CONTENTS

Introduction

1. Electroresponsive polymer materials

1.1. Maxwell pressure

1.2. Electrostriction

2. On the role of engineering design in the development of soft robots

2.1. Additive manufacturing technologies

2.2. Application of numerical methods in the development of soft robots

3. Application of electroresponsive materials for robotic devices

Conclusions

INTRODUCTION

The diversity of the biological and animal world, its perfection and incredible versatility have led to the emergence of nature-like technologies [1–3], which should recreate the processes of wildlife for obtaining novel materials and devices. The nature-like paradigm is reflected in various scientific and social fields, such as green chemistry [4], energy [5, 6], biotechnology [7, 8], medicine [9, 10], modern nanocomposites [11, 12], and information technologies (neural networks) [13].

One of the vivid examples of nature-likeness is soft robotics, a section related to the design of robotic systems from soft materials, which provides flexibility and adaptability in performing tasks [14]. A significant advantage of soft robots compared to rigid ones is greater safety when interacting with people. The main direction in the development of soft robotics is the solution of special tasks in medicine during minimally invasive surgery and the postoperative rehabilitation of patients, for biomimicry in ocean research or in space in order to collect scientific information, as well as for intelligence and military purposes. Many of these applications are associated with the operation of robots in nonstandard environmental conditions, which requires the formulation and solution of unique problems of mechanics, and the search for and development of novel materials. A fundamental feature of such robots is the greater number of degrees of freedom (ideally infinite, as in real living systems) compared to six (three rotational and three translational) in classical rigid robotics [15].

The main components of a soft robot are a power source, elements of movement and interaction with the outside world, systems of masking and protection from external influences, as well as control, operation and feedback [16]. Currently, approaches have been developed to implement all of the above elements. A detailed description of the corresponding principles has been considered in several reviews [15, 17, 18] and is not the subject of this work. Thus, the development of a fully autonomous, biosimilar soft robot is a matter of the foreseeable future. However, in practice, researchers have encountered a number of experimental and engineering difficulties, which have led to intense scientific research in the materials science industry.

Actuators are key components for the movement and control of any mechanical system. However, materials commonly used in robotics (metals, polymers, composites) have elastic-modulus values that are 2–3 orders of magnitude higher than the tissues of living organisms (skin, muscle tissue, ligaments, and tendons) [19]. Therefore, an urgent task is to develop novel materials that operate on other principles, with characteristics (including mechanical) comparable to biological objects, especially in relation to the movement, safety and energy efficiency of the developed devices. The movement and interaction of a soft robot with the environment can be carried out due to several principles: the use of materials with shape memory, the use of pneumatic or hydraulic systems, electrostriction, phase transition, as well as jet motion caused by the occurrence of “explosive” chemical reactions [17, 19, 20]. The most promising approaches under active development, apparently, are pneumatic systems and electroactive-polymer materials. The disadvantage of pneumatic systems is the need to use often bulky auxiliary equipment, such as a compressor, to generate pressure and fill channels in structural elements made of polymer material. The implementation of such an approach to the movement and interaction of a soft robot with the environment is difficult and practically impossible when performing deep-sea tasks in the ocean or deep space. In recent decades, “smart” or stimuli-responsive materials that can change their properties under external influence have attracted much attention [21]. Such materials include polymer gels, films, and fibers that change their shape when an electric field is applied: electrostrictive, piezoelectric, conductive materials, etc. Nevertheless, despite the active development of “smart” materials science for soft robotics, there is no mass production of soft robots yet. Research is underway to develope novel electroresponsive materials with the subsequent design of structural elements of soft robots based on them. This review is devoted to generalization of the properties of modern electroresponsive materials and the analysis of promising approaches to the manufacturing of actuators for soft robotics.

1 ELECTRORESPONSIVE POLYMER MATERIALS

The electroresponsive polymer materials used to produce soft-robot actuators include dielectric [22], electrostrictive [23], liquid-crystal polymers [24], ionic polymers and composites [25], electrorheological fluids [26], and stimuli-responsive gels [27]. Each of these types of materials is a separate area of materials science worthy of special consideration, however, within the framework of this review, we will focus on the basic principles and recent achievements in only two of these areas: dielectric and electrostrictive polymer materials.

