Sequential Multimodal Morphing of Single-Input Pneu-Nets

Abstract

Soft actuators provide an attractive means for locomotion, gripping, and deployment of those machines and robots used in biomedicine, wearable electronics, automated manufacturing, etc. In this study, we focus on the shape-morphing ability of soft actuators made of pneumatic networks (pneu-nets), which are easy to fabricate with inexpensive elastomers and to drive with air pressure. As a conventional pneumatic network system morphs into a single designated state, achieving multimodal morphing has required multiple air inputs, channels, and chambers, making the system highly complex and hard to control. In this study, we develop a pneu-net system that can change its shape into multiple forms as a single input pressure increases. We achieve this single-input and multimorphing by combining pneu-net modules of different materials and geometry, while harnessing the strain-hardening characteristics of elastomers to prevent overinflation. Using theoretical models, we not only predict the shape evolution of pneu-nets with pressure change but also design pneu-nets to sequentially bend, stretch, and twist at distinct pressure points. We show that our design strategy enables a single device to carry out multiple functions, such as grabbing—turning a light bulb and holding—lifting a jar.

Introduction

Shape-morphing of physical objects in response to external stimuli has recently emerged as an essential technology for soft robotics,^1,2 flexible electronics,^3,4 and smart architecture.^5,6 Although novel in artificial systems, shape-morphing has played a pivotal role in survival and prosperity of some animals and most of plants through millions of years of evolution. A number of biological morphing behaviors and structures have already been emulated by artificial actuators, including folding of mimosa leaves,^7,8 snapping of Venus flytraps,^9,10 circumnutation of tendrils,^11,12 and bending or coiling of seed awns.^13–16

Besides these organisms exhibiting a single mode of shape change, there are creatures capable of multiple modes of shape morphing, which have defied mimicry by soft actuation technologies thus far. For instance, cuttlefish can change into a variety of shapes depending on the surrounding environments for camouflage,^17–19 and cone snails can extend their proboscis to paralyze and tether their prey fish, then proceed to engulf it using their rostrum.^20,21 Just as the multimodal morphing (referred to as multimorphing henceforth) has conferred extreme flexibility and functionality upon those animals, it would enable unprecedented applications of soft machines, such as multipurpose transformable soft robots for medical surgery,^22,23 exploration of unknown environments,^24,25 and rescue tasks.^24,26

Combining multiple soft actuation systems activated by distinct stimuli (e.g., light and humidity) was demonstrated previously,²⁷ but the fabrication and operation processes are complicated and costly and thus may lead to defects and errors. In this study, we present a simple but versatile design methodology to achieve sequential multimorphing of soft machines using a single input, thereby eliminating complex wiring, plumbing, and multiple stimulation devices. Our approach is based on a pneumatic network (pneu-net), which is easy to fabricate, fast in response, capable of generating forces of a wide range of magnitude, and scalable.⁶

Our key idea for sequential multimorphing in a simple manner comes from the fact that a softer part in pneu-net will deform before a stiffer region when pressurized simultaneously. We also need to make sure that the softer part, which has initiated swelling earlier, does not overexpand in the course of the stiffer part's swelling to achieve targeted morphology while preventing disruption. In this work, we provide pneu-net systems with contrast in stiffness embodied by combining networks of different wall thicknesses or materials of different elastic moduli. Overexpansion of the softer part is suppressed by exploiting the strain-hardening effect of the softer elastomers, which is tuned to arise at the activation pressure of the stiffer part.

In the following, we first explain the mechanical model for the activation condition for a pneu-net, which forms the basis of sequential morphing through strain-hardening. We then present the design and demonstration of various multimorphing pneu-nets, including those combining networks of different-modulus materials and of different thicknesses, which can sequentially perform bending-twisting, stretching-bending, or bending deformations of opposite curvatures. We show that these multimorphing pneu-net schemes enable a single device to carry out multiple functions with a single pressure input.

