An optimization design method for fiber-reinforced soft bending actuator

Abstract

The present invention discloses an optimization design method for a fiber-reinforced soft bending actuator, which belongs to the field of soft robots and aims to solve the time-consuming and labor-intensive problems existing in the simulation and design of fiber-reinforced soft bending actuators. According to the structural parameters of the initialized soft fiber-reinforced bending actuator and the given bending angle, the bending moment of the input pressure to the equilibrium point on the free-end sealing cap, the bending moment of the actuator body to the equilibrium point, and the bending moment of the actuator skin to the equilibrium point are calculated. Then, the relationship between the input pressure and the initial structural parameters of the actuator is obtained from the bending moment balance condition, and the actuator structural parameters corresponding to the bending angle conditions of the actuator in a given equilibrium state are obtained with minimizing the input pressure as the optimization goal. The present invention can realize the posture speed tracking, positioning, and optimization of the soft fiber-reinforced soft bending actuator in a free state when pressurized, and can solve the time-consuming and labor-intensive problems existing in traditional design methods.

Description

Technical Field

[0001] The present invention relates to the field of soft robots, and in particular to the field of soft actuators, and specifically to an optimization design method for a fiber-reinforced soft bending actuator, which can realize the analysis and structural optimization of the fiber-reinforced soft bending actuator in a free state. Background Art

[0002] Soft actuators are a rapidly developing research field that integrates materials chemistry technologies. Soft actuators offer low-cost manufacturing, strong environmental adaptability, and the ability to generate full-degree-of-freedom motion. They are well-suited for gripping and manipulating delicate, fragile, and soft objects, such as fruits and vegetables. In recent years, soft actuators have been designed to replace manual labor in applications such as fruit and vegetable harvesting, marine debris collection, and healthcare. Fiber-reinforced soft bending actuators, a key branch of soft actuators, have been widely used in fruit and vegetable harvesting and wearable medical devices due to their strong bending capacity and minimal radial expansion. However, the design of these fiber-reinforced soft bending actuators is often empirical or poorly considered, resulting in time-consuming and labor-intensive design methods, which severely hinders their rapid development. Furthermore, the optimization of fiber-reinforced soft bending actuators often relies on simple proportional relationships, and mature optimization algorithms are still lacking. Therefore, proposing an optimization design algorithm for fiber-reinforced soft bending actuators is of great research significance for guiding and optimizing the design of fiber-reinforced soft bending actuators.

[0003] Common optimization methods for fiber-reinforced flexible bending actuators include the moment balance method and the virtual work balance method. However, both require the construction of a fiber-reinforced flexible bending actuator for calibration, resulting in material parameters that differ significantly from the actual material parameters. Finite element analysis can yield relatively accurate results, but this method is time-consuming and labor-intensive. Common optimization algorithms rely on empirically established proportional relationships between structural parameters to optimize fiber-reinforced flexible bending actuators. However, this method is often not universally applicable and is closely related to the properties of the flexible material used.

[0004] All these have brought great difficulties to the optimization design of fiber-reinforced soft bending actuators. Therefore, there is an urgent need for an optimization design method for fiber-reinforced soft bending actuators that does not require physical calibration, is universal, comprehensive, and has low time cost. Summary of the Invention

[0005] To address the limitations of the aforementioned fiber-reinforced flexible bending actuator design methods, the present invention provides a method for optimizing the design of fiber-reinforced flexible bending actuators in a free state. This fiber-reinforced flexible bending actuator optimization algorithm eliminates the influence of soft material properties on the optimization design. It eliminates the need for physical calibration, is universal and comprehensive, and reduces time and labor costs.