1.1 Dielectric Elastomers. Maxwell Pressure

Dielectric elastomeric materials usually include organosilicon (silicones), polyurethane and polyacrylic rubbers capable of large reversible deformations [28]. The principle of operation of such materials is based on the Maxwell pressure that arises between oppositely charged electrodes applied to a polymer film due to the electrostatic force [29]. In this case, pressure arises, the elastomer contracts in the axial direction and expands in the radial direction (Fig. 1):

$${{\sigma }_{{\text{M}}}} = {{\varepsilon }_{0}}{{\varepsilon }_{{\text{r}}}}{{\left( {\frac{E}{d}} \right)}^{2}},$$

where σM is the Maxwell pressure in the film, ε0 is the dielectric constant (8.854 × 10−12 F/m), εr is the relative permittivity of the material, E is the strength of the electric field applied to the sample, and d is the film thickness.

Fig. 1.
figure 1

Principle of operation of Maxwell pressure. When an electric field is applied to a dielectric elastomer, pressure is generated, leading to axial compression and radial expansion.

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One of the most important scientific tasks in the development of artificial muscles based on dielectric elastomers is the transition to low actuation voltages (less than 1 kV) [30–32], which will increase the safety of devices based on such artificial muscles and replace expensive high-voltage equipment with cheaper variants. Currently, such attempts are being made in several directions. For example, this may be achieved due to an increase in the dielectric constant [33, 34], a decrease in the elastic modulus [35], and a decrease in film thickness [31, 36–38]. In this case, another important task in creating an actuator based on dielectric elastomers is the deposition of a flexible electrode layer. Films and coatings with conductive additives based on carbon or metal particles, such as carbon black [39], graphite and its derivatives [40], carbon nanotubes [41], silver powders [42], etc., are used as materials for electrodes. The main problems are poor adhesion of the conductive layer to the elastomer and destruction of the percolation network of particles during operation, which leads to conductivity loss [43]. As solutions, it is proposed to apply an electrode layer on predeformed membranes, as well as to use particles with a high aspect ratio as fillers, which makes it possible to preserve the percolation network during material deformation. By the example of individual studies, we will consider in more detail existing approaches to the manufacturing of dielectric elastomeric materials and an increase in their efficiency.

The study [44] considered a method for obtaining anisotropic dielectric elastomer films from an amorphous poly(styrene-b-butyl acrylate-b-styrene) triblock copolymer (Mn = 150 kDa, PS145-b-PBA940-b-PS145, 20 wt % of polystyrene). The copolymer was obtained by RAFT polymerization with reversible chain transfer. The films were obtained by pouring from a solution of tetrahydrofuran (10 wt %), followed by uniaxial stretching by factors of 2, 4, and 6, and annealing at 120°C for 8 h. The annealing temperature was chosen above the glass-transition temperature of the polystyrene blocks (100°C), but below the order-disorder transition for this copolymer (200°C). When the films were cooled to ambient temperature, shrinkage by 10–20% was observed. Microphase separation during the formation of thin films leads to the appearance of polystyrene domains that play the role of physical crosslinks (Fig. 2a). The tensile strength and Young’s modulus of the material increased in the stretching direction depending on the stretching ratio from 3.0 to 12.8 and from 0.3 to 2.9 MPa, respectively, while maintaining the initial mechanical characteristics in the perpendicular direction (Figs. 2c and 2d). Usually, improvement in the mechanical properties is associated with a change in the conformation of polymer chains during stretching and the appearance of orientation, which is often observed in plastic materials. For elastomers, the stretched conformation of polymer chains cannot be easily fixed; therefore, in this case, the reinforcing effect in the stretching direction was associated with a change in the morphology and orientation of the polystyrene domains. Coatings of single-walled carbon nanotubes were used as electrodes in studying the film response to an electrical stimulus. The anisotropy of the mechanical characteristics of preliminarily stretched films led to more significant deformations of the film in an electric field in the direction perpendicular to stretching (Fig. 2e). On the basis of the obtained materials, a soft gripper with high maneuverability at a response voltage in the subkilovolt range (~800 V) (Figs. 2f–2h) was developed, which is significant progress in improving the safety of elastomeric actuators.

