The Soft Ray-Inspired Robots Actuated by Solid–Liquid Interpenetrating Silicone-Based Dielectric Elastomer Actuator

Abstract

Dielectric elastomer actuators (DEAs) are widely used in robotics and artificial muscles because of their large energy densities and short response time. In this study, we developed two types of soft ray-inspired robots using solid–liquid interpenetrating silicone-based DEAs, named SIS DEAs. The optimized SIS DEA had an actuation strain of 79.8% at 20.43 kV/mm in a freestanding state, which was used as the muscle of the ray robot. To imitate the swimming behavior of the ray, the effect of the driving frequency on the velocity of the ray robot was explored. The ray robot achieved a maximum swimming rate of 5.7 mm/s when the driving frequency was ∼0.6 Hz. In addition, the steady-state and the transient simulation were carried out to reveal the mechanism of the ray robot's electro-swimming. The results revealed that the actuating deformation of the SIS DEAs caused the electro-deformation of the ray robot, and the periodical electro-deformation generated the high-speed vortex beneath the robot to push the ray robot forward. The high actuation strain in the freestanding state and the shape customizability of the SIS DEAs made it an ideal alternative to muscles for various soft robots.

Introduction

Soft robotics have the potential to replace conventional robots owing to their light weight, environmental adaptability, deformability, resilience to high loads, and compliance and safety around humans.^1–4 They have developed rapidly lately, thanks to the use of elastomeric materials, convenient manufacture methods, and computer-based systems.⁵ There have been numerous soft actuators developed for the applications in biomimetic robot, such as thermally responsive actuators,^6,7 photonic responsive actuators,⁸ pneumatic and hydraulic actuators,^5,9–13 magnetically responsive actuators,^14,15 and electroactive polymers (EAPs).^16,17 Among them, pneumatic actuators are widely used because they enable high actuating force and large strokes.¹⁸ An untethered pneumatic actuator device has a low response speed, so a tradeoff between execution speed and portability is inevitable.^11,19,20 In addition, it requires heavy and bulky reservoirs or compressors to achieve high-power operation.¹¹

Silicone-based dielectric elastomer actuators (DEAs) possess large actuated strain, the ability to operate in indiscriminate surroundings, a silent operation, and a self-sensing ability.²¹ Silicone-based dielectric elastomers (DEs) have high energy efficiency and fast electrical response, and thus are prevalently used in fabrication of microrobotics²² and bioinspired robotics.^{1,3,7,23–26} Recently, underwater soft robots like ray-, leptocephalus-, and frog-inspired robotics have been developed by Li et al, Christianson et al, and Wang et al, respectively.^2,27,28 Underwater soft robots are expected to be underwater monitoring devices that can survive in harsh surroundings and unobtrusively study marine life.¹¹ Aquatic animals like rays, octopuses, and so on, are commonly used prototypes to fabricate bioinspired underwater robots. Among the reported imitation objects of underwater soft robots, ray was known as one of the most imitated underwater creatures because of its undulating flapping motion.²⁹

In 1964 Klausewitz³⁰ created the full sequence of pectoral fin motion of a manta ray through video analysis and observation in nature. He described that the pectoral fins of manta ray were divided into two parts: the relatively rigid basal part (first third part nearest to the body) and the relatively flexible distal part (the remaining part). When the basal part was moving upward, the distal part might point down under the resistance of water and vice versa. In addition, Brower³¹ studied the quantified dimensions and wing oscillation frequency (∼0.5 Hz) of manta ray through detailed video analysis. The efforts to create ray-inspired robots can be traced back to 2004, when Punning et al³² developed a ray resemble underwater robot using EAP pectoral fins. The fins were able to generate undulating motions and propel the body forward. The appearance of the robot also did not look like a ray at all.

Since then, series of efforts to improve both the appearance and the performance of ray-inspired robots has been ongoing.^2,8,33–36 In a quite recent work, Shin et al³⁷ explored electrically driven microengineered ray-like soft robots, which displayed self-driven motion in line with the direction of cellular contractile forces and could be locally electrically stimulated and controlled. However, the contractile force of the cells could not propel the body forward with considerable speed. Lately, Li et al.³⁸ invented an untethered robot applied in undersea exploration inspired by a snailfish. The carefully designed acrylic-based DE fixed by a rigid frame was used for the flapping fin of the robot. However, the electrical response speed of the acrylic-based DE was slow, so the deformation of the robot's fin was small under alternating driven voltage.

Referencing the previous efforts on soft ray robots, in fabricating a manta ray inspired robot, a DE with fast electrical response, customizability, and high actuation performance is preferred. In this article, the soft ray-inspired robots actuated by the solid–liquid interpenetrating silicone-based dielectric elastomer actuators (SIS DEAs) were devised. The liquid would increase the deformation hysteresis of the SIS DEA in response to the high frequency alternating electric field. Therefore, SIS DEAs had better actuation performance at low driving frequencies, which might meet with the wing oscillation frequency of the manta ray.

