Quality and Testing of Red Pepper Soft Picking Manipulator Based on RD-DEM Coupling

Abstract

Due to a shortage of labor, the harvesting of fruits and vegetables faces significant challenges. Soft robotic hands, adaptable to variable environments due to their high-curvature bending and twisting, have garnered widespread attention and usage. However, their application in Sichuan pepper picking remains largely unexplored. Therefore, this study proposes a picking soft robotic hand composed of a rigid skeleton and flexible skin for pepper harvesting. Through analyzing the characteristics of peppers, the structure of the robotic hand is determined. Inflatable airbags are employed to drive finger bending, utilizing a rotating–twisting method for Sichuan pepper picking. Structural parameters influencing the bending angle of the airbags were determined through theoretical analysis and validated via simulation. Optimal parameter combinations for the airbags were obtained through response surface experiments to establish the robotic hand model. To assess the feasibility of the robotic hand’s movement, dynamic simulations were conducted using R D (RecurDyn V9R2) software. Subsequently, a discrete element model of Sichuan pepper clusters was established and coupled with the simulation of the Sichuan pepper picking process. The results indicate that the robotic hand does not cause damage to the Sichuan peppers during picking. Finally, field tests were conducted in pepper orchards to validate the success rate of the robotic hand in picking, yielding an 85% success rate and a 0.3% damage rate.

1. Introduction

On account of its labor-intensive nature and the declining enthusiasm for agricultural work among laborers, fruit and vegetable harvesting faces increasingly daunting challenges [1,2,3]. There is an urgent need for stable and reliable picking robots to address these challenges. Traditional rigid robots often have shortcomings in compliance, environmental adaptation, and human–machine interactions in unstructured environments [4,5,6]. Scientists have shifted their focus to bio-inspired soft robotics, leading to the design of biomimetic soft robots such as elephant trunks [7], earthworm bodies [8], plant twining structures [9,10,11], and octopus tentacles [12]. Soft robotic hands pose no harm to humans in various environments [13,14], and their high-curvature bending and twisting capabilities [15,16] allow them to adapt to environmental shapes and gripping requirements in irregular spaces [17], making them widely recognized and utilized.

Soft robotic hands have achieved remarkable results after many studies. In terms of grasping objects, Woongbae designed a biomimetic dual-deformable origami structure inspired by the motion of pelicans and eels [18], Bianca S. Homberg et al. designed a combination robot with a soft gripper hand [19], and Ohio State University developed soft robotic hands for embedded SMA actuators and flexible sensors [20], which can be applied in narrow spaces and complex structures, ensuring safety and human–computer interactions. In medicine, Harvard University’s Polygerinos designed a soft palm glove and wearable soft glove to assist in the long-term wearable therapy for hand rehabilitation in individuals with hand disabilities [21,22]. KAIST has developed a novel variable stiffness structure designed with the connective structure of echinoderm ossicles [23], which can interact with unpredictable environments. Aslan Miriyev of Columbia University designs hard and soft composite materials that stretch and contract like muscles [24]. In agriculture, soft robots are also very important. Yuseung Jo et al. [25]. designed a suction cup-based soft manipulator for cucumber harvesting that can adjust its shape and surface parameters in response to the surface and shape characteristics of cucumbers. Wang proposed a soft manipulator for apple picking consisting of four tapered soft robotic fingers (SRFs) and a multi-modal suction cup [26]. Henry A.M. Williams et al. [27] develop an autonomous kiwi fruit harvesting robot. Anthony L. Gunderman proposed a novel tendon-driven soft robot gripper for picking blackberries, with a success rate of 95.24%.

Soft robotic hands are favored by researchers for their advantages such as flexibility, safety, and adaptability to complex environments, and are developing rapidly. However, in the agricultural field, the application of soft robotic hands is mainly concentrated in fruit and vegetable picking, while the application of Sichuan peppers picking has not been fully explored. There are many varieties of Sichuan peppercorns with different characteristics. Red peppercorns are more difficult to harvest than other peppercorns. Their branches and buds will grow into new peppercorns for the next year and must not be damaged during the picking process. The protrusions on the red peppercorn fruit are the main source of their numbing aroma. Because their epidermis is weak, the surface oil cells must not be damaged during harvesting. This study proposes a soft robotic hand for harvesting, consisting of a rigid skeleton and flexible skin, which mimics the process of human hands picking Sichuan peppers. The rigid skeleton provides stability, while the flexible skin adapts to the variable shapes of Sichuan peppers. Through rotational motion, the robotic hand twists off the Sichuan peppers, addressing issues such as the vulnerability of Sichuan peppers and their buds to existing mechanical harvesters. The device is not only suitable for harvesting red pepper, but can also be used for harvesting other varieties of pepper.