Fig. 2.
figure 2

Manufacturing process of PS145-b-PBA940-b-PS145 anisotropic films (a): schematic illustration of uniaxial tension and thermal annealing to obtain films with oriented PS domains. Scheme of manufacturing a multilayer composite material from prestretched films (10 active layers, 1 adhesive layer and 1 passive layer, width of 6 mm, length of 21 mm) (b). Mechanical testing of films in different directions depending on the degree of prestretching (L/l = 2, 4, and 6) (c, d). Deformation direction was parallel (D ∥ S) (c) or perpendicular (D ⊥ S) (d) to the orientation of the PS domains (stretching direction). Bending angle and curvature of actuators based on the initial and uniaxially stretched films (thickness of each layer 22 μm, L/l = 4) at different control voltages (е). Various deformation modes achieved for actuators due to different orientations of the PS domains: perpendicular, at an angle of 45°, and parallel to the length of the actuator (f–h). Adapted from [44] with permission from the Royal Society of Chemistry.

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In the study [36], electroresponsive materials that are active at lower potential values were proposed. An elastic element in the form of a flat membrane made of polydimethylsiloxane (PDMS) was molded on a polyethylene-terephthalate substrate with a layer of polyacrylic acid, which was subsequently removed. Before removing the layer of polyacrylic acid, layers based on PDMS filled with carbon black were deposited onto the elastomeric film as electrodes. A polymethyl methacrylate (PMMA) ring was used as an insulator and frame. With a significant decrease in the membrane thickness down to 3 μm, 7.5% deformation in the radial direction was achieved at an electric potential of 245 V. In the case of membranes, it is most rational to reduce the thickness (inverse quadratic dependence), since it is known from the relations of elasticity theory that

$${{\varepsilon }_{x}} = - \frac{{{{\varepsilon }_{z}}}}{2} = {{\varepsilon }_{0}}\frac{{{{E}^{2}}}}{{2Y}} = {{\varepsilon }_{0}}\frac{{{{V}^{2}}}}{{2t_{m}^{2}Y}},$$

where εz and εx are membrane deformations in the direction of the axes z (perpendicular to the plane of the membrane) and x, ε0 is the dielectric constant, Y is Young’s modulus, E is the strength of the applied electric field, and tm is membrane thickness. The relation also suggests that it is possible to increase the deformation by increasing the dielectric constant of the material. It was noted that with an increase in the membrane thickness from 3 to 30 μm, the required voltage for comparable deformation increases from 245 V to 3.3 kV. A lower response potential was achieved for a PDMS membrane with a single layer of a composite of multilayer carbon nanotubes with poly(thiophene) as an electrode [37]. When an electrical potential of 100 V was applied, a strain of 4% was achieved.

The lack of soft high dielectric elastomers that respond to a low voltage has long been an obstacle to the development of linear actuators. In the study [33], elastomers with not only high dielectric permittivity but also with good elastic and insulating properties were obtained and characterized. The advantages of the considered materials also include low cost and ease of molding into thin films (24 and 35 µm). When using elastomers based on polysiloxanes with polar nitrile and vinyl groups from polymethylvinylsiloxane and 2,2'-(ethylenedioxy)diethanethiol (CL2) and pentaerythritol tetrakis(3-mercaptopropionate) (CL4) in the form of membranes molded on a polyvinyl chloride (PVC) substrate, it was possible to achieve the stable deformation of membranes in the radial direction up to 13% at a field strength of 13 kV/mm for a material with an elastic modulus of 350 kPa, tanδ = 0.007 at a frequency of 0.05 Hz. Results for a stiffer material with an elastic modulus of 790 kPa with stable membrane deformation in the radial direction up to 10% at field strengths up to 41 kV/mm were also presented. Based on the materials obtained, an actuator with a noticeable response at low voltages below 200 V was developed.