To fabricate the ray robot with good actuation performance, the structurally optimized SIS DEs were used as the abdominal and flanking muscles of the ray robots. The effect of the driving frequency on the velocity of the ray robot was explored. Furthermore, the steady-state and the transient simulations were carried out to reveal the mechanisms of electro-deformation and electro-swimming of the ray robot. The “electro-deformation” means that the ray robot will deform as soon as the electric field is applied on the artificial muscles of the ray robot. The “electric swimming” means that when an AC voltage is applied on the artificial muscles of the ray robot, it moves forward like a natural ray.

Materials and Methods

Materials

The solid of solid–liquid interpenetrating (SI) structure was composed of Sylgard 184 (Dow Corning), which was prepared by mixing part A and B in a mass ratio (MR) of 10:1. The cubic NaCl particles were used as porogen whose purity was larger than 99.5% (Aladdin). The liquid of SI structure was composed of hydroxyl silicone oil (Shandong Xingchi Chemical Company) with hydroxyl content of 6 wt% to 10 wt%. The ecoflex 00–50 (Smooth-on) was used as encapsulation and sealing materials, which was prearranged by mixing part A and B in an MR of 1:1. Different shapes of compliant electrodes were painted using carbon conductive grease (MG Chemicals). And the conductive wires were made of conductive tape with a thickness of 0.06 mm (Zhejiang You Bisheng Adhesive Products Co., Ltd.).

Fabrication of the SIS DEAs

The interconnected pores of porous silicone elastomer were generated by etching the interlinked NaCl particles mixed with silicone rubber. The 60, 80, 100, and 200 meshes was used to divide NaCl particles into categories with particle sizes of <75, 75–150, 150–200, and 200–250 μm. These NaCl particles served as porogens and were added to silicone rubber (Sylgard 184) with MRs of 2:1, 3:1, 4:1, and 6:1. Referring to our previous work,³⁹ these mixtures were vulcanized at 150°C with a flat vulcanizer for 15 min to form salt-silicone cakes with thicknesses of 1.0, 0.5, and 0.3 mm. After tailoring the dried silicone foam into 15 mm radius disks, the hydroxyl silicone oil was filled in pores to prepare an SI matrix. The elastomeric shells were manufactured with 0.75, 0.5, and 0.25 mm film applicators for encapsulate the SI matrix for the production of SIS DE. Ultimately, the SIS DEAs were formed by coating compliant electrodes (thickness = 0.05 mm, radius = 10 mm) on both sides of the SIS DEs.

Fabrication of the ray-inspired soft robot

The porous silicone elastomer with thicknesses of 1.0 mm were tailored into cuboids (50 × 25 × 1 mm³), cylinder (diameter = 30 mm), and elliptical cylinder (long axis = 3 mm, short axis = 2 mm). Then, they were filled with hydroxyl silicone oil. The ray robot 1 composed of a pair of cuboids SI matrixes encapsulated with 0.25 mm thickness elastomeric shells. After coating a pair of compliant electrodes (40 × 15 × 0.05 mm³) on the surface of the composite elastomer, the electrodes with 0.05 mm thickness were sealed with 0.25 mm elastomeric film. Then, we cut out the leftovers according to the designed shape of the ray robot 1 (total length = 110 mm, total width = 140 mm), and flexible wires acted as the tails of the robot. Similarly, the fabrication method of ray robot 2 was to replace the pair of cuboids SI matrixes in ray robot 1 with a cylinder and an elliptical cylinder SI matrixes, and changed the electrode shape to a circle (diameter = 20 mm) and an ellipse (long axis = 2 mm, short axis = 1.5 mm), respectively. In addition, the shape of the ray robot 2 with the total body length of 110 mm and the total body width of 120 mm.

Characterization

The SU-3500 scanning electron microscopy was used to photograph cross-sectional morphology of a porous silicone elastomer. The porosity of the porous silicone elastomer was counted by one minus the porous silicone elastomer density divided by the silicone rubber density. The density was derived from the measured mass divided by measured volume. The Young's modulus was tested using an Instron 3300 series universal testing machine with a tensile speed of 50 mm/min according to GB16421-1996. A broadband dielectric analyzer (Concept 40; Novocontrd, Germany) was used to test the dielectric performance of the samples at room temperature with frequencies from 1 to 10⁷ Hz.

The actuated performance of SIS DEA at freestanding state was tested under voltage from 0 to 30 kV. The TD2202 high-voltage amplifier was sold by Dalian Taisiman Technology in China. Simultaneously, the cameras recorded the area strain and deformation along the plane normal of the SIS DEA. Then, the actuation strain would be calculated referring to Supplementary Figures S1 and S2. The ray-inspired robot was actuated under an alternative electric field that was served by Model 20/20C high-voltage amplifier (TREK). The amplitude of the sine wave was 20 kV with a frequency ranging from 0.2 to 10 Hz. The electro-swimming process was recorded by cameras on the sides and top of the fish tank, and the swimming speed of the ray robot was calculated by dividing the distances within 15 s by the time.