2. Materials and Methods

2.1. Overall Structure and Working Principle of Soft Robotic Bands

2.1.1. Overall Structure of Soft Robotic Hands

A harvesting robotic hand mainly consists of an outer skin, a finger skeleton, joint airbags, and a palm, as shown in Figure 1. The finger skeleton consists of three phalanges, which are connected by pins between each phalanx, and a riser plate is provided on the back of each knuckle. The rigid skeleton is encased in silicone. The joint airbags are fixed between phalanxes 1 and 2 and between phalanxes 2 and 3. An entire finger is secured to the palm by bolts. Small holes are set at the corresponding positions of the joint airbags and the vertical plates for the passage of an inflation tube. The inflation tube is used to inflate the airbags, realizating the bending of the fingers.

2.1.2. The Working Principle

Its working process is as follows: When the vision system on the robotic arm successfully identifies a Sichuan pepper, the robotic hand is moved to the position of the Sichuan pepper. Subsequently, the inflation of the joint airbags is performed, causing the airbags to expand in the axial direction, pushing phalanx 1 and phalanx 2 to bend. At the same time, the three fingers move toward the center line and perform a grasping motion, holding the Sichuan pepper cluster tightly with the fingertips. After the robotic hand grips the cluster of Sichuan peppers, the motor connected to the palm is activated to rotate and twist off the stems of the Sichuan pepper cluster. In order to prevent the inflatable tube from becoming entangled, the motor will quickly reversely rotate back to the initial position after rotating forward. Then, the robot hand moves to the collection basket, releases its fingers, and successfully completes the picking action of a Sichuan pepper.

2.2. Robotic Hand Size and Airbag Bending Parameter Determination

2.2.1. Robotic Hand Size Determination

To ensure that the robotic hand can fully grasp clusters of Sichuan pepper without damaging the oil vesicles, the mechanical hand’s finger joint length, palm length, and airbag bending angle need to be designed based on the three-dimensional dimensions of Sichuan pepper clusters. Field experiments cannot measure the dimensions of all Sichuan pepper clusters, and the maximum size of the Sichuan pepper clusters is unknown. However, the stems of Sichuan pepper are elastic, and when the clusters are subjected to pressure from the mechanical hand, they tend to contract inward. The larger the Sichuan pepper cluster, the greater the space available for contraction. Therefore, the dimensions of larger Sichuan pepper clusters can be used as a reference for designing the dimensions of the mechanical hand. After measuring Sichuan pepper clusters with stems of various thicknesses and at different heights, as illustrated in Figure 2, the maximum width of the peppercorn clusters was found to be l =57.94 mm, with a length of h =54.66 mm. A simplified diagram of finger inflation movement is depicted in Figure 3.

The following was derived from the schematic of finger movement:

$$\left\{\begin{array}{c}\min h=L_1+L_2\cos {\theta }_1+L_3\cos {\theta }_2\\ \min x=L_2\sin {\theta }_1+L_3\sin {\theta }_2\\ 50<h<60\\ 30<x<40\\ L_1>0,L_2>0,L_3>0\\ 0<{\theta }_1<90\\ 0<{\theta }_2<90\end{array}\right.$$

where h—Length of fingers from palm;

x—The length of the front end of the finger from the knuckle 1 during bending;

L₁—Length of joint 1;

L₂—Length of joint 2;

L₃—Length of joint 3;

θ₁—The first airbag bending angle;

θ₂—The second airbag bending angle.

Through MATLAB program calculations, the lengths of joint 1, joint 2, and joint 3 were determined as follows: L₁ = 28 mm, L₂ = 25 mm, and L₃ = 27 mm. Additionally, the first airbag bending angle is θ₁ = 51°, and the second airbag bending angle is θ₂ = 39°.