Another approach to enhance the Maxwell effect in dielectric elastomers is through obtaining composite materials. For example, materials for artificial muscles based on γ-methacryloxypropyltrimethoxysilane (commercial designation KH570) and composites containing up to 50 wt % particles of barium titanate, which is also a precursor during vulcanization, were studied in the study [35]. A round membrane was used as a test specimen. Films with different amounts of the crosslinking agent hydrogenated xylylene diisocyanate (TAKENATE 600) were obtained under pressing at 15 MPa, followed by vulcanization at a temperature of 140°C for 5 h in vacuum. Graphite powder in silicone oil was applied to the surface as electrodes. As a result, due to the introduction of a filler, it was possible to achieve high values of the dielectric constant of the material while maintaining low values of the elastic modulus. Large deformations of the material (up to 26%) were achieved at a filler content of 10 wt % and electric-field strength of 12 kV/mm. It has been shown that all composite materials are more sensitive to an external stimulus compared to the commercial dielectric elastomer VHB4910 (3 M, acrylic rubber) for a conical actuator at a comparable electric-field strength. Samples with a higher mass fraction of barium titanate (30 and 50 wt %) exhibited a deformation of up to 10% at an electric-field strength of up to 17 kV/mm. However, the operating potential range for composite materials is lower compared to commercial unfilled analogs. Much emphasis in the study was placed on an attempt to reduce the modulus of elasticity of the material for artificial muscle. The modulus of elasticity of the elastomer matrix is difficult to effectively reduce only by increasing the mass fraction of the plasticizer, since the stability of the response deteriorates. However, some research in this direction is underway. For example, adding 0.01 wt % dimethylsiloxane oil to a composite with titanium dioxide made it possible to obtain a homogeneous composition at the molecular level and significantly reduced the elastic modulus of the dielectric elastomer composites from 820 to 95 kPa [45].

Recent scientific studies are devoted to investigation of the operation durability of dielectric elastomer-based actuators under cyclic loading. For example, in the study [46], a dielectric elastomer based on cyanoethyl cellulose added to PVC gel was developed. This composition was selected to increase the conductivity of the final product and reduce viscoelastic effects (reduction in the mechanical-energy loss in terms of the loss tangent tanδ). The commercial acrylic elastomer (3 M VHB) were used as reference. The experimental sample was a thin membrane. In bench tests, the actuator showed deformations of ~12% at field strengths up to 9 kV/mm, and the drift effect of the viscoelastic properties at a frequency of 1 Hz was only 3.5% over 1000 cycles compared to 232% over 500 cycles for the 3 M VHB actuator. It is important that the return force in the sample reached 300 g, i.e., the membrane, after removing the stress, was able to return to its initial state with a load of 300 g.

The electrical conductivity of the material under cyclic deformations was retained for a nonwoven polymer mat [47]. The composite membrane was fabricated by electrospinning from a poly(styrene-b-butadiene-b-styrene) copolymer (Mn = 142 kDa, 28.4 wt % polystyrene, which corresponded to the PS195-b-PB1880-b-PS195 composition). The conductivity was increased by saturating the nonwoven material with a solution of a silver-containing precursor (a solution of silver trifluoroacetate in ethanol) followed by the in situ reduction of nanoparticles with a hydrazine solution, leading to the appearance of a percolation network both on the surface and inside the polymer fibers. The silver content in the final material was 62 wt %. It is important to note that polystyrene blocks did not form microdomains due to rapid evaporation of the solvent during spinning: fiber formation occurred before the self-organization of polymer chains. Heating the material up to 150°C led to an increase in the mobility of polymer chains and phase separation, while silver nanoparticles migrated from the bulk of the fiber to the surface, and the electrical conductivity of the material decreased significantly at a deformation of 30%. Despite the fact that the conductivity during deformation of the mats varied in a wide range from 5500 to 71 S/cm with deformations from 20 to 140% and a change in the thickness of the samples from 150 to 30 μm, it was possible to achieve a stable conductivity value during cyclic tensile tests of the membrane. The number of cycles reached 300 for all levels of deformation, and the conductivity remained almost constant. The study also presented an approach for applying a conductive layer to the membrane by sputtering onto a mask.