Results and Discussion

Working principle of SIS DEA

The hydroxyl silicone oil in the interconnected pores was compressed and migrated under the Maxwell stress generated by electric field (Fig. 1). The migrating liquid applied hydraulic pressure to the pore's walls as well as the elastic shell to expand the area of the SIS DEA plane (Fig. 1D). The noncentrosymmetric cross-section of the SIS DEA (Fig. 1E and Supplementary Fig. S3) resulted in the out-of-plane deformation of the actuator. As the voltage increased from V₁ to V₂, the increase of electrostatic force gradually outpaced that of mechanical restoring force. Simultaneously, a pull-in instability of SIS DEA occurred with a sharp decrease in the thickness and a sudden increase in the area (Fig. 1F).⁴⁰

FIG. 1.

SEM of silicone rubber foams and deformation schematic. (A) Pore size = 75–150 μm; (B) pore size = 150–200 μm; (C) pore size = 200–250 μm; (D) deformation schematic of DEA with different foam cell sizes. (E) Appearances of the SIS DEA actuated under driving voltages, where V₂ > V₁ > V₀; (F) the dotted line shows typical actuation response of an SIS actuator with geometry shown in (E) and the grey line shows the electrical breakdown voltage of the actuator. SEM, scanning electron microscopy; SIS DEA, solid–liquid interpenetrating silicone-based dielectric elastomer actuator.

An analytical model was deduced to compute the actuation strain based on the relative permittivity (ɛ_r) and elastic modulus (Y) of composite material.^22,41,42 The ɛ_r and Y of composite material were derived from the relative permittivity of shell (ɛ_r,_shell), the elastic modulus of shell (Y_shell), the fraction of elastomeric shell (ϕ_shell), the relative permittivity of SI matrix (ɛ_r_,si) and elastic modulus of SI matrix (Y_si) (Data presented are shown in Supplementary Table S1), and the fraction of SI matrix (ϕ_si)⁴³ as given by $S_{z} = - \frac{δ_{0} δ_{r}}{Y} E^{2} = - \frac{δ_{0} (ϕ_{s h e l l} δ_{r, s h e l l} + ϕ_{s i} δ_{r, s i})}{ϕ_{s h e l l} Y_{s h e l l} + ϕ_{s i} Y_{s i}} E^{2}$ (1)

when $d_{z} = 2 d_{s h e l l} + d_{s i}, ϕ_{s h e l l} = \frac{2 d_{s h e l l}}{d_{z}}, ϕ_{s i} = \frac{d_{s i}}{d_{z}}, δ_{r, s i} = p δ_{r, l i q u i d} + (1 - p) δ_{r, s o l i d}$ , $Y_{s i} \approx Y_{f o a m}$ , where d_z is the thickness of actuator and p is the porosity of the silicone foam, Equation (1) was developed as follows: $S_{z} = - \frac{δ_{0} (δ_{r, s h e l l} + \frac{d_{s i}}{2 d_{s h e l l}} (p δ_{r, l i q u i d} + (1 - p) δ_{r, s o l i d}))}{Y_{s h e l l} + \frac{d_{s i}}{2 d_{s h e l l}} Y_{f o a m}} E^{2} .$ (2)

The elastomer was incompressible, thus the relationship between thickness strain (S_z) and area strain (S_A) is $S_{A} = \frac{|S_{z}|}{(1 - |S_{z}|)} .$ (3)

For the sake of analysis, we set electromechanical efficiency as $β = \frac{δ_{r}}{Y} = \frac{δ_{r, s h e l l} + \frac{d_{s i}}{2 d_{s h e l l}} (p δ_{r, l i q u i d} + (1 - p) δ_{r, s o l i d})}{Y_{s h e l l} + \frac{d_{s i}}{2 d_{s h e l l}} Y_{f o a m}},$ (4)

so $S_{z} = - δ_{0} β E^{2} .$ (5).

Influence of SIS DEA structure parameters on actuation strain

Porosity of the silicone foam was related to the MR of porogen to silicone rubber, pore size, and foam thickness. As given in Table 1, when the foam thickness and pore size were constant, the actuation strain and the porosity increased with the exaltation in MR, whereas the Young's modulus (Y_foam) decreased with the exaltation in MR. In the case of the same MR and foam thickness, the larger the pore size, the higher is the foam porosity (Fig. 2A).⁴⁴ There was a skin layer with low porosity on the surface of the foam (Fig. 1D), and as the foam thickness decreased, the proportion of the skin layer increased, resulting in a decrease in porosity. When other parameters were constants, (pɛ_r,_liquid + (1 – p)ɛ_r,_solid) in Equation (4) would increase with the increase of the porosity (p in the equation), and the decrease in Y_foam would further enhance the β, thereby improving $| S_{z} |$ . See Supplementary Figure S4 for more details.

FIG. 2.

The relationship between foam thickness, pore size, and porosity of the silicone foam (A), the silicone foam Young's modulus (B), and maximum actuation strain (C).

Table 1.