[0006] To achieve the above solution, the present invention is implemented using the following technical solutions:

[0007] An optimization design method for a fiber-reinforced soft bending actuator comprises the following steps:

[0008] 1) Initialize the structural parameters of the fiber-reinforced soft bending actuator, including actuator length L, actuator body cavity radius a, actuator body rectangular wall thickness b1, actuator skin rectangular wall thickness b2, actuator body semicircular ring wall thickness t1, actuator skin semicircular ring wall thickness t2, actuator sealing cap length l c and the bending angle θ of the actuator in a given equilibrium state;

[0009] 2) Combined with the initial structural parameters and the selected material model, the input pressure P is calculated under the given bending angle θ of the actuator in the equilibrium state. in Bending moment M on the balance point O on the sealing cap at the free end of the actuator a , the bending moment of the actuator body to the balance point O on the sealing cap at the free end of the actuator The bending moment of the actuator outer skin to the balance point O on the sealing cap at the free end of the actuator

[0010] 3) According to the moment equilibrium condition, the input pressure P is obtained under a given equilibrium state. in The relationship between the actuator structure parameters P in =f(L,a,b1,b2,t1,t2,l c );

[0011] 4) Using the relation P in =f(L,a,b1,b2,t1,t2,l c ) is the target optimization function, and the structural parameters of the actuator are optimized by combining the multi-objective optimization algorithm so that the input pressure P under the bending angle θ of the actuator in a given equilibrium state is in Reach minimum.

[0012] Furthermore, the proposed optimization design method is applicable to but not limited to Arruda-Boyce, Mooney-Rivlin, Neo-Hookean, Ogden, and Yeoh material models.

[0013] Furthermore, the fiber-reinforced soft bending actuator includes a fiber reinforcement layer, an actuator skin, an actuator body, a strain limiting layer, a fixed end sealing cap and a free end sealing cap; the actuator skin is arranged on the periphery of the bending actuator body, and both are semicircular cavity-shaped; the interior of the two ends of the bending actuator body is sealed by a semicircular fixed end sealing cap and a free end sealing cap respectively; the strain limiting layer is installed on the outside of the bottom plane of the bending actuator body, and the bottom plane of the strain limiting layer and the outside of the top semicircular surface of the bending actuator body are wrapped by the fiber reinforcement layer.

[0014] Furthermore, in step 2), the input pressure P in the equilibrium state in Bending moment M about the equilibrium point O on the free end sealing cap a for:

[0015]

[0016] Where ρ represents the polar diameter of the polar coordinate system of the cross section of the free end sealing cap where the equilibrium point O is located, Represents the polar angle of the polar coordinate system;

[0017] The bending moment of the actuator body to the equilibrium point O on the free end sealing cap in the equilibrium state for:

[0018]

[0019]

[0020]

[0021] Where, and are the bending moments of the rectangular section and semicircular section of the actuator body to the equilibrium point O on the free end sealing cap, is the axial elongation of the rectangular cross-section of the actuator body, is the axial elongation of the semicircular section of the actuator body, S(λ * ) is the axial stress, β1 is the distance from any point on the rectangular cross section of the actuator body to the bottom plane where the equilibrium point O is located, and τ1 is the difference between the distance from any point on the semicircular cross section of the actuator body to the equilibrium point O and the radius a of the actuator body cavity;

[0022] The bending moment of the actuator outer skin to the equilibrium point O on the free end sealing cap in the equilibrium state for:

[0023]

[0024]

[0025]

[0026] Where, and are the bending moments of the rectangular cross section and the semicircular cross section of the actuator skin to the equilibrium point O on the free end sealing cap, is the axial elongation of the rectangular cross-section of the actuator skin, is the axial elongation of the semicircular cross-section of the actuator outer skin, β2 is the distance from any point of the rectangular cross-section of the actuator outer skin to the bottom plane where the equilibrium point O is located, and τ2 is the difference between the distance from any point of the semicircular cross-section of the actuator outer skin to the equilibrium point O and the radius a of the actuator body cavity.

[0027] Furthermore, the functional relationship between axial stress and axial elongation S(λ * ) is determined by the selected material model. The relationship between the axial elongation and the actuator structural parameters is:

[0028]

[0029]

[0030] Furthermore, the moment balance condition is:

[0031]

[0032] Where M θ It represents the total bending moment of the actuator on the equilibrium point O on the free end sealing cap.

[0033] Furthermore, in the equilibrium state, the relationship between the input pressure and the actuator structural parameters is:

[0034]

[0035] Furthermore, the multi-objective optimization algorithm includes but is not limited to particle swarm optimization, ant colony optimization, simulated annealing algorithm, genetic algorithm, firefly algorithm, artificial neural network and other optimization algorithms.