Materials and Methods

Fabrication of pneu-net combinations of different materials

For a pneu-net system as shown in Figure 1, plastic molds to fabricate bending, twisting, and shaft modules were 3D printed using Form 2 and 3 printers from Formlabs™ (XY resolution 25 μm, layer thickness 25 μm). After print, they are washed in isopropyl alcohol for 1 h, then postcured using UV light. Commercial elastomers corresponding to each module (elastomer V for central shaft, elastomer III for twisting, elastomer II for bending) are poured into the molds and degassed for 5 min using a vacuum chamber. Constraint layer for bending module was made by pouring degassed elastomer VI on a wafer and rotated using a spin coater to make a thin layer of elastomer. They were then cured in an oven at 50°C for 2 h, then demolded. Uncured elastomer was used as an adhesive to assemble the modules, which were all cured in the oven at 50°C for 2 h. After assembly is complete, a pneumatic tube is attached to the bending module through the central hole of the shaft which is connected to the three twisting modules, to enable actuation of the entire structure through one single input. Additional details are given in Supplementary Table S2.

FIG. 1.

Pneu-net system combining modules of different elastic moduli. (A) Schematics of a pneu-net system combining modules of different elastic moduli. Detailed information of geometry and materials is given in Supplementary Table S2. (B) Experimental images of the device undergoing sequential morphing from the undeformed initial configuration (P₀ = 0). As the actuation pressure increases to P₁ = 30 kPa, the lower modules bend with insignificant twisting of the upper shaft. As the pressure further increases to P₂ = 50 kPa, the upper modules twist as much as 56° from the initial state with the further bending of lower modules suppressed. (C) Numerically predicted shapes of the device at the same pressure values as (B). (D) Dimensionless curvature, dκ/(2π), of the lower bending module and rotation angle (Supplementary Fig. S7) of the upper twisting module as a function of actuation pressure, P/ $\bar{μ}$ , where $\bar{μ}$ is the average shear modulus of elastomer II and III. (E) The sequential bending and twisting of the pneu-net system can turn a bulb in a socket and switch it on. (F) Grabbing and turning a door knob with our sequential multimorphing actuation system. Movies corresponding to (B, C, E, F) are provided in Supplementary Movie S1.

Fabrication of pneu-net combinations of different thicknesses

For a pneu-net system as shown in Figure 2, a plastic mold to fabricate the upper module was 3D printed using Form 2 and 3 printers (Formlabs). After print, it was washed in isopropyl alcohol for 1 h, then postcured using UV light. Elastomer III was poured into the mold and degassed for 5 min using a vacuum chamber. The bottom module was made by pouring degassed elastomer III on a wafer and rotating at 500 rpm using a spin coater for 10 s to make a thin layer. They were then cured in an oven at 50°C for 2 h, then demolded. Uncured elastomer III was used as an adhesive to assemble the modules. After curing in the oven at 50°C for 2 h, a small patch of elastomer III was applied at the bottom of the flat plate to act as a constraint to prevent inflation downwards. Additional details are given in Supplementary Table S3.

FIG. 2.

Pneu-net system with contrast in wall thickness. (A) Schematics of a pneu-net system with contrast in wall thickness. Detailed information of geometry is given in Supplementary Table S3. (B) Experimental images of the device undergoing sequential morphing from the undeformed initial configuration (P₀ = 0). As the actuation pressure increases to P₁ = 120 kPa, the lower chamber is bulged with insignificant bending of the upper chamber. As the pressure further increases to P₂ = 150 kPa, the upper chamber bends with the further bulging of the lower chamber suppressed. (C) Numerically predicted shapes of the device at the same pressure values as (B). (D) Amount of stretching (Supplementary Fig. S8) and bending of the lower and upper chamber, respectively, as a function of the actuation pressure. Here, μ = 80 kPa is the shear modulus of elastomer III. (E) A pneu-net system first holds a jar by bulging in the lower part and then lifts it out of a sand pile without spilling by bending in the upper stalk. Movies corresponding to (B, C, E) are provided in Supplementary Movie S2.