2.2.2. Determining the Structural Parameters of the Joint Airbags

When the joint airbags are inflated and operational, they can be viewed as cantilever beams, subjected only to bending moments. Figure 4a shows the cross-section of the airbag, where r, w, a, and t, respectively, represent the inner radius, chamber wall thickness, internal dimensions, and bottom thickness. If the cross-sectional area of the chamber is regular, such as circular, spherical, or rectangular, the neutral axis will pass through the centroid of the pressure, and the airbag will expand uniformly in all directions without bending. However, if there is a slight offset between the pressure centroid and the neutral axis, the actuator will bend toward the side where the neutral axis is located. The torque causing this bending is simply the tension force F multiplied by the offset “e” between the pressure centroid and the neutral axis, as shown in Figure 4b.

The formula for the radius of curvature is

$${\displaystyle \frac{1}{\rho }}={\displaystyle \frac{M}{EI}}={\displaystyle \frac{Fe}{EI}}={\displaystyle \frac{PAe}{EI}}$$

(1)

where ρ—radius of the curvature of the airbag;

P—inflation pressure;

A—cross-sectional area inside the channel;

E—modulus of elasticity of the airbag material;

I—cross-sectional moment of inertia.

The bending angle of the airbag is determined by the following equation:

$$\theta ={\displaystyle \frac{L}{\rho }}={\displaystyle \frac{LPAe}{EI}}$$

(2)

where L—total length of airbag.

In this study, L, P, A, and E remain constant. Therefore, the bending angle θ is mainly influenced by the ratio e/I.

To calculate the offset e between the center of pressure and the neutral axis, find the center of pressure and the neutral axis. The calculation formula is based on the pressure center coordinates:

$$x_p={\displaystyle \frac{{\displaystyle {\int }_{s}xp\left(x,y\right)dxdy}}{{\displaystyle {\int }_{s}p\left(x,y\right)dxdy}}}$$

(3)

$$y_p={\displaystyle \frac{{\displaystyle {\int }_{s}yp\left(x,y\right)dxdy}}{{\displaystyle {\int }_{s}p\left(x,y\right)dxdy}}}$$

(4)

Since the pressure is constant, the pressure function p is a constant p. From Figure 4a, we can obtain the range of x and y as x∈[−r,r] and y∈[− √(r2 − x2),a], with

$$x_p={\displaystyle \frac{P{\displaystyle {\int }_x{\displaystyle {\int }_{y}xdxdy}}}{P{\displaystyle {\int }_x{\displaystyle {\int }_{y}dxdy}}}}={\displaystyle \frac{{\displaystyle {\int }_{-r}^r{\displaystyle {\int }_{-\sqrt{r^2-x^2}}^{a}xdxdy}}}{{\displaystyle {\int }_{-r}^r{\displaystyle {\int }_{-\sqrt{r^2-x^2}}^{a}dxdy}}}}$$

$$y_p={\displaystyle \frac{P{\displaystyle {\int }_x{\displaystyle {\int }_{y}ydxdy}}}{P{\displaystyle {\int }_x{\displaystyle {\int }_{y}dxdy}}}}={\displaystyle \frac{{\displaystyle {\int }_{-r}^r{\displaystyle {\int }_{-\sqrt{r^2-x^2}}^{a}ydxdy}}}{{\displaystyle {\int }_{-r}^r{\displaystyle {\int }_{-\sqrt{r^2-x^2}}^{a}dxdy}}}}$$

The calculated coordinates of the pressure center are [xp, yp] = [0].

The calculation formula of the central axis is

$$N.A.={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{A}_i{y}_i}}{{\displaystyle {\sum }_{i=1}^n{A}_i}}}$$

(5)

From the calculated centroid coordinates and formula (5), the offset e is obtained as

$$e=\left|y_p-N.A.\right|=\left|0-{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{A}_i{y}_i}}{{\displaystyle {\sum }_{i=1}^n{A}_i}}}\right|={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{A}_i{y}_i}}{{\displaystyle {\sum }_{i=1}^n{A}_i}}}$$

(6)

Divide the cross-section into four parts, a ring and three rectangles, and calculate the centroid coordinates, respectively; thus, we obtain

$$\begin{array}{c}e={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{A}_i{y}_i}}{{\displaystyle {\sum }_{i=1}^n{A}_i}}}\hfill \\ ={\displaystyle \frac{aw\cdot \frac{a}{2}+aw\cdot \frac{a}{2}+2bt\cdot \left(a+\frac{t}{2}\right)-\frac{\pi w^2}{2}\cdot \frac{4\left(r^3-r^{2}b+w^{2}b\right)}{3\pi w^2}}{2aw+2bt+\frac{\pi w}{2}}}\hfill \\ ={\displaystyle \frac{6a^{2}w+12abt+6b{t}^2-4\left(r^3-r^{2}b+w^{2}b\right)}{12aw+12bt+3\pi w}}\hfill \end{array}$$

(7)

$$b=2r+2w$$

(8)

The moment of inertia I of the cross-section is calculated as follows:

$$I={\displaystyle {\int }_A{y}^2}dA$$

(9)

where y—the distance from element dA to the z-axis.