[0036] The beneficial effect of the present invention is that compared with the traditional empirical design method, the present design method can realize the automation of the design of fiber-reinforced soft bending actuators, and has the advantages of low time cost and strong robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a schematic flow chart of the design method of the present invention;

[0038] Figure 2 Schematic diagram of the structural parameters of the actuator targeted by the design method of the present invention in (a) free and (b) pressurized states;

[0039] Figure 3 Schematic diagram of the measurement system for verifying the design method of the present invention;

[0040] Figure 4 This is a structural diagram of the actuator targeted by the design method of the present invention;

[0041] Figure 5 Schematic diagram of theoretical analysis of the design method of the present invention;

[0042] Figure 6 Schematic diagram of the comparison results in the embodiment;

[0043] In the figure: 1-air compressor, 2-pneumatic hose, 3-fixed bracket, 4-calibration plate, 5-fiber reinforced soft bending actuator, 51-actuator shell, 52-actuator body, 53-strain limiting layer, 54-fiber reinforcement layer, 55-fixed end sealing cap, 56-free end sealing cap, 6-saddle-shaped fixing piece, 7-hexagonal screw, 8-industrial CCD. DETAILED DESCRIPTION

[0044] In order to better illustrate the purpose and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0045] Taking fiber-reinforced soft bending actuators with different structural parameters as an example, the application of the optimization design method of the fiber-reinforced soft bending actuator proposed in the present invention in the optimization design of the fiber-reinforced soft bending actuator is explained.

[0046] like Figure 1 As shown in Figure 2, the main steps of the optimization design method for fiber-reinforced soft bending actuators are as follows:

[0047] 1) Initialize the structural parameters of the fiber-reinforced soft bending actuator, including actuator length L, actuator body cavity radius a, actuator body rectangular wall thickness b1, actuator skin rectangular wall thickness b2, actuator body semicircular ring wall thickness t1, actuator skin semicircular ring wall thickness t2, actuator sealing cap length l c and the bending angle θ of the actuator in a given equilibrium state.

[0048] like Figure 2 As shown, Figure 2 (a) shows the structural parameters of the actuator in the free state. Figure 2 (b) shows the structural parameters of the actuator under pressurized state.

[0049] 2) Combined with the initialization structural parameters and the selected material model, the input pressure P in the equilibrium state is calculated under the condition of setting the bending angle θ of the actuator in the equilibrium state. inBending moment M about the equilibrium point O on the free end sealing cap a , the bending moment of the actuator body to the balance point O on the free end sealing cap Bending moment of the actuator outer skin to the equilibrium point O on the free end sealing cap

[0050] 3) According to the moment equilibrium condition Get the input pressure P in The relationship between the initial structural parameters of the actuator P in =f(L,a,b1,b2,t1,t2,l c ), M θ It represents the total bending moment of the actuator on the equilibrium point O on the free end sealing cap.

[0051] 4) P in =f(L,a,b1,b2,t1,t2,l c ) is the target optimization function, and the initialization structural parameters are optimized by combining the multi-objective optimization algorithm so that the input pressure P under the bending angle θ of the actuator in a given equilibrium state is in Reach minimum.

[0052] Design as Figure 2 The fiber-reinforced soft bending actuator shown in FIG. Figure 3 The fiber-reinforced soft bending actuator measurement system shown in the figure is used for experiments, where 1 is an air compressor, 2 is a pneumatic hose, 3 is a fixing bracket, 4 is a calibration plate, 5 is a fiber-reinforced soft bending actuator, 6 is a saddle-shaped fixing part, 7 is a hexagonal screw, and 8 is an industrial CCD.