Fabrication of pneu-net combinations of different air chamber geometries

For a pneu-net system as shown in Figure 3, plastic molds to fabricate upper and bottom modules were 3D printed using Form 2 and 3 printers (Formlabs). After print, it was washed in isopropyl alcohol for 1 h, then postcured using UV light. Elastomer III was poured into the molds and degassed for 5 min using a vacuum chamber. They were then cured in an oven at 50°C for 2 h, then demolded. Uncured elastomer III was used as an adhesive to assemble the top and bottom modules. After curing in the oven at 50°C for 2 h, a small patch of elastomer V was applied at the middle section of the top module as a constraint to prevent inflation upwards. Additional details are given in Supplementary Table S4.

FIG. 3.

Pneu-net system with different air chamber geometries. (A) Schematics of a pneu-net system having a smaller side wall thickness in the middle than the upper and lower chambers. Detailed information of geometry is given in Supplementary Table S4. (B) Experimental images of the device developing multiple curvatures as the activation pressure increases. (C) Numerically predicted shapes of the device at the same pressure values as (B). (D) The curvatures (Supplementary Fig. S9) of middle and lower chambers versus the actuation pressure. (E) A pneu-net system grasps a peach with bending of the middle chamber (P = 105 kPa), and then an orange with bending of the lower chamber at an increased pressure (P = 130 kPa). Movies corresponding to (B, C) are provided in Supplementary Movie S3.

Evaluation of hyperelastic properties

Material hyperelasticity was obtained using tensile test results performed using an Instron Universal Testing Machine. Tensile repetition test was conducted to observe the effect of repetition on elastomers (Supplementary Fig. S2). The test specimens of the ASTM D 412 series specimen dimensions were made using a 3D printed mold using Form 2 and 3 printers (Formlabs). After print, it was washed in isopropyl alcohol for 1 h, then postcured using UV light. Each kind of elastomer was poured into the mold and left to cure at room temperature for 18 h, then postcured in the oven at 50°C for 2 h. Using Abaqus evaluation tool for the stress–strain curve obtained in Figure 4C, hyperelasticity was fitted using the reduced polynomial strain energy potential sixth curve fitting, and Poisson's ratio was taken to be 0.5 assuming incompressibility.

FIG. 4.

Schematics of a unit cell in its (A) preinflated and (B) postinflated states. Experimentally measured (C) stress-strain and (D) elastic modulus-strain curves of the four elastomers used in the experiments. (E) Dimensionless curvature, dκ/(2π), versus dimensionless pressure, P/μ, for different wall thicknesses, d_f/d. (F) Dimensionless curvature versus pressure for different elastic moduli with the cell dimensions w_c = 6 mm, w_s = 2 mm, w = 10 mm, d_c = 16 mm, d_f = 2 mm, d = 20 mm, h_c = 2 mm, h_t = 2 mm, h_b = 1 mm, h = 5 mm, μ_b = 600 kPa, J = 15, ν = 0.5.

Finite element analysis

Numerical analysis of sequential multimodal single-input pneu-nets was performed using Abaqus standard, with each part constructed as a 3D deformable part. Material density was obtained from the datasheet on Smooth-On™ and material hyperelasticity as obtained above using reduced polynomial coefficients of parameters. For simple structures, parts were separated into partitions, and C3D8H mesh was used. For complicated structures for which parts could not be separated into partitions, C3D4H mesh was used, in addition to using reduced integration mesh type for constraint layers to improve the convergence of simulation results. Curvatures, stretching distance, and rotation angles from simulation results were all obtained using mesh node coordinates at each step and inputting them into Matlab to calculate the respective values.