Since the airbag cross-section is a combined cross-section, to calculate the moment of inertia of the combined cross-section on the z-axis, the first step is to calculate the moment of inertia of each component on that axis, and the parallel axis theorem can be used for the calculation. From the parallel axis theorem, we obtain

$$I_z=I_{z0}+A{d}^2$$

(10)

where I_Z—The moment of inertia of the cross-section about the z-axis;

I_Z0—The moment of inertia of the cross-section about its own centroidal axis z₀;

D—The distance between the two axes.

From Equations (7) and (10), it can be seen that the chamber wall thickness and bottom thickness will affect the ratio e/I, which also implies that they will affect the bending angle of the airbag. In this study, the chamber wall thickness variation range is 1 mm ≤ w ≤ 1.8 mm, and the bottom layer thickness variation range is 3 mm ≤ t ≤ 7 mm [28]. When studying the effect of the chamber wall thickness on the bending angle, the thickness of the bottom layer remains unchanged, and the increment of the chamber wall thickness is 0.2 mm. The offset e between the pressure center and the neutral axis and the cross-sectional moment of inertia I is calculated; similarly, when considering the effect of the bottom layer thickness on the bending angle, the chamber wall thickness remains unchanged, and the bottom layer thickness increment is 1 mm, and the offset e and cross-sectional moment of inertia I are calculated. The results are shown in Figure 5: As the wall thickness increases, the e/I ratio becomes smaller and the bending angle becomes smaller; as the bottom layer thickness increases, the e/I ratio first increases and then decreases, and the bending angle also increases with the bottom layer thickness. The thickness increases first and then decreases.

Chamber clearance, that is, the gaps that exist between different chambers in the airbag, has a certain influence under the action of external pressure [28]. When the airbag is subjected to external pressure, the existing gaps may cause an uneven distribution of gas in the chamber, thereby affecting the overall stability and bending angle of the airbag. This is because the gap may cause the gas to not be transferred evenly when stressed, causing the airbag to produce inconsistent stress distribution when it bends. This uneven distribution may lead to instability of the local structure of the airbag, thereby affecting the overall shape change.

3. Result and Discussion

3.1. Simulation Test on Factors Affecting Airbag Bending Angle

3.1.1. Airbag Single Factor Simulation Test

According to the influencing factors of the airbag bending angle discussed previously, including the chamber wall thickness, bottom layer thickness, and chamber gap, it was planned to conduct a single-factor simulation test and use the airbag bending angle as a performance indicator. The levels of each factor were determined based on the reference and preliminary experimental results, which are listed in

Table 1. Single-factor test level.

Level	Chamber Wall Thickness/mm	Bottom Layer Thickness/mm	Chamber Clearance/mm
1	1	3	1
2	1.2	4	1.2
3	1.4	5	1.4
4	1.6	6	1.6
5	1.8	7	1.8

.

3.1.2. Simulation Test to Determine Air Bag Inflation Pressure

It can be seen from formula (1) that when A, E, and I remain unchanged, the airbag bending angle θ increases as the inflation pressure p increases. In order to present this relationship more intuitively, the airbag chamber wall thickness was set to 1.5 mm, the bottom layer thickness was 4 mm, and the chamber gap was 1.5 mm, while other factors remain unchanged. Under this setting, the air pressure was simulated, ranging from 0.1 MPa to 0.5 MPa, changing in increments of 0.1 MPa, and then the changes in the airbag bending angle were recorded under different inflation pressures. The results of the simulation are presented in Figure 6.

From the analysis of Figure 6, it can be seen that the bending angle of the air bag increases with the increase in inflation pressure, which is the same as the result obtained by Formula (1). When the inflation pressure is too small, the walls of the airbag chambers do not touch each other when the airbag is inflated, and the bending curvature is small. To achieve the target bending curvature, more airbag chambers are needed, and the size of the manipulator becomes larger, which increases the weight of the manipulator; It is inconsistent with the principle of reducing the weight of the robot. when the inflation pressure is too high, the air bag chamber walls squeeze each other when the air bag is inflated, and the air bag chamber walls become thinner under the action of air pressure. If the air bag is inflated multiple times, there is a risk of rupture, and the service life is shortened. The inflation pressure is obtained by analyzing and calculating the stress points. In practical applications, in order to ensure sufficient gripping force of the manipulator, the energy loss during the inflation process is usually taken into consideration. Therefore, take the inflation pressure, which is slightly greater than the calculated inflation pressure, as the actual inflation pressure to ensure that the manipulator has sufficient grip strength during actual operation.