[0053] The fiber-reinforced soft bending actuator is composed of Figure 4 As shown, the actuator comprises a fiber-reinforced soft bending actuator outer skin 51, a fiber-reinforced soft bending actuator body 52, a strain-limiting layer 53, a fiber-reinforced layer 54, a fixed end sealing cap 55, and a free end sealing cap 56. The actuator outer skin 51 is sleeved around the outer periphery of the bending actuator body 52, both of which are semicircular cavities. The interiors of the bending actuator body 52 are sealed by two semicircular sealing caps, designated as the fixed end sealing cap 55 and the free end sealing cap 56, respectively. The strain-limiting layer 53 is mounted on the outer side of the bottom plane of the bending actuator body 52 to limit the length of the bottom plane of the bending actuator body 52 to remain constant. The fiber-reinforced layer 54 is disposed around the outer periphery of the bending actuator body 52 and the strain-limiting layer 53, encapsulating both. For example, a fiber rope may be wound around the top semicircular surface and the outer side of the bottom plane of the overall structure formed by the actuator body 52 and the strain-limiting layer 53 to provide reinforcement. The actuator outer skin 51 is located on the outermost side. The strain limiting layer 53 , the bending actuator body 52 and the actuator outer skin 51 have the same length, that is, the actuator length L.

[0054] Figure 5 The analysis process of the structural parameters and design methods of the fiber-reinforced soft bending actuator is presented. Let Λ be the center of the curvature circle of the fiber-reinforced soft bending actuator in the bending state, and represents the length l of the fixed end sealing cap 55 and the free end sealing cap 56 c , the structural parameters of the two are consistent; is the bottom plane length of the inner cavity of the fiber-reinforced soft bending actuator body. is the length of the bottom of the fiber-reinforced soft bending actuator in the bending state, which is the same as the initial length L of the actuator. Combined with the initial structural parameters and the selected material model, the input pressure P in the equilibrium state is calculated under the condition of the bending angle θ of the actuator in the equilibrium state. in Bending moment M about the equilibrium point O on the free end sealing cap a , the bending moment of the actuator body to the balance point O on the free end sealing cap Bending moment of the actuator outer skin to the equilibrium point O on the free end sealing cap

[0055] 1) Since the structural parameters of the sealing cap can be ignored during the bending process of the actuator, the input pressure P in the equilibrium state is obtained in Bending moment M about the equilibrium point O on the free end sealing cap a for:

[0056]

[0057] Where ρ represents the polar diameter of the polar coordinate system of the cross section of the free end sealing cap where the equilibrium point O is located, Represents the polar diameter of the polar coordinate system.

[0058] 2) In addition, during the bending process, the effect of the fiber reinforced layer 54 will make the radial stress and circumferential stress of the rectangular cross section and the semicircular cross section of the actuator body to the equilibrium point O negligible. Therefore, only the axial stress and It will produce a bending moment on O. Therefore, the bending moment of the actuator body to the equilibrium point O on the free end sealing cap in the equilibrium state can be obtained. for:

[0059]

[0060]

[0061]

[0062] Where, and are the bending moments of the rectangular section and semicircular section of the actuator body to the equilibrium point O on the free end sealing cap, is the axial elongation of the rectangular cross-section of the actuator body, is the axial elongation of the semicircular cross-section of the actuator body, β1 is the distance from any point of the rectangular cross-section of the actuator body to the bottom plane where the equilibrium point O is located, and τ1 is the difference between the distance from any point of the semicircular cross-section of the actuator body to the equilibrium point O and the radius a of the actuator body cavity;

[0063] Under the action of the strain limiting layer 53, the bottom plane length of the inner cavity of the fiber reinforced soft bending actuator body is and free end sealing cap 56 length It is basically unchanged. Because the freedom of the fixed end sealing cap 55 is completely restricted by the saddle-shaped fixing member 6 during the bending test, the axial elongation λ of the rectangular cross section and the semicircular cross section of the actuator body is obtained by the arc length formula:

[0064]

[0065] 3) Similarly, during the bending process, the rectangular cross-section and semicircular cross-section of the actuator skin will only have axial stress on the equilibrium point O. and The bending moment of the actuator skin to the equilibrium point O on the free end sealing cap in the equilibrium state is obtained. for:

[0066]

[0067]

[0068]

[0069] Where, and are the bending moments of the rectangular cross section and the semicircular cross section of the actuator skin to the equilibrium point O on the free end sealing cap, is the axial elongation of the rectangular cross-section of the actuator skin, is the axial elongation of the semicircular cross-section of the actuator outer skin, β2 is the distance from any point of the rectangular cross-section of the actuator outer skin to the bottom plane where the equilibrium point O is located, and τ2 is the difference between the distance from any point of the semicircular cross-section of the actuator outer skin to the equilibrium point O and the radius a of the actuator body cavity.