Actuation Performances of SIS DEAs with Different Structural Parameters

MR	Pore size, μm	Foam thickness, mm	Shell thickness, mm	Porosity, %	Y_foam, MPa	Actuation strain at E_breakdown, %	E_breakdown, kV/mm
2:1	<75	1.0	0.75	46.6	0.424 ± 0.052	7.1	12.96
3:1	<75	1.0	0.75	53.1	0.347 ± 0.028	10.1	10.32
4:1	<75	1.0	0.75	68.5	0.134 ± 0.006	14.7	12.60
6:1	75–150	1.0	0.75	81.2	0.0600 ± 0.0059	18.7	13.06
		1.0	0.5	81.2	0.0600 ± 0.0059	35.7	19.01
		1.0	0.25	81.2	0.0600 ± 0.0059	36.4	16.66
		0.5	0.75	81.0	0.0612 ± 0.0028	42.0	20.15
		0.5	0.5	81.0	0.0612 ± 0.0028	30.4	22.68
		0.5	0.25	81.0	0.0612 ± 0.0028	71.8	27.72
		0.3	0.75	64.3	0.110 ± 0.017	22.3	22.84
		0.3	0.5	64.3	0.110 ± 0.017	28.3	22.95
		0.3	0.25	64.3	0.110 ± 0.017	31.9	14.26
6:1	150–200	1.0	0.75	81.9	0.0550 ± 0.0127	43.6	16.26
		1.0	0.5	81.9	0.0550 ± 0.0127	43.2	17.16
		1.0	0.25	81.9	0.0550 ± 0.0127	42.1	12.00
		0.5	0.75	79.0	0.102 ± 0.016	45.5	18.59
		0.3	0.75	56.4	0.0579 ± 0.0079	20.3	17.71
6:1	200–250	1.0	0.75	88.1	0.0370 ± 0.0137	45.0	14.79
		1.0	0.5	88.1	0.0370 ± 0.0137	52.3	22.76
		1.0	0.25	88.1	0.0370 ± 0.0137	79.8	20.43
		0.5	0.75	79.0	0.0775 ± 0.048	28.5	20.72

The direction of the arrow is the direction in which the value increases.

MR, mass ratio.

The samples packaged with the 0.25 mm thickness shells had better actuation strain than those packaged with thicker shells (details discussed in Supplementary Fig. S5). If the pore size and foam thickness were fixed, as the d_shell decreased sharply, β would increase significantly, thereby enhancing the actuation performance.

Fabrication of two types of ray-inspired robots

According to the previous study on structural optimization of SIS DEA, we chose the SIS DEA with the following structural parameters: pore size = 200–250 μm, porosity = 88.1%, d_bi = 1.0 mm, and d_shell = 0.25 mm as the actuation muscles of ray robots. As given in Figure 3, a simple means to produce ray-inspired soft robots was demonstrated. Ray robot 1 was created by replacing a pair of muscles in the fins by two pieces of cuboid SIS DEAs, whereas ray robot 2 was created by replacing the muscles in chest and abdomen by discoid and oval disk SIS DEAs, respectively, as given in Figure 3B.

FIG. 3.

Schematic of ray-inspired robots preparation processes. (A) Fabrication process of SI matrix; (B) fabrication process of two kinds of ray robots and the predicted swimming postures of the ray robots. The squares and circles correspond to where artificial muscles replace natural ray muscles. SI, solid–liquid interpenetrating.

The out-of-plane deformation of the SIS DEA drove the body of the ray robot to slap the surrounding liquid. The resulting up-and-down flaps of the fins and undulatory movement of the soft body led to the forward propulsion of the ray robot. The MEMS module in the COMSOL software was used to simulate the deformation performance of two ray robots under different voltage (as given in Fig. 4). Steady-state research was used to calculate the electromechanical force after the multiphysics coupling between solid mechanics and static electricity on the ray model. The material model used for the solid part in these simulations was liner elastic material model.

FIG. 4.

Steady-state simulation results of two ray models. (A) Scatter plot of the Max out-of-plane displacement versus voltage; (B) the out-of-plane deformation of two ray models under V = 0 and 20√2 kV.

Electro-swimming performance of two kinds of ray robots

The electro-swimming performance of two kinds of ray robots was investigated by applying a sine wave voltage range from 0 to 20√2 kV with the frequency of 0.2 to 10 Hz on the ray robots, and the swimming posture and velocity of the ray robots were recorded by cameras. The postures of two types of ray robots before and after actuation at a frequency of 0.3 Hz were consistent with the steady-state simulation results as given in Figures 4B and 5 (Supplementary Videos S1 and S2). In addition, the simulated plot of out-of-plane displacement versus voltage (Fig. 4A) was similar to that of actuation strain versus voltage (Fig. 1F). There was also a rapid increase process similar to the pull-in process. The lower electrode of the ray model was set as a fixed constraint area, so the deformation of the active area was constrained.

FIG. 5.

The swimming postures of ray robot 1 and ray robot 2 (frequency = 0.3 Hz). (A, D) The side and top view before test; (B, E) the side and top view at maximum actuation deformation state; (C, F) the side and top view after test.

Besides, the liner elastic material model was based on the small deformation assumption, which made Young's modulus invariant with strain during the calculation. But the modulus in the large strain range was smaller than that in the small strain range according to uniaxial tensile test results (Supplementary Fig. S6). Therefore, the simulated result of out-of-plane displacement of the ray model was lower than the test result of the ray robot. Overall, the electro-deformation of the SIS DEAs induced by the electromechanical force generated the out-of-plane displacement of the ray robot.