Results

Mechanical model

As a simple model to describe how we control the onset of morphing by modulating stiffness (determined by dimensions and elastic modulus) of a pneu-net, we consider a unit cell that can bend about the x-axis upon pressurizing, as shown in Figure 4A. We design depth to be much longer than width to ignore bending about the y-axis. When unactivated, the cuboid air chamber having width w_c, height h_c, and depth d_c is surrounded by top and bottom walls of thickness h_t and h_b, side walls of identical thickness w_s, and front and rear walls of identical thickness d_f. The entire cell consisting of the air chamber and the surrounding walls has width w = w_c + 2w_s, height h = h_c + h_t + h_b, and depth d = d_c + 2d_f. We assume that all the walls have the same shear modulus μ except the bottom wall of a higher modulus μ_b. Then the cell with d≫w deforms as shown in Figure 4B when the inner chamber is pressurized.

The deformation behavior of the cell is represented by a curvature κ, which is defined by κ = θ/d with θ being the central angle of the bent cell, as shown in Figure 4B. The curvature κ is determined by the cell dimensions and material properties when the pressure P is applied, so that we write κ = F(w_s, w, d_f, d, h_t, h, μ, P), where we assume that the modulus and thickness of the bottom wall are kept constant and that all the walls are incompressible with Poisson's ratio of 0.5. For geometrically similar cells with constant ratios of w/d and h/d, the dimensionless curvature, κd, can be expressed as a function of four dimensionless variables using Buckingham's pi-theorem²⁸: κd = f(w_s/d, d_f/d, h_t/d, P/μ).

We compute the equilibrium bending curvature κ at a pressure input of P by minimizing the total energy coming from the pressure work and the deformation of the cell walls.²⁹ Figure 4C and D, respectively, show the experimentally measured curves of stress-strain and elastic modulus-strain for the materials used in our experiments (Table 1). Just as most of elastomers used for pneu-nets, our materials are far from linear elastic. Except for elastomer VI, the moduli decrease for small strains, but eventually increase beyond the initial moduli at larger strains, which is referred to as strain hardening. We use the incompressible Gent model³⁰ to express the stored strain energy density function (see Supplementary Fig. S1A, Supplementary Table S1, and Supplementary Data for details).

Table 1.

Elastomers Used in the Experiments

Elastomer	Component
I	Dragon Skin™ 10 rubber
II	Mixture of Dragon Skin 10 and 30 rubber with the weight ratio of 2:1
III	Mixture of Dragon Skin 10 and 30 rubber with the weight ratio of 1:2
IV	Dragon Skin 30 rubber
V	Smooth-Sil™ 960 and Dragon Skin 10 rubber with the weight ratio of 1:1
VI	Smooth-Sil 960 rubber

Numerical computation of the total energy based on the measured material properties yields the dimensionless curvature dκ/(2π), a ratio of dκ to 2π, which is equivalent to the bending angle θ in Figure 4B compared to a complete circle, as a function of the dimensionless input pressure P/μ for different dimensionless wall thicknesses (w_s/d, d_f/d, and h_t/d), a representative result of which is displayed in Figure 4E. In this study, we assume that all the walls are made of elastomer III except for the bottom wall made of a stiff elastomer VI with the shear modulus of μ_b. We see that the curvature increases mildly for small pressure, but rises rapidly when the pressure further increases due to the classical ballooning instability of top walls.^30–32 Then the curvature increase becomes relatively mild again as the strain hardening effect comes in. Therefore, the cell exhibits significant deformation (bending in this case) within a narrow range of activation pressure causing ballooning instability, and the degree of deformation is limited due to strain hardening.

As the wall in the depth-wise (y)-direction becomes thicker, or stiffer, with a higher d_f/d, the critical pressure for rapid curvature rise, P_c, increases, and the same tendency is observed for h_t/d and w_s/d (see Supplementary Fig. S1A and Supplementary Data for details). Although it is obvious that P_c and μ go together by Buckingham's pi-theorem, Figure 4F confirms that the critical pressure for rapid curvature rise increases as the modulus increases. The pressure value at which the curvature slope begins to rise rapidly is taken to be P_c.