The prospects for the use of silver nanofibers as a conductive layer were demonstrated in study [48]. A two-layer composite in the form of a grid on a PDMS substrate was obtained: a layer of a mixture of poly(styrene-b-butadiene-b-styrene) with silver nanofibers acted as an electrode, and the outer layer of the copolymer was an insulator. Changing the mesh pattern made it possible to control its mechanical characteristics, and the formation of a domain structure of conductive and nonconductive fragments allowed the creation of an implant that supports the contractile function of the heart and is stimulated by an electrical impulse. Despite the fact that in the last two studies the change in the mechanical characteristics of the materials under the action of an electric field was not studied, the considered works contain extremely important results and show the stability of the properties of elastomeric materials during cyclic operation, as well as the fundamental possibility of controlling the properties of the final product by changing the composition and topology of elements.

It is obvious that the structure of composite elastomeric materials is of decisive importance in the formation of products with increased electrical activity, so structural studies become fundamentally necessary to develope such materials and understand the physical-chemical foundations of their operating. A promising tool for studying the structure of composite dielectric elastomers, including those subjected to the action of an external stimulus, are in situ studies of small-angle X-ray scattering (SAXS). The change in the structure of thermoplastic elastomer gels of the poly(styrene-b-ethylene-butylene-b-styrene) block copolymer (Kraton G1650, Mw = 110 kDa, 29.2 wt % of polystyrene, which corresponds to the composition PS155-b-PEB930-b-PS155) or its functional copolymer with maleic-anhydride ester (Kraton FG1901X, PS160-b-(PEB-g-MA)900-b-PS160), with an anhydride content of 1 wt %, under the action of an electrical stimulus was studied previously [49]. The polymer content in the gel was 20–40 wt %. White mineral oil was used as a plasticizer. These commercially available copolymers have a very narrow molecular-weight distribution (polydispersity index of <1.05). The structure of the gels depends on the molding temperature: at a temperature close to room temperature, the gel has a pronounced structure of a disordered micellar network; and if the gel is obtained by heating and uniaxial stretching (pressing at a temperature above 100°C), it has a body-centered-cubic structure. The presence of an ordered structure makes such gels a convenient object for X-ray diffraction studies. It is known that when thermoplastic elastomers are stretched, a correspondence between the deformation at the microlevel and the macrodeformations of the sample occurs. When an electric field is applied to a sample, it becomes thinner and its longitudinal dimensions increase due to the Maxwell pressure. The change in the position of the SAXS reflections under the action of a field indicates deformation of the structure. The results showed that regardless of the direction of deformation and the degree of orientation of micelles in the structure, when an electric field is applied, radially isotropic expansion is observed in the samples. The change in the distance between the domains significantly depends on the concentration of the polymer in the gel, which made it possible to reveal the dependence of deformations on the composition and control the properties of the obtained materials. It was also noted that the strain values obtained from the SAXS data are closest to the true ones, since they exclude translational motion, as well as bending, which leads to an overestimation of the value when using the classical laser-probing method.

In recent years, there have been no significant breakthroughs in the development of new dielectric elastomers for use as actuators [50–53]. Despite this, publication activity in this field is very high. At present, it is impossible to ensure movement under a sufficiently large load only using dielectric elastomers; therefore, variants of hybrid actuators are often found in publications, which, among other things, use the classical Maxwell pressure effect. In the study [54], a hybrid actuator with a dielectric elastomer and a pneumatic system is considered. This actuator was an air pseudospring; between two membranes made of dielectric elastomer, there was a cavity with air under pressure. The variant with preliminary inflation of such hybrid actuators is quite common in publications, since it allows a high level of response from the entire system to be obtained [55–58].