To achieve electro-swimming of the ray robots using the out-of-plane deformation, a periodically changing driving voltage was necessary. When the driving voltage was fixed, the swimming speed of ray robot was closely related to the driving frequency and the shape of the SIS DEA. The speed–frequency curve of both types of ray robots showed that the optimal frequency to achieve the fast swimming speed was not the maximum frequency (Fig. 6). The nonmonotonicity of this curve was caused by the dynamic competition between thrust and fluid drag at different frequencies.² The highest velocity of ray robot 1 was 3.6 mm/s at 0.5 Hz, whereas the highest velocity of ray robot 2 was 5.7 mm/s at 0.6 Hz. The swimming postures of the two ray robots at highest velocity were recorded in Supplementary Videos S3 and Video S4, respectively.

FIG. 6.

The velocity of ray robots under different driving frequencies range from 0.2 to 10 Hz. Velocity versus frequency of ray robot 1 (A) and ray robot 2 (B).

In higher frequency regions, the velocity of the ray robot was negligible. Owing to the viscoelasticity of the actuator material, the deformation of the actuator could not keep up with the changes in stress generated by the electric field at higher frequencies. The out-of-plane deformation of the SIS DEAs decreased rapidly, so they were unable to provide sufficient propulsion to drive the robot. In addition, the velocity of ray robot 2 was higher than that of ray robot 1 at lower driving frequencies (<1.0 Hz), which indicated that the structural design of ray robot 2 resulted in less hydrodynamic drag or stronger propulsion under lower driving frequencies.

However, the velocity of ray robot 2 was lower than that of ray robot 1 at higher driving frequencies (≥1.0 Hz), which could be owing to the asymmetrical deformation ability of the two pieces of SIS elastomers on ray robot 2. The deformation response hysteresis of the circular active region was more obvious than that of the elliptical region of ray robot 2, so the circular region had little deformation at high driving frequencies, preventing the ray robot 2 from moving forward. The above statement was consistent with the performance of two ray robots swimming at 2 Hz as shown in Supplementary Video S5.

By investigating the reported bionic manta ray robots (detailed in Table 2), it was found that half of them were rigid ray robots actuated by metal motors^{34–36,45–48} or shape memory alloy.³³ Compared with other soft actuators used to prepare soft bionic manta ray robots,^{2,8,32,37,38,49–51} the SIS DEA with SI structure as the actuator for the first time was used in our work as a kind of the soft biomimetic rays with good flexibility. The optimal driving frequency of the ray robots was consistent with the wing oscillation frequency of the natural manta ray (∼0.5 Hz³¹).

Table 2.

Comparison of the Ray-Like Robots

Actuator material, years	Actuator mechanism	Rigid bracket for actuator	Body flexible/soft/rigid	Tethered, yes/no	Maximum body length velocity, BL/s	Optimal driving frequency, Hz (test range)
Natural manta ray (2006)³¹	—	—	—	—	—	About 0.5
SIS DE (this study)	Electrostatic force	No	Flexible	Yes	0.033 (Rob. 1) 0.052 (Rob. 2)	0.5 (Rob.1) 0.6 (Rob. 2) (0.2–10)
VHB DE (2017)²	Electrostatic force	Need	Soft	No	0.69	5 (1–44)
SBAS DE (2021)³⁸	Electrostatic force	Need	Soft	No	0.45	1 (1, 2)
IPMC (2012)⁴⁹	Electro-ion migration	No	Soft	No	0.067	0.167 (0.05–0.9)
IPMC (2004)³²	Electro-ion migration	No	Rigid	Yes	0.038	0.4
Polyurethane (2015)⁵⁰	Pneumatic drive	—	Soft	Yes	0.13	4 (1–4)
Cardiomyocytes (2016)⁸	Photoactivated	—	Flexible	No	0.09	1.5–2 (1–4)
Cardiomyocytes (2018)³⁷	Electrical activation	Need	Flexible	Yes	—	0.5, 1.0, or 2.0
Shape memory alloy and PDMS (2021)⁵¹	Periodic current drive	—	Soft	No	0.25	0.25
Shape memory alloy (2009)³³	Periodic current drive	—	Rigid	No	0.23	0.62 (0.62–0.68)
Motor (2010)³⁴	Electrical motor	—	Rigid	No	1	12
Servomotor (2015)³⁵	Electrical motor	—	Rigid	No	1.783	0.9 (0.3–1)
DC motor (2015)³⁶	Electrical motor	—	Rigid	No	0.94	1 (0.4–1)
Servomotor (2015)⁴⁵	Electrical motor	—	Rigid	Yes	30 cm/s	—
Motor (2016)⁴⁶	Electrical motor	—	Rigid	No	0.58	1.4 (0.2–1.4)
Servomotors (2018)⁴⁷	Electrical motor	—	Rigid	No	0.82	2.5
Servomotors (2019)⁴⁸	Electrical motor	—	Rigid	No	0.66	0.5 (0–0.5)

IPMC, ion-exchange polymer metal composite; SIS DE, solid–liquid interpenetrating silicone-based dielectric elastomer; PDMS, polydimethylsiloxane; SBAS, styrene-butadiene-acrylonitrile-styrene; VHB, very high bonding.