The theoretical results imply that we can design a pneumatic actuation device that can be deformed to a designated extent at a preset activation pressure by modulating the wall thickness and the elastic modulus. It is through combining multiple cells with deliberately modulated activation pressures that we achieve sequential multimorphing pneu-nets, as demonstrated in the following.

Combining pneu-nets of different materials

We first present a multimorphing pneu-net device that combines two sets of network modules made of elastomers with different elastic moduli, as shown in Figure 1A. Its upper portion has a long triangular prism-shaped shaft in the center surrounded by three identical twisting modules of pneu-net, and the lower portion consists of three identical bending modules of pneu-net. Each twisting module is a long strip with a tilted (with respect to the strip's longitudinal axis) array of air chambers which are connected to a central duct in the shaft.

When pressurized, the chamber arrays in the modules swell, eventually causing the entire upper part to twist (Supplementary Fig. S3). It is because the inflation direction is perpendicular to the tilted chambers, exerting a force in both depth-wise and width-wise directions (depth-wise force induces twisting). Each twisting module and the shaft are made of elastomer III and V, respectively. Each bending module in the lower part has a linear array of thin cuboid air chambers, which is connected to the central duct. Because the bending module's bottom wall made of elastomer VI is stiffer than the other walls made of elastomer II, the pressurized air chambers bulge upward to cause each module to bend downward.

Figure 1B and Supplementary Video S1 show the actuation sequence of the integrated device. When pressurized, the device begins to exhibit dominantly the bending of the lower modules, and as the pressure increases, the twisting of upper portion dominates with the lower part's bending stopped. Because all the air chambers in the device are connected to a single pressure input through the central duct, modulating the actuation pressure alone could stimulate multiple morphing modes of bending and twisting. The dimensions of the twisting and bending modules were tuned in the design stage to achieve sequential multimorphing, with the aid of numerical computations.

We used a finite element analysis package, Abaqus, to predict the shape evolution of the device based on the geometric dimensions and the hyperelastic properties we measured. Figure 1C shows that the theoretically predicted shapes are consistent with the experimental results. Quantitative comparisons of theory and experiment are given in Figure 1D, which plots the curvature of the lower bending module and the rotation angle of the upper twisting module versus actuation pressure. We see that the bending curvature increases rapidly in the small pressure region (P/ $\bar{μ}$ < 0.44), which corresponds to the bending-dominant phase. In the larger pressure region (P/ $\bar{μ}$ > 0.44), the bending of the lower portion is suppressed thanks to strain hardening of elastomer II while the continual twisting dominates the device morphing, corresponding to the twisting-dominant phase. In this study, $\bar{μ}$ corresponds to the average shear modulus of elastomer II and III.

Decreasing the pressure gradually from 50 to 30 kPa can sequentially reverse the morphing process to untwist the gripper, then unbend from 30 to 0 kPa as shown in Supplementary Figure S10. If a pressure greater than the predetermined pressure of 50 kPa is applied, the gripper will continue to twist without further bending. The bending components, having already reached strain-hardening at 30 kPa, will not contribute to the deformation beyond this pressure. Increasing the pressure further beyond 50 kPa would eventually result in the bending components to fail first as they are strain-hardened at a lower pressure than the twisting components. It is important to design sequential multimorph pneu-nets accordingly to perform different tasks at distinct pressures without any of its components reaching failure.