[0070] Similarly, we can get:

[0071]

[0072] S(λ *) is the functional relationship between the axial stress S and the axial elongation λ. The specific expression is determined by the selected material model.

[0073] Under the condition of moment equilibrium, we have:

[0074]

[0075] Finally, the input pressure P is obtained in and the actuator initial structural parameters L, a, b1, b2, t1, t2, l c The multi-objective relationship in equilibrium:

[0076]

[0077] The multi-objective relationship under the above equilibrium state is used as the target optimization function, and the multi-objective optimization algorithm is combined to make the input pressure P in the target optimization function in The actuator structural parameters are optimized with the minimum constraint. Multi-objective optimization algorithms include but are not limited to particle swarm optimization, ant colony optimization, simulated annealing, genetic algorithm, firefly algorithm, artificial neural network and other optimization algorithms.

[0078] In order to ensure the uniformity of the force on the fiber-reinforced soft bending actuator, it is assumed that the rectangular wall thickness b1 of the constrained fiber-reinforced soft bending actuator body is equal to the semi-circular wall thickness t1 of the actuator body, and the rectangular wall thickness b2 of the actuator skin is equal to the semi-circular wall thickness t2 of the actuator skin. In this embodiment, the structural parameters (L, a, b1, t1, b2, t2, l c ) is (100,6,2,2,1,1,15), (100,8,2,2,1,1,15), (130,6,2,2,1,1,15), (130,8,2,2,1,1,15), (160,6,2,2,1,1,15), (160,8,2,2,1,1,15).

[0079] The main body of the fiber-reinforced soft bending actuator selected in this experiment is made of Elastosil M4601 silicone material, the outer skin is made of Ecoflex 00-30 silicone material, the strain limiting layer is made of glass fiber material, and the fiber reinforcement material is Kevlar fiber.

[0080] Considering the robustness of Arruda-Boyce, Mooney-Rivlin, Neo-Hookean, Ogden, and Yeoh material models in the strain range of 0-1, the Neo-Hookean material model is selected to reconstruct the relationship between radial stress and radial elongation of Elastosil M4601 silicone material and Ecoflex 00-30 silicone material, respectively. The functional relationship between the axial stress S and the axial elongation λ of the Neo-Hookean material model is:

[0081]

[0082] The initial shear moduli μ0 of the two materials are determined by the materials themselves and are 0.246 MPa and 0.024 MPa, respectively.

[0083] By utilizing Figure 3 The fiber-reinforced soft bending actuator measurement system shown in the figure was used to conduct experiments. The bending angle of the actuator was measured using an industrial CCD 8 combined with image measurement and compared with the traditional design method (P. Polygerinos et al., "Modeling of Soft Fiber-Reinforced Bending Actuators," in IEEE Transactions on Robotics, vol. 31, no. 3, pp. 778-789, June 2015, doi: 10.1109 / TRO.2015.2428504.). The results are shown in Figure 2. Figure 6 shown. Figure 6 It shows that, in the actuator parameters (L,a,b1,t1,b2,t2,l c ) are (160,6,2,2,1,1,15) and (160,8,2,2,1,1,15) respectively. Figure 6 As shown in (a) and (b) in the figure, the design method proposed by the present invention and the traditional design method have similar results. When the actuator parameters are other combinations, such as Figure 6 As shown in (c) to (f), the analysis results of the design method proposed in the present invention are better than those of the traditional design method.

[0084] For those skilled in the art, according to the teachings of the present invention, without departing from the principles and spirit of the present invention, changes, modifications, substitutions and variations made to the implementation methods are still within the scope of protection of the present invention.