Different from the viscoelastic polyacrylate-based DE (including very high bonding DE² and styrene-butadiene-acrylonitrile-styrene DE³⁸), SIS DE had a faster electro-response rate. Therefore, SIS DE generated considerable electrical deformation in time at a lower driving frequency, whereas the polyacrylate-based DE had better actuation performance at higher driving frequencies. In addition, the polyacrylate-based elastomer must be prestretched when it was served as an actuator and the prestretched film had to be fixed with rigid brackets, which brought inconvenience to the robot preparation process and structural design.

Swimming mechanism of the ray robots

For a more intuitive understanding of the swimming mechanism of the ray robot actuated under the electric field, we simulated the flow field surrounding the electro-swimming ray robot with Computational Fluid Dynamics module in the COMSOL software. The Ray Model 2′ was established by referring to the geometric structure parameters of the ray robot 2 as given in Figure 7A. The calculation model was established by multiphysics coupling, and the transient solver was used to calculate the moving velocity of the Ray Model 2′ and fluid velocity distribution under different driving frequencies. Figure 7C–O shows the fluid velocity distribution on the plane Y-Y′ in Figure 7A.

FIG. 7.

Simulation model and result of Ray Model 2′. (A) Geometric model of Ray Model 2′; (B) mesh distribution of Ray Model 2′; (C–O) simulation result of the fluid velocity field on the plane Y-Y′ in (A). The circles indicate vacuum zones and arrows indicate the development and formation of vortices in the flow field.

When the voltage rose, the head and tail of Ray Model 2′ underwent more obvious upturning deformation, which caused a low-speed or vacuum zone, as shown in the red circle area in Figure 7E. Therefore, as the deformation of Ray Model 2′ restituted, the surrounding fluid would move quickly to fill the vacuum zone, forming a high-speed vortex under the body of Ray Model 2′, pushing it upward, as given in Figure 7F.

Moreover, the influence of multiple driving frequencies of 0.2–10 Hz on the moving velocity of Ray Model 2′ and the fluid velocity field was studied, as given in Figure 8 (details in Supplementary Fig. S7). We chose four representative driving frequencies to analyze the simulation results (Fig. 8). From Figure 8A–L, it can be seen that as the frequency increased, the displacement of Ray Model 2′ first increased and then decreased. The fluid velocity field revealed that as the frequency increased, the high-speed vortex area below Ray Model 2′ first increased and then decreased. The higher the frequency, the more asymmetrical is the high-speed vortex area. In addition, the high-speed vortex in the head area was more intense than that in the tail area. This resulted in an upturned swimming posture of Ray Model 2′, which led to the model gradually moving upward and backward.

FIG. 8.

The simulation results of the fluid velocity field and the moving velocity of Ray Model 2′ under different driving frequencies. The fluid velocity distribution under 0.3 Hz (A–C), 0.6 Hz (D–F), 1.0 Hz (G–I), and 6.0 Hz (J–L); (M) The moving velocity of Ray Model 2′ under different driving frequencies.

The swimming posture of Ray Model 2′ was consistent with the swimming posture of ray robot 2. Under high driving frequency, Ray Model 2′ was not able to recover from deformation instantly and deformed rapidly again, resulting in the decrease in the flapping amplitude of the Ray Model 2′. Thus, the high-speed vortex area below Ray Model 2′ developed slowly, and swimming velocity was low. The viscoelasticity of the SIS DEA caused the hysteresis response of Ray Model 2′ to high-frequency alternating driving voltages. These results matched the experimental results of ray robot 2 as explained before. Additional intuitive simulation results are given in Supplementary Video S6, in which the simulation result was treated by three-dimensional mirroring. Owing to the asymmetry of the head and tail parts of Ray Model 2′, the deformation recovery speed of the head and tail parts was different, which made the high-speed vortex area develop asymmetrically.

In addition, the moving velocity of Ray Model 2′ first steadily increased as time increased, but then began to change periodically in sine waveforms. At the initial stage, it took some time to generate a stable high-speed vortex field for the disturbance of the fluid surrounding the Ray Model 2′. As the high-speed vortex area expanded, the moving velocity of Ray Model 2′ improved steadily. The sine wave moving velocity curve of Ray Model 2′ was affected by the sine wave driving voltage in Figure 8M. The simulated value of the moving velocity was higher than that of the experimental value. This was because the simulated model removed the two wires at the tail of the real object to simplify the calculation. The weight and moving resistance of Ray Model 2′ was smaller than that of ray robot 2, and the gravity center of Ray Model 2′ was shifted compared with that of ray robot 2.