Thus, at present, the field of dielectric elastomeric materials for soft-robotic actuators has undergone serious development. The main areas of research are related to increasing the response of materials to an electrical stimulus by adjusting various parameters: the permittivity of the material, its topology and thickness, as well as mechanical characteristics.

1.2 Electrostriction

Another promising principle for developing soft actuators is the use of electrostrictive polymer materials capable of rapid and reversible deformation under the action of an electric field. Electrostriction is deformation (elongation) of the body in the direction of the electric field due to the accumulation and separation of charges in the material.

Ferroelectric and piezoelectric copolymers and filled systems have been widely developed. The principle of operation of these materials is associated with the heterogeneity of the structure, namely, the presence of an electroresponsive domain, which causes the different mobility and polarizability of components or segments [59]. The development of such materials is also difficult to imagine without high-precision structural studies using mega-science facilities, for example, a synchrotron. Currently, scientists around the world are actively using an integrated approach to identify the structure–property relationship when developing electroresponsive materials.

Polyurethane elastomer matrices are promising for electroresponsive elements of soft robotics. In the study [60], the effect of the solvent (1‑methyl-2-pyrrolidone and N,N-dimethylformamide) on the structure and electrostrictive activity of polyurethane composite films (Estane 58888-NAT 021) consisting of 4,4'-methylene diphenyl isocyanate and 1,4-butanediol as hard segments and polytetramethylene oxide (Mw = 1 kDa) acting as soft blocks was studied. The content of hard segments was ~46 wt %. Polyaniline emeraldine salt grafted onto lignin was used as a filler; the particle size was 2–3 μm. Polymer films were obtained by pouring from a solution with curing at 60°C for 24 h and subsequent annealing at 125°C for 3 h. The thickness of the obtained films was ~80 μm. The application of an electric field led to film deformation. The dependence of the electrostrictive response on the electric-field strength was quadratic; however, when the field strength exceeded 4 kV/mm, it barely changed. This was associated with saturation of the polarization of dipole moments in the heterogeneous polyurethane matrix and the mobility of rigid segments. The SAXS results showed an increase in the distance between hard domains in the film structure with an increase in the filler concentration, which was associated with processes of phase separation and particle agglomeration. It was found that the distances between hard domains were greater for samples prepared from 1-methyl-2-pyrrolidone. Obviously, this solvent led to more pronounced aggregation and the formation of ordered crystalline domains when obtaining the material. It is likely that hydrogen bonds between adjacent rigid segments promoted aggregation. Studies of the mechanical characteristics of the composite materials have shown that films obtained from 1-methyl-2-pyrrolidone have an increased electrostrictive activity. Thus, the pronounced domain structure of polymer films increases the response of the material to an external stimulus.