Claims

1. An optimization design method for a fiber-reinforced soft bending actuator, characterized in that: The following steps are involved: 1) Initialize the structural parameters of the fiber-reinforced soft bending actuator, including actuator length L, actuator body cavity radius a, actuator body rectangular wall thickness b1, actuator skin rectangular wall thickness b2, actuator body semicircular ring wall thickness t1, actuator skin semicircular ring wall thickness t2, actuator sealing cap length l c and the bending angle θ of the actuator in a given equilibrium state; 2) Combined with the initial structural parameters and the selected material model, the input pressure P is calculated under the given bending angle θ of the actuator in the equilibrium state. in Bending moment M on the balance point O on the sealing cap at the free end of the actuator a , the bending moment M of the actuator body to the balance point O on the sealing cap at the free end of the actuator θ1 , the bending moment of the actuator skin to the balance point O on the sealing cap at the free end of the actuator 3) According to the moment equilibrium condition, the input pressure P is obtained under a given equilibrium state. in The relationship between the actuator structure parameters P in =f(L,a,b1,b2,t1,t2,l c ); 4) Using the relation P in =f(L,a,b1,b2,t1,t2,l c ) is the target optimization function, and the structural parameters of the actuator are optimized by combining the multi-objective optimization algorithm so that the input pressure P under the bending angle θ of the actuator in a given equilibrium state is in Reach minimum.

2. The optimization design method of a fiber-reinforced soft bending actuator according to claim 1, characterized in that: The material models described include Arruda-Boyce, Mooney-Rivlin, Neo-Hookean, Ogden, and Yeoh.

3. The optimization design method of a fiber-reinforced soft bending actuator according to claim 1, characterized in that: The fiber-reinforced soft bending actuator includes a fiber reinforcement layer, an actuator skin, an actuator body, a strain limiting layer, a fixed end sealing cap and a free end sealing cap; the actuator skin is arranged on the periphery of the bending actuator body, and both are semicircular cavity-shaped; the interior of the two ends of the bending actuator body are sealed by a semicircular fixed end sealing cap and a free end sealing cap respectively; the strain limiting layer is installed on the outside of the bottom plane of the bending actuator body, and the bottom plane of the strain limiting layer and the outside of the top semicircular surface of the bending actuator body are wrapped by the fiber reinforcement layer.

4. The optimization design method of a fiber-reinforced soft bending actuator according to claim 1 or 3, characterized in that: In step 2), the input pressure P in the equilibrium state is in Bending moment M about the equilibrium point O on the free end sealing cap a for: Where ρ represents the polar diameter of the polar coordinate system of the cross section of the free end sealing cap where the equilibrium point O is located, Indicates the polar angle corresponding to the polar coordinate system; The bending moment of the actuator body to the equilibrium point O on the free end sealing cap in the equilibrium state for: Where, and are the bending moments of the rectangular section and semicircular section of the actuator body to the equilibrium point O on the free end sealing cap, is the axial elongation of the rectangular cross-section of the actuator body, is the axial elongation of the semicircular section of the actuator body, S(λ * ) is the axial stress, β1 is the distance from any point on the rectangular cross section of the actuator body to the bottom plane where the equilibrium point O is located, and τ1 is the difference between the distance from any point on the semicircular cross section of the actuator body to the equilibrium point O and the radius a of the actuator body cavity; The bending moment of the actuator outer skin to the equilibrium point O on the free end sealing cap in the equilibrium state for: Where, and are the bending moments of the rectangular cross section and the semicircular cross section of the actuator skin to the equilibrium point O on the free end sealing cap, is the axial elongation of the rectangular cross-section of the actuator skin, is the axial elongation of the semicircular cross-section of the actuator outer skin, β2 is the distance from any point of the rectangular cross-section of the actuator outer skin to the bottom plane where the equilibrium point O is located, and τ2 is the difference between the distance from any point of the semicircular cross-section of the actuator outer skin to the equilibrium point O and the radius a of the actuator body cavity.

5. The optimization design method of a fiber-reinforced soft bending actuator according to claim 4, characterized in that: The relationship between axial elongation and actuator structural parameters is:

6. The optimization design method of a fiber-reinforced soft bending actuator according to claim 1, characterized in that: The moment equilibrium condition is: Where M θ It represents the total bending moment of the actuator on the equilibrium point O on the free end sealing cap.

7. The optimization design method of a fiber-reinforced soft bending actuator according to claim 5, characterized in that: In the equilibrium state, the relationship between the input pressure and the actuator structural parameters is:

8. The optimization design method of a fiber-reinforced soft bending actuator according to claim 1, characterized in that: The multi-objective optimization algorithms include particle swarm optimization, ant colony optimization, simulated annealing algorithm, genetic algorithm, firefly algorithm, and artificial neural network.

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