Conclusions

In summary, we developed two types of soft ray-inspired robots without any rigid frames by replacing the natural muscles of rays with SIS DEAs. The SIS DEA was composed of a solid–liquid interpenetrating silicone-based matrix sandwiched by silicone elastomer film (SIS DEA). The test results indicated that a higher foam porosity, larger pore size, thicker foam thickness, and thinner shell thickness were ideal for enhancing the actuation strain of the SIS DEA. The optimized SIS DEA had an actuation strain of 79.8% at 20.43 kV/mm in a freestanding state. This was used as the muscle of the ray robot. To imitate the swimming behavior of the ray, the effect of driving frequency on the velocity of the ray robot was explored. The ray robot achieved a maximum swimming rate of 5.7 mm/s when the driving frequency was ∼0.6 Hz.

In addition, the steady-state and the transient simulations were carried out to reveal the mechanisms of electro-swimming of the ray robot. The simulation result revealed that the actuation deformation of the SIS DEAs caused the electro-deformation of ray robot, and the periodical electro-deformation generated the high-speed vortex beneath the robot to push the ray robot forward. Therefore, the high actuation strain in a freestanding state and the shape customizability of the SIS DEA made it an ideal alternative to muscles for various soft robots.

Authors' Contributions

The concept and the research plans were designed by K. C. and J.Y. supervised the research. J.H.X. performed the experiments and developed the analytic model. J.H.X. wrote the article, and J.Y., Y.L.D., Z.Y.J., L.C.T., X.R.C., and K.C. revised the article.

Footnotes

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This study was supported by the National Key Research and Development Program of China (No. 2016YFB0302202) and the National Natural Science Foundation of China (No. 51673163).

Supplementary Material

References

Rus

, Tolley

. Design, fabrication and control of soft robots. Nature, 2015; 521:467–475.

, Li

, Liang

, et al. Fast-moving soft electronic fish. Sci Adv, 2017; 3:e1602045.

Hines

, Petersen

, Lum

, et al. Soft actuators for small-scale robotics. Adv Mater, 2017; 29:1603483.

Duraisamy

, Kumar Sidharthan

, Nagarajan Santhanakrishnan

. Design, modeling, and control of biomimetic fish robot: a review. J Bionic Eng, 2019; 16:967–993.

Whitesides

. Soft robotics. Angew Chem Int Ed, 2018; 57:4258–4273.

Tan

, Wang

, Xu

, et al. A fast, reversible, and robust gradient nanocomposite hydrogel actuator with water-promoted thermal response. Macromol Rapid Commun, 2018; 39:1700863.

, Wang

, Song

, et al. Bioinspired design of vascular artificial muscle. Adv Mater Technol, 2018:1800244.

Park

, Gazzola

, Park

, et al. Phototactic guidance of a tissue-engineered soft-robotic ray. Science, 2016; 353:158–162.

Mosadegh

, Polygerinos

, Keplinger

, et al. Pneumatic networks for soft robotics that actuate rapidly. Adv Funct Mater, 2014; 24:2163–2170.

10.

Acome

, Mitchell

, Morrissey

, et al. Hydraulically amplified self-healing electrostatic actuators with muscle-like performance. Science, 2018; 359:61–65.

11.

Kellaris

, Venkata

, Smith

, et al. Peano-HASEL actuators: muscle-mimetic, electrohydraulic transducers that linearly contract on activation. Sci Robot, 2018; 3:eaar3276.

12.

Schaffner

, Faber

, Pianegonda

, et al. 3D printing of robotic soft actuators with programmable bioinspired architectures. Nat Commun, 2018; 9:878.

13.

Takizawa

, Kanno

, Miyazaki

, et al. Grasping force estimation in robotic forceps using a soft pneumatic actuator with a built-in sensor. Sensor Actuat A Phys, 2018; 271:124–130.

14.

Kim

, Ko

, Park

, et al. Enhanced ferro-actuator with a porosity-controlled membrane using the sol-gel process and the HF etching method. Smart Mater Struct, 2016; 25:017001.

15.

Kim

, Ko

, Park

, et al. Development of a cantilever-type ferro-actuator using a porous PVDF membrane. Proc Inst Mech Eng C J Mech Eng Sci, 2016; 230:3594–3605.

16.

Brochu

, Pei

. Advances in dielectric elastomers for actuators and artificial muscles. Macromol Rapid Commun, 2010; 31:10–36.

17.

Carpi

, Kornbluh

, Sommer-Larsen

, et al. Electroactive polymer actuators as artificial muscles: are they ready for bioinspired applications?. Bioinspir Biomim, 2011; 6:045006.

18.

Meller

, Bryant

, Garcia

. Reconsidering the McKibben muscle: energetics, operating fluid, and bladder material. J Intell Mater Syst Struct, 2014; 25:2276–2293.

19.

Tolley

, Shepherd

, Mosadegh

, et al. A resilient, untethered soft robot. Soft Robot, 2014; 1:213–223.

20.

Wehner

, Truby

, Fitzgerald

, et al. An integrated design and fabrication strategy for entirely soft, autonomous robots. Nature, 2016; 536:451–455.

21.

Keplinger

, Kaltenbrunner

, Arnold

, et al. Capacitive extensometry for transient strain analysis of dielectric elastomer actuators. Appl Phys Lett, 2008; 92:192903.

22.

Pelrine

, Kornbluh

, Joseph

, et al. High-field deformation of elastomeric dielectrics for actuators. Mater Sci Eng C Biol Sci, 2000; 11:89–100.