In the study [61], the effect of the morphology of polyurethanes based on a copolymer of butadiene with acrylonitrile and hydroxyl terminal groups (Mw = 3.5 kDa, content of cyano groups is 13.9 wt %), hexamethylene diisocyanate, and linear aliphatic dihydric alcohols with different chain lengths on their dielectric and electromechanical properties was studied. The alcohols acted as “stretchers” of the chain of the rigid isocyanate block. Ethylene glycol, 1,4-butanediol, and 1,6-hexanediol were used in the study. Polyurethane materials were prepared by reacting hexamethylene diisocyanate and a copolymer at 70°C for 2 h to form an isocyanate-terminated precursor. Then, the obtained precursor was reacted with the selected type of dihydric alcohol at 60°C for 2 h to form the desired product. The final polyurethanes were cured under vacuum at 80°C for 12 h and pressed at 200°C to obtain films 100–200 µm thick. The content of the hard segments was 37.6, 40.0, and 42.2 wt % for materials with ethylene glycol, 1,4-butanediol, and 1,6-hexanediol, respectively. Wide-angle X-ray-scattering data made it possible to reveal the influence of the alcohol chain length on the crystal structure and microphase separation in polyurethane films. The X‑ray diffraction patterns of the polyurethane elastomer sample with ethylene glycol showed weak peaks at 6.7° and 20.8°, corresponding to interplanar distances of 13.3 and 3.9 Å, respectively. The profile of the sample with 1,4-butanediol showed diffraction peaks at 20.5°, 22.2°, and 24.1°, while the profile of polyurethane with 1,6-hexanediol showed diffraction peaks at 11.8°, 19.8°, 21.6°, and 23.7°. The degree of crystallinity and crystallite size of the polyurethane films depended on the chain length of the rigid segments. The structural features of the films with microphase separation were also studied by the SAXS method, which showed the presence of a large period between the hard and soft domains perpendicular to the lamellae. The presence of two peaks (at small and very small angles) suggested the formation of two periodic structures and indicated the multiphase structure of polyurethane films, which included a crystalline phase and microphase separated hard and soft domains. The different intensity and position of the reflections for the samples synthesized with different alcohols indicated different degrees of microphase separation, which was reflected in the electromechanical characteristics of the materials: the electrostrictive coefficient Q at a frequency of 1 Hz varies in terms of absolute value from 1.22 × 104 to 2.92 × 104 and 8.48 × 104 m4/C2 for samples with ethylene glycol, 1,4-butanediol, and 1,6-hexanediol, respectively. The deformation of films under the action of an electric field is associated with the simultaneous action of Maxwell pressure and the electrostriction effect, while the contribution of electrostriction to the total actuation deformation is from 64 to 76% at a field strength of 40 kV/mm, depending on the composition of the film.

Block copolymers and composites based on polyvinylidene fluoride (PVDF), which exhibit a giant electrostrictive response on account of the large dipole moment of the monomer unit due to the electronegativity of fluorine atoms, hold great promise for soft-robotic actuators [62]. A significant contribution to the study of the properties of ferroelectric polymers, in particular PVDF and a number of its copolymers, was made by Kochervinsky et al. [63–66]. Materials based on PVDF and its copolymers change their electrophysical characteristics with extremely low mechanical impact. They are also characterized by a reversible mechanical response to a pulsating electromagnetic field [67]. Ferroelectric polymers based on PVDF can crystallize in the form of various polymorphs: α (II), αp (IV), β (I), γ (III), which differ in the type of chain packing in the unit cell. In this case, the type of phase depends on various parameters, such as the concentration of the polymer in the solution, the type of solvent, temperature, crystallization rate, etc. The balance of crystalline phases, as well as their transformation under mechanical or electrical action, determine the ferroelectric properties of the material [68]. For example, due to the polycrystalline structure of the β-PVDF film, after polarization, piezoelectricity is detected with a nonclassical mechanism that persists for a long time, which makes it possible to consider products based on them simultaneously as a sensor and a sonar actuator that implements both electric and acoustic and/or electro-acoustic stimulation. Particular attention is paid to the influence of the structure of PVDF copolymers. The function of changing the film thickness in the general case should have two components, one of which is related to the fundamental frequency ω, and the other, to its harmonic 2ω. For example, a piezoresponse signal at the second harmonic, caused by the manifestation of the electrostriction effect, was found on ferroelectric polymer samples [69]. In the initial film, two types of regions were found that contribute to the measured signal. In an annealed film, the change in the nature of the piezoresponse signal at the second harmonic is associated with a change in the contribution to the macroscopic piezoresponse from the electrostriction effect. Review [70] considers the nature of large strains caused by electrostriction in modified fluorine-containing polymer ferroelectrics. A promising method for modifying materials is the irradiation of PVDF copolymers with trifluoroethylene (TrFE) by electrons with an energy of several megaelectronvolts. In this case, for isotropic films, the polarization hysteresis loop sharply decreases, and the decrease in film thickness does not depend on the direction of the applied field: the deformation mechanism does not correspond to a linear piezoelectric effect. Irradiation (both by electrons and protons) reduces the degree of crystallinity and leads to the transition of the ferroelectric phase to a relaxor state and a paraelectric phase. These structural changes are caused by the formation of new functional groups in PVDF chains upon radiolysis. It is shown that the increase in electrostrictive deformation after irradiation is associated with an increase in the proportion of the amorphous phase. This increased stress (all other things being equal) in oriented films compared to isotropic ones indicates that the field of the regions of the anisotropic amorphous phase (mesomorphic state) plays an important role. An analysis of the experimental data indicates that structural changes in the field (leading to electrostrictive deformations) are largely controlled by the segmental mobility of amorphous chains.

In the study [71], the possible mechanisms of the electroactive behavior of materials based on PVDF copolymers were considered. Random copolymers P(VDF-TrFE), 75/25) and the ternary copolymer poly(vinylidene fluoride-trifluoroethylene-chlorofluoroethylene) (P(VDF-TrFE-CFE); 62.2/30.2/7.6 mol %) were used. The average molecular weight of the copolymers was ~250 kDa with a polydispersity index of 2.5. Films with a thickness of 30–40 μm were obtained by pressing at a temperature approximately 30°C higher than the melting point: 190 and 160°C for the binary and ternary copolymers, respectively. Uniaxial stretching was performed at room temperature up to 500% at a rate of 18 mm/min. The resulting films had a complex structure, in which crystalline, oriented (OAP), and isotropic (IAP) amorphous phases can be distinguished. The content of the crystalline phase was ~25 and 35% for the double and ternary copolymer, respectively. When an electric field less than a certain critical value Ec is applied to the films, only the amorphous phase responds to the stimulus, and the conformation of the twisted polymer chain is transformed into a more extended conformation with dipoles oriented in the direction of the electric field, which leads to compression and stretching of the sample in the corresponding directions (Fig. 3a). There is no large hysteresis in this process, and this response can be regarded as true electrostriction. When ferroelectric domains are large and the applied electric field is close to Ec, switching occurs with a large hysteresis (Fig. 3b). Such switching cannot be considered true electrostriction, although it may also involve chain conformational changes during the process. However, when the ferroelectric domains are reduced to the nanometer scale, the hysteresis decreases, and in this case, the nanocrystals and OAP can be polarized at a rather weak electric field. As a result, the electrical repulsion and OAP lead to the elongation of the film in the transverse direction and compression in the longitudinal direction (Fig. 3c). To assess the contribution of various structural domains to the process of electrostriction, X-ray diffraction studies of the films were carried out. The SAXS data show different distances between the crystalline domains in the samples, equal to 7.8 and 9.5 nm, respectively, which is associated with different chain lengths of the double and ternary copolymers. The corresponding X-ray-scattering patterns show characteristic reflections of the ferroelectric phase. The scattering-intensity distribution corresponds to the orientation of polymer chains along the stretching axis. There are two analytical methods for estimating the content of crystallites, OAP and IAP in highly drawn fibers of semicrystalline polymers. The first method is based on analysis of the complete scattering pattern in order to separate crystalline diffraction from the background and amorphous halo. However, for random copolymers with a random unit-cell composition, the application of this method is difficult. The second method involves the analysis of IAP scattering in regions free from crystal diffraction and OAP scattering. Appropriate software makes it possible to deconvolve the scattering peaks and determine the parameters of the scattering regions. The obtained data correspond to the structure shown in Fig. 3. Comparison of the obtained structural data with the electromechanical characteristics of materials made it possible to obtain ideas about the mechanism of material deformation in an electric field. The first reason is mechanical electrostriction, which occurs due to field-induced conformational rearrangements of chains and is the main mechanism of electrostriction in low-intensity fields. The second reason is related to electrical repulsion between oriented ferroelectric domains and is the main mechanism of electrostriction in strong fields.

Fig. 3.
figure 3

Probable mechanisms of the electrostrictive response in partially crystalline polymers containing an oriented and isotropic amorphous phase for the cases of true (a), hysteresis (b), and total (c) electrostriction. Adapted from [71] with permission from the American Chemical Society.

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In the study [72], a material was developed based on a (P(VDF-TrFE-CFE), 61/29/10 mol %) matrix and poly(3-hexylthiophene)-b-poly(methyl methacrylate) (P3HