through the gripper jaw and compared with the commercially available three-finger gripper.

The experimental result record is shown in Figure 22. The input pressure is positively correlated with the maximum load weight. When the maximum input pressure is 80kPa, the maximum load weight of the gripper is 5117g, which is compared with the maximum load of the commercially available SRT gripper under the same pressure. At 2217g, its maximum load weight is 131% higher and its average load weight is 140% higher.

It should be added that although the above-mentioned clamping jaws take the combination of two or three soft actuators (100) as an example, the implementation is not limited to this. As shown in FIG. 23, more than four The soft actuator (100) of this embodiment forms a clamping jaw with a flange interface (400).

It should be noted that the above content is only a preferred embodiment of the present invention, and the purpose is to enable those with ordinary knowledge in the field to understand the present invention and implement it accordingly, and not to limit the scope of the application for patent of the present invention; therefore, it relates to the present invention All equivalent changes or modifications are covered by the scope of the patent application.

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Claims (8)

A design method of a soft actuator includes designing with a topology optimization method, and the objective function of the topology optimization method is mutual potential energy (MPE):

, where: K is the global stiffness matrix including the spring constants of the input and output connections:

; U ₁ is the global displacement vector under only the input load; U ₂ is the global displacement vector under only the output load,

The superscript T in is the meaning of the transposed matrix, and the fixed end displacement in the global displacement vector is set to 0; K _s is the rigidity matrix of the virtual spring; Ke is the rigidity matrix of a single element _; Σ _e is the matrix of all elements to sum up;

is the element density after filtering, the subscript i represents the ith element in the design interval, the superscript p is the penalty coefficient, and x _i is the element density before filtering, which is a continuous between 0 and 1 positive real number. The design method for a soft actuator according to claim 1, wherein the topology optimization method is to update the design variables with an element density filtering algorithm, and the calculation formula of the element density filtering algorithm is as follows:

w _ij =max(0, r min - r _ij ); among them, _{Ne,i is} the set of elements within the filtering radius around the i - th element; the subscript j represents the element is the j - th element in _Ne,i element; w _ij is the filtering weight function; v _j is the volume of the element; r _min is the filtering radius; r _ij represents the center distance between the i element and the j element. The design method of a soft actuator according to claim 2, wherein the topology optimization method is to update the variables by a method of moving asymptotes (Method of Moving Asymptotes, MMA). A soft actuator is manufactured by using the design method of the soft actuator according to any one of claim 1 to claim 3, comprising a gripping portion for gripping an object, and the gripping portion is provided with a gripping portion. A plurality of airbag parts are arranged at intervals along a length direction, and a joint part is connected between every two adjacent airbags to form a curved surface opposite to the clamping part. Each of the airbag parts has an inflatable flow channel which is communicated with each other, and the inflation flow channel is in the shape of a circular tube and the diameter of the inflatable flow channel is tapered and extended along the length direction. A soft actuator, comprising a clamping portion for clamping an object, the clamping portion has a clamping surface, a curved surface opposite to the clamping surface, and two side surfaces connecting the clamping surface and the curved surface , the curved surface is provided with a plurality of airbag parts at intervals along a length direction, a joint part is connected between each two adjacent airbags, the joint part has a raised part in the center, and the raised part tapers to both sides It is generally a trapezoid, wherein the maximum width of the airbag portion in the longitudinal direction is about twice that of the joint portion, and the height of the raised portion is about half of the height of the airbag portion, The clamping portion and each of the airbag portions have an inflatable flow channel communicated with each other, and the inflation flow channel is in the shape of a circular tube and the diameter of the inflatable flow channel is tapered and extended along the length direction. A clamping jaw, comprising a plurality of soft actuators as described in any one of claim 4 to claim 5, mounted on a flange interface. A computer program product, which stores a program, when the computer loads the program and executes the program, it can complete the design method of the soft actuator as described in any one of the first to third claims. A computer-readable recording medium stores a program, and when the computer loads the program and executes the program, the design method of the soft actuator described in any one of the first to third claims can be completed.

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