Our pneu-net system capable of sequential morphing of bending and twisting can perform essential daily functions of our hands, as demonstrated in Figure 1E and F. In Figure 1E, the bending module of the device first grips a bulb as actuated by a low pressure, and then the bulb is rotated and fits into a socket by the twisting module to be switched on at a higher actuation pressure. If the bulb is replaced by a door knob, our device can grip (by bending the lower modules) and rotate (by twisting the upper modules) the knob to open the door, as shown in Figure 1F. Because the pneu-net actuators are soft, the bending modules can grip a wide size range of objects of diverse shapes and excessive rotation of bulbs or knobs can be avoided. Although the multimode actuations of gripping and rotation of a bulb or a door knob usually require complicated mechanical elements, electronic circuits, and sophisticated control inputs in conventional rigid robots,³³ our simple pneu-net system made of elastomers can perform the similar multiple tasks using only a single pressure input.

Combining pneu-nets of different thicknesses

We can confer contrast in stiffness on a pneu-net system by giving each chamber different wall thicknesses. We show such a device, which is capable of sequential stretching-bending, in Figure 2. Its schematic is shown in Figure 2A, where a cuboid made entirely of elastomer III houses a long slender upper chamber connected to a wide lower chamber (Supplementary Fig. S4). Although the chambers have the identical side wall thickness w_s and the bottom height h_b, the difference in top wall height (h_t^u and h_t^l) allows us to attain sequential multimorphing. Detailed geometric information on the device is given in Supplementary Table S3.

Figure 2B shows the experimental images of the device actuated at different pressure through a single pressure input source (Supplementary Video S2). Because the lower chamber has a smaller wall height h_t^l than the upper chamber's wall height h_t^u, the deformation of the lower chamber—stretching in the y-direction in this case—is dominant in the lower pressure conditions (P₁ = 120 kPa). As the pressure exceeds the critical pressure to induce the significant bending of the upper chamber with a thick top wall, the device with the lower chamber already bulged is now bent at the upper stalk, as shown in Figure 2B at P₂ = 150 kPa.

Figure 2C shows that the device shapes numerically predicted by the finite element analysis are consistent with the experimental results. Quantitative comparison of the experimental and computational results is made in Figure 2D, where the stretch of the lower chamber and the bending curvature of the upper chamber are plotted versus the actuation pressure. In addition to the agreement of theory and experiment, we see that the critical pressure values for the rapid rise of the upper chamber's bending curvature and for the strain hardening of the lower chamber coincide (P/μ = 0.49), a result of our deliberate design through iterative simulations with changing parameters. By matching the critical pressure values, the stretching-dominant regime smoothly transitions to the bending-dominant regime as the critical pressure is crossed over.

Such pneu-net system performing sequential stretching and bending can be used to hold, seal, and move a jar, as demonstrated in Figure 2E. At zero activation pressure, the slender device is inserted in the opening of a jar. Then the device is inflated near its end to seal and hold the jar from inside at the activation pressure P₁ = 120 kPa (P/μ = 0.49). Increasing the pressure to P₂ = 150 kPa (P/μ = 0.61) bends the device to pull the jar off the unwanted environment without spilling the inner content owing to the seal provided by the inflated pneu-net body. A self-standing crawling pneu-net can also be designed to stand upright using stretching, to crawl forwards by bending (Supplementary Fig. S6).

Combining pneu-nets of different air chamber geometries

In this study, we demonstrate a pneu-net system having different air chamber geometries within a device to achieve multiple bending curvatures depending on the activation pressure from a single-input source. Figure 3A shows a schematic of the device, a long cuboid housing three chambers—slender upper and lower chambers connected by a middle chamber consisting of three relatively wide subchambers. The entire pneu-net was made of elastomer III except the bottom wall of the middle chamber made of stiffer elastomer VI (Supplementary Fig. S5). Detailed geometric information on the device is given in Supplementary Table S4. Because wide chambers with a smaller side wall thickness w_s^m can bulge more easily than narrow chambers with a larger side wall thickness w_s^l, the middle chamber is activated earlier than the upper and lower chambers.