23.

Carpi

, Bauer

, De Rossi

. Stretching dielectric elastomer performance. Science, 2010; 330:1759–1761.

24.

Huang

, Liu

, Zhao

, et al. Flexible electronics: stretchable electrodes and their future. Adv Funct Mater, 2019; 29:1805924.

25.

Kim

, Laschi

, Trimmer

. Soft robotics: a bioinspired evolution in robotics. Trends Biotechnol, 2013; 31:23–30.

26.

Chen

, Zhao

, Mao

, et al. Controlled flight of a microrobot powered by soft artificial muscles. Nature, 2019; 575:324–329.

27.

Christianson

, Goldberg

, Deheyn

, et al. Translucent soft robots driven by frameless fluid electrode dielectric elastomer actuators. Sci Robot, 2018; 3:eaat1893.

28.

Wang

, Huang

, McCoul

, et al. A soft breaststroke-inspired swimming robot actuated by dielectric elastomers. Smart Mater Struct, 2019; 28:045006.

29.

Pinskier

, Howard

. From bioinspiration to computer generation: developments in autonomous soft robot design. Adv Intell Syst, 2021; 4:2100086.

30.

Klausewitz

. The locomotive mode of stingrays (myliobatidae) [in German]. Zool Anz, 1964; 173:110–120.

31.

Brower

. Design of a Manta Ray Inspired Underwater Propulsive Mechanism for Long Range, Low Power Operation, in Mechanical Engineering. USA: Tufts University, 2006.

32.

Punning

, Anton

, Kruusmaa

, et al. A biologically inspired ray-like underwater robot with electroactive polymer pectoral fins. IEEE Int Conf Mech Robot, 2004; 2:241–245.

33.

Wang

, Wang

, Li

, et al. A micro biomimetic manta ray robot fish actuated by SMA. IEEE Int Conf Robot Biomim, 2009; 1–4:1809–1813.

34.

Zhou

, Low

. Better Endurance and load capacity: an improved design of Manta Ray Robot (RoMan-II). J Bionic Eng, 2010; 7:S137–S144.

35.

Chew

, Lim

, Yeo

. Development of propulsion mechanism for robot Manta Ray. IEEE Int Conf Robot Biomim, 2015; 2015:1918–1923.

36.

, Cai

, Wang

, et al. A biomimetic cownose ray robot fish with oscillating and chordwise twisting flexible pectoral fins. Ind Robot, 2015; 42:214–221.

37.

Shin

, Migliori

, Miccoli

, et al. Electrically driven microengineered bioinspired soft robots. Adv Mater, 2018; 30:1704189.

38.

, Chen

, Zhou

, et al. Self-powered soft robot in the Mariana Trench. Nature, 2021; 591:66–71.

39.

, Dong

, Jiang

, et al. Self-healing high-performance dielectric elastomer actuator with novel liquid-solid interpenetrating structure. Compos Part A Appl Sci, 2021; 149:106519.

40.

Zhao

, Wang

. Harnessing large deformation and instabilities of soft dielectrics: theory, experiment, and application. Appl Phys Rev, 2014; 1:021304.

41.

Pelrine

, Kornbluh

, Joseph

. Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation. Sensor Actuat A Phys, 1998:77–85.

42.

Hajiesmaili

, Clarke

. Dielectric elastomer actuators. J Appl Phys, 2021; 129:151102.

43.

Chortos

, Hajiesmaili

, Morales

, et al. 3D printing of interdigitated dielectric elastomer actuators. Adv Funct Mater, 2019; 30:1907375.

44.

Gibson

, Ashby MF

S FR

. The mechanics of three-dimensional cellular materials. Proc R Soc Lond Ser A, 1982; 382:43–59.

45.

Sfakiotakis

, Fasoulas

, Gliva

. Dynamic modeling and experimental analysis of a two-ray undulatory fin robot. IEEE RSJ Int Conf Intell Robot Syst, 2015; 2015:339–346.

46.

, Deng

, Osen

, et al. A bio-inspired swimming robot for marine aquaculture applications: from concept design to simulation. Oceans, 2016:1–7.

47.

Zhang

, Wang

, et al. Design and control of bionic Manta Ray robot with flexible pectoral fin. In: 2018 IEEE 14th International Conference on Control and Automation (ICCA), Anchorage, AK, USA: IEEE. 2018, pp. 1034–1039.

48.

Cao

, Lu

, Cai

, et al. CPG-fuzzy-based control of a cownose-ray-like fish robot. Ind Robot, 2019; 46:779–791.

49.

Chen

, Um

, Bart-Smith

. Bio-inspired robotic manta ray powered by ionic polymer–metal composite artificial muscles. Int J Smart Nano Mater, 2012; 3:296–308.

50.

Urai

, Sawada

, Hiasa

, et al. Design and control of a ray-mimicking soft robot based on morphological features for adaptive deformation. Artif Life Robot, 2015; 20:237–243.

51.

Kim

, Heo

, Choi

, et al. Shape memory alloy-driven undulatory locomotion of a soft biomimetic ray robot. Bioinspir Biomim, 2021; 16:066006.

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