3.2. Effect of Chamber Wall Thickness on Airbag Bending Angle

According to the observation in Figure 5, it can be known that when other conditions remain unchanged, an increase in the wall thickness of the airbag chamber will lead to a decrease in the bending angle of the airbag. To explore this relationship in more detail, a simulation study of changes in airbag curvature at different airbag chamber wall thicknesses was performed. In this single-factor test, the chamber wall thickness increased by equivalent values. The bottom layer thickness was 4 mm, the chamber gap was 1.5 mm, and the model was built for testing. The inflation pressure was 0.2 MPa. The simulation results were drawn on a line chart, as shown in Figure 7a,b.

In the above two figures, the tendency of the airbag bending angle to decrease as the airbag chamber wall thickness increases is clearly demonstrated. The observation of this trend is consistent with the theoretical expectations in Figure 5 and further emphasizes the important influence of airbag chamber wall thickness on the airbag bending performance.

3.3. Effect of Chamber Clearance on Airbag Bending Angle

According to Figure 5, it can be seen that when other conditions remain unchanged, the bending angle of the airbag first increases and then decreases as the thickness of the airbag bottom layer increases. In order to study this relationship in more detail, a simulation study was conducted on the bending changes in the airbag under different airbag bottom thicknesses. The thickness of the bottom layer was selected as the test factor, keeping other parameters unchanged, taking the chamber wall thickness of 1.5 mm and the chamber gap of 1.5 mm, and used to establish a corresponding airbag model for testing. The test inflation pressure was 0.2 MPa. Through the simulation results, the bending angle change data at different values of the airbag bottom layer thickness were obtained, and a line chart was drawn, as shown in Figure 8a,b.

Through observing Figure 8, it can be clearly seen that when other conditions remain unchanged, the bending angle of the airbag shows a trend in first increasing and then decreasing as the thickness of the bottom layer of the airbag increases, which is consistent with the previous theoretical analysis conclusion.

When the thickness of the bottom layer is in the range of 3.0–4.0 mm, it is observed that the bending angle of the airbag increases with the thickness of the confinement layer. The reason for this phenomenon is that the restricting layer is too thin, causing the restricting layer to expand when air pressure is introduced, thereby hindering the normal bending of the air bag. Changes in the thickness of the bottom layer have a significant impact on the performance of the airbag: especially when the limiting layer is thin, the airbag is restricted, and it is difficult to achieve the ideal bending effect. When the thickness of the bottom layer is greater than 4.0 mm, it is observed that the bending angle of the airbag decreases as the thickness of the restricting layer decreases. This is because as the thickness of the bottom layer increases, the torque generated under the same air pressure is not enough to fully bend the airbag. When the thickness of the bottom layer is too large, it is difficult for the airbag to generate sufficient torque when inflated, thus affecting the bending effect of the airbag.

3.4. Effect of Chamber Clearance on Airbag Bending Angle

According to the previous analysis, we know that the chamber gap has a significant impact on the airbag bending angle. In order to study the specific influence of the chamber gap on the airbag bending angle more deeply, further simulation studies are necessary. In the simulation, the inflation pressure, chamber wall thickness, and bottom layer thickness are kept unchanged at 0.2 MPa, 1.5 mm, and 4 mm respectively, the chamber gap value is adjusted, and the bending change in the airbag is measured under different chamber gaps. The results were drawn on a line chart, as shown in Figure 9a,b.

Through observing Figure 9, it can be clearly seen that the airbag bending angle decreases as the airbag chamber gap increases. The observation of this phenomenon is consistent with the theoretical analysis and highlights the important influence of the chamber gap on the bending performance of the airbag. The observation of this trend shows that within a certain range, the bending angle of the airbag shows a downward trend as the chamber gap increases. This may be due to the fact that the chamber gap is too large, which prevents adjacent chambers from effectively contacting each other during expansion, thus affecting the bending effect of the airbag.

3.5. Multifactorial Experiments

3.5.1. Second-Order Orthogonal Rotation Center Combination Experimental

Based on the horizontal range determined through single-factor experiments for chamber wall thickness $𝒳$1, bottom thickness $𝒳$2, and chamber clearance $𝒳$3, the bending angle of the airbag $𝒴$ was selected as the performance evaluation index. In using a three-factor, five-level, second-order orthogonal rotation center combination experimental design, each experiment was repeated three times, and the average value was taken as the experimental result. The experimental factors are coded as shown in

Table 2. Test factor coding.

Coding	Chamber Wall Thickness $𝒳$1/mm	Bottom Layer Thickness $𝒳$2/mm	Chamber Clearance $𝒳$3/mm
−1.682	1	3	1
−1	1.2	3.5	1.2
0	1.4	4	1.4
1	1.6	4.5	1.6
1.682	1.8	5	1.8

. The coded values for the chamber wall thickness, bottom thickness, and chamber clearance are X1, X2, and X3, respectively.

3.5.2. Test Results and Analysis

The test results of Design-Expert 13 software were used for the analysis, and the regression equation of the airbag bending angle y was obtained. The significance test of the regression equation is shown in

Table 3. Analysis of variance.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	5995.09	9	666.12	20.96	<0.0001 **
A-A	898.48	1	898.48	28.27	0.0005 **
B-B	2338.97	1	2338.97	73.59	<0.0001 **
C-C	634.54	1	634.54	19.96	0.0016 **
AB	180.5	1	180.5	5.68	0.041 *
AC	12.5	1	12.5	0.3933	0.5462
BC	1404.5	1	1404.5	44.19	<0.0001 **
A2	377.25	1	377.25	11.87	0.0073 **
B2	11.81	1	11.81	0.3715	0.5573
C2	149.78	1	149.78	4.71	0.058
ABC	0	0
Residual	286.07	9	31.79
Lack of Fit	206.07	5	41.21	2.06	0.2517
Pure Error	80	4	20
Cor Total	6281.16	18

Note: * indicates significant impact (p ≤ 0.05), ** indicates extremely significant impact (p ≤ 0.01).

. It can be seen from Table 3 that the chamber wall thickness, bottom layer thickness, chamber gap, and the interaction between the bottom layer thickness and the chamber gap have a very significant impact on the airbag bending angle. The interaction between the chamber wall thickness and the bottom layer thickness has an extremely significant impact on the airbag bending angle. The coding values of the airbag chamber wall thickness, bottom layer thickness, and chamber gap are A, B, and C, respectively.

3.5.3. Parameter Optimization

In order to obtain the best performance parameters of the soft manipulator’s inflatable airbag, the constraints for parameter optimization are selected based on the actual working conditions and bending performance requirements. The single-objective optimization algorithm of Design-Expert 13 software was used for parameter optimization. The objective and constraint functions were

$$\left\{\begin{array}{c}maxy\\ s.t.\left\{\begin{array}{c}-1.681\le A\le 1.681\\ -1.681\le B\le 1.681\\ -1.681\le C\le 1.681\end{array}\right.\end{array}\right.$$

(11)

where A—chamber wall thickness;

B—bottom layer thickness;

C—chamber gap.

Since the optimization result has too many decimal places, if this optimization result is used directly, the error will be large when making the actual object, so the optimization result is rounded; when the inflation pressure is 0.2 MPa, the airbag chamber wall thickness is 1.6 mm, the bottom layer thickness is 4 mm, the chamber gap 1.6 mm, and the airbag bending angle is at its largest.

The optimization results were used to re-establish the three-dimensional model of the airbag and perform simulation. The bending angle of the airbag after simulation was measured, and the bending curvature of a single chamber was obtained to be 10.39°. The above calculation shows that the bending angle of the first airbag is θ1 = 51°, and the bending angle of the second airbag is θ2 = 39°. It was calculated that the first airbag should have five chambers, and the second airbag should have four chambers.

3.6. Sichuan Peppercorn Model

In using Sichuan Hanyuan tribute pepper as the test material, a simulation model of Sichuan pepper was built based on the actual Sichuan pepper branch. Since Sichuan pepper clusters vary in size, discrete element models of the largest cluster and the smallest cluster obtained during measurement were established during modeling to take into account the differences between Sichuan pepper clusters. Based on the Hertz–Mindlin with bonding contact model, the mutual bonding structure of spherical particles of different sizes was used to construct a discrete element model of Sichuan pepper branches. The sphericity rate of Sichuan pepper particles is 93.02%, so it can be established as a single particle when modeling. When picking Sichuan pepper, the robot mainly acts on the branches of Sichuan pepper, thereby fixing the branches and Sichuan pepper particles, as shown in Figure 10.

3.7. Simulation Parameter Settings

The mechanical property parameters of Sichuan pepper, as well as the contact attribute parameters and bonding parameters between materials were measured experimentally and referred to in the literature [29,30,31]. The results are shown in

Table 4. Mechanical property parameters.

Material	Parameter	Value
Sichuan Pepper Fruit	Poisson’s Ratio	0.168
	Shear Modulus/Pa	1.568 × 107
	Solid Density/(kg/m3)	997
Sichuan Pepper Branches	Poisson’s Ratio	0.38
	Shear Modulus/Pa	1.15 × 108
	Solid Density/(kg/m3)	1321.6
Ecoflex 00–30 Silica gel	Poisson’s Ratio [32]	0.127
	Shear Modulus/Pa [33]	6.35 × 104
	Solid Density/(kg/m3)	1080

,

Table 5. Contact attribute parameters.

Parameter	Coefficient of Restitution	Coefficient of StaticFriction	Coefficient of Rolling Friction
Sichuan Pepper Fruit–Sichuan Pepper Fruit	0.378	0.56	0.0143
Sichuan Pepper Fruit–Sichuan Pepper branches	0.305	0.621	0.0131
Sichuan Pepper Fruit–Ecoflex 00–30 Silicone	0.437	0.758	0.0136
Sichuan Pepper branches–Ecoflex 00–30 Silicone	0.359	0.786	0.0138

and

Table 6. Stem bonding parameters.

Normal Stiffness per Unit Area (N/m3)	Shear Stiffness per Unit Area (N/m3)	Critical Normal Stress (Pa)	Critical Shear Stress (Pa)	Bonded Disk Radius
3.59 × 109	1.44 × 109	2.17 × 106	1.26 × 106	1.25

.

3.8. Simulation and Bench Testing

3.8.1. Manipulator Kinematics Simulation Test

The size of the picking robot was calculated based on the size of the pepper clusters, that is, the length of knuckle 1 $L_1=28 \mathrm{m}\mathrm{m}$, the length of knuckle 2 $L_2=25 \mathrm{m}\mathrm{m}$, the length of knuckle 3 $L_3=27 \mathrm{m}\mathrm{m}$, the first airbag bending angle ${\theta }_1=51^{\circ }$, and the second bending angle of the air bag ${\theta }_2=39^{\circ }$. SOLIDWORKS 2020 software was used to conduct a three-dimensional modeling of the picking manipulator, it was saved in STEP format, and the three-dimensional model was imported into RecurDyn (Version:V9R2) software for dynamic simulation to simulate the finger movement process.

The simulation test process was as follows: the first step is to set up the kinematic pair, fix the palm and the ground and knuckle 3 and the palm, and set the rotary pair between knuckle 1 and knuckle 2 and between knuckle 2 and knuckle 3. The second step is to divide the mesh: the maximum mesh size of the flexible body is 0.8 mm, the minimum is 0.5 mm, the maximum mesh size of the rigid body is 2.4 mm, and the minimum is 0.8 mm; the third step of flexibility processing is to set the airbag and flexible skin material parameters as mentioned above, and define the contact surface; the fourth step is to set the contact and motion. In order to reduce the amount of calculation, the contact between the airbag and the flexible skin and the finger contact surface was set to fixed. Both sides of the airbag chamber gap and fingertip–fingertip contact were all Geo Surface, and then the pressure on the inner surface of the airbag was defined so that the pressure grows linearly, with the maximum pressure being 0.2 MPa. The simulation test saved data every 0.01 s. The total duration was preset to 0.5 s, and the time step was 1 × 10 ⁻⁶ s. The setup flow is shown in Figure 11.

The dynamics simulation results are shown in Figure 11. It can be clearly observed from the figure that the soft manipulator after the previous tests and subsequent optimization successfully achieved the predetermined movement process and results.

3.8.2. EDEM-RD Coupled Simulation Test

To simulate the process of Sichuan pepper harvesting and the fracture process of the pepper stalks, it is necessary to couple the discrete element simulation software EDEM (Version: 2021) with the multibody dynamic software RecurDyn (Version: V9R2). In Recurdyn, the motion and contact settings were configured as described in Section 3.8.1, along with the addition of the rotational movement of the entire manipulator. The wall file was then exported and imported into EDEM to complete the simulation model import, as shown in Figure 12.

The sizes of Sichuan pepper clusters vary greatly, so it is necessary to conduct a coupled simulation analysis for both the largest and smallest pepper clusters to investigate whether the soft robotic gripper exerts excessive pressure on the pepper particles during harvesting. A simulation diagram is shown in Figure 13, and the pressure exerted by the soft robotic gripper on the pepper particles is shown in Figure 14. From Figure 14, it can be seen that the pressure on the pepper clusters gradually increases as the robotic gripper harvests them. At 0.5 s, the gripper performs a rotational motion, during which the pressure on the pepper particles first decreases and then increases until the harvesting is complete. The gripper exerts pressure on the larger pepper clusters earlier than on the smaller ones because the smaller clusters only come into contact with the gripper fingers and generate pressure when the fingers are in a nearly closed, bent state. The maximum pressure exerted by the gripper on the particles of the large pepper cluster is 1.105 N, and for the small pepper cluster, it is 1.5642 N. As stated in Chapter 2, the rupture force of the pepper oil cells is 6.05 N. Therefore, the pressure exerted by the soft robotic gripper on the pepper particles of both large and small clusters during harvesting is less than 6.05 N, ensuring that the pepper oil cells are not damaged.

3.8.3. Bench Test

Based on the results of multifactor experiments and parameter optimization, a physical prototype of the soft robotic gripper was created. The joints of the soft robotic gripper designed in this study use hyperelastic silicone material and consist of multiple air chamber structures, which cannot be produced using traditional manufacturing techniques. To achieve the complex features and shapes of the air chambers, new manufacturing methods were required [34]. Considering the structural characteristics of the soft robotic gripper designed in this study and the advantages and disadvantages of various manufacturing methods [32,33,35,36], the plate printing method was found to be the most compatible with the fabrication of the soft fingers. The process of creating the air chambers and flexible skin using the plate printing method is shown in Figure 15.

In this study, a bench test was conducted by tying Sichuan pepper branches to a tree branch to simulate the growth state of the peppers. A corresponding control system was designed as the control core for the soft robotic pepper-picking gripper. A physical picking test was performed, as shown in Figure 16 and Figure 17. The gripper successfully harvested the pepper clusters by grasping them and twisting the stalks to detach them from the branches.

The differences in size and shape of Sichuan pepper clusters, as well as the presence of obstacles or complex shapes, can indeed affect the efficiency and cleanliness of mechanical harvesting. To address these challenges, a strategy of multiple picking attempts can be employed. By rotating the robotic gripper multiple times, the peppers can be gradually twisted off until all are harvested. According to the test results, up to four rounds of picking can be performed to ensure the maximum possible harvest of peppers.

Out of the twenty test groups conducted, seventeen were successful in harvesting, resulting in an 85% success rate. The time required to harvest one cluster was approximately 1.5 s. The damage rate of successfully harvested peppers was 0.3%, indicating that the robotic gripper effectively protects the peppers during operation.

4. Conclusions

This study proposes a novel soft robotic gripper composed of a rigid skeleton and flexible skin, with the bending motion of the gripper achieved through the inflation of airbags. Research was conducted on factors influencing the bending angle of the airbags. In viewing the airbags as cantilever beams, a mathematical model of airbag bending in relation to various influencing factors was derived through the theoretical analysis of the bending process. This model was then validated and optimized through structural parameter optimization using a central composite experimental design method, in conjunction with simulation results from finite element software. The optimized parameters were determined to be as follows: an airbag chamber wall thickness of 1.6 mm, base thickness of 4 mm, and chamber gap of 1.6 mm. When the airbag inflation pressure was set to 0.2 MPa, it was calculated that the first airbag required five chambers, while the second airbag required four chambers. To verify that the soft robotic gripper would not damage the oil cells of Sichuan peppers during operation, a coupled simulation of the robotic gripper twisting and harvesting peppers was conducted. Finally, a physical prototype of the proposed soft robotic gripper was fabricated and field-tested. The results show a harvesting success rate of 85% with a damage rate of 0.3%. Future plans involve further improving the motion and inflation control systems of the gripper. Additionally, more experiments are planned to provide a more comprehensive assessment of the harvesting performance of the entire system.