Experimental images in Figure 3B and Supplementary Video S3 show that the initially straight device at P = 0 morphs into a C-shape due to the bending of the middle chamber until the activation pressure reaches P₁ = 105 kPa. The free end of the device is pointing to the right. Further increase in the pressure causes the upper and lower chambers to bend in the sense opposite to the middle chamber's, making the free end point to the left, as shown in the panel corresponding to P = 130 kPa.

The pneu-net shapes predicted by numerical computation, shown in Figure 3C, are consistent with the experimental images. Figure 3D quantitatively compares the experimental and computational results of the curvatures of middle and lower chambers versus the dimensionless actuation pressure, P/μ. In this study, μ corresponds to the shear modulus of elastomer III. While the curvature increase of the middle chamber is dominant in the low pressure regime (P < P₁), the middle chamber's curvature is saturated when P > P₁ owing to strain hardening. But in the high pressure regime, the curvature of the lower chamber (also that of the upper chamber) steeply increases with the pressure. The smooth transition from the middle chamber bending dominant regime to the upper and lower chamber bending dominant regime is a result of our deliberate design to match the pressure values (P₁) of middle chamber's strain hardening and of rapid rise of the other parts' bending, through iterative simulations.

Multiple curves achieved by a single pneu-net can be utilized to grasp multiple objects, as demonstrated in Figure 3E. While the middle chamber grasps a red peach at a low actuation pressure, increasing the pressure allows the pneu-net to grasp another object, an orange, with its lower chamber's curvature. Such multiple-object grasping by forming multiple curves at different activation pressures is controlled by a single pressure input.

Discussion

We have fabricated an actuator that can sequentially multimorph using a single pressure input based on a pneumatic network that can bend, stretch, or twist. Our actuator used the strain-hardening effect of elastomers as a stopping mechanism to prevent overexpansion of the softer part within our pneu-net system, which is tuned to arise at the activation of the stiffer part. Using the actuators, we designed multiple high degree-of-freedom soft devices that only rely on a single input to perform complex tasks. Our approach can also be integrated with other mechanisms, such as a soft bistable valve,³⁴ to increase morphing complexity as shown in Supplementary Figure S11. Although we used a pneumatic stimulus and elastomer-based actuators, single-input multimorphing can be implemented in other soft robotic systems. Hydrogels, for example, also display strain-hardening behavior,^35,36 allowing the design of single-input multimorphing soft robots that use stimuli not limited to air pressure. We further proposed a theoretical model of the actuator which provides a design framework for utilizing the strain-hardening effect in multimorphing soft robots.

Strain hardening can also serve as a tool to encode physical intelligence in existing soft robotic systems. Conventional methods of increasing deformation modes and functions have relied on increasing the number of external stimuli (extra pumps, more valves, etc.)^25,37 or changing the environment (e.g., magnetic, electric, humidity),^38,39 leading to higher costs and control complexity. Using high moduli materials with the strain-hardening behavior,^40,41 multimorph soft robots with a high load capacity can also be created.

Footnotes

Acknowledgment

H.-Y.K. acknowledges administrative support from SOFT Foundry Institute.

Authors' Contributions

H.B.J. and H.-Y.K. conceived the idea and wrote the main article text. H.B.J. and C.K. carried out the experiments and analyzed the data. H.B.J., C.K., A.L., and H.-Y.K. developed the mathematical model. A.L. and H.-Y.K. supervised this study and provided intellectual and technical guidance. All authors discussed the results and commented on the article.

Author Disclosure Statement

H.-Y.K., H.B.J., and C.K. are inventors on the patent applications (Nos. 10-2020-0177365 and 10-2020-0177266, Republic of Korea) submitted by SNU R&DB Foundation that cover a pneu-net device capable of sequential deformation. The other author declares that she has no competing interests.

Funding Information

This work was supported by National Research Foundation of Korea (NRF) grants funded by the Korean Government (MSIT) (grant numbers NRF2018R1A3B105254122, NRF2021M3F7A101747621, and NRF2020R1A4A3079853).

Supplementary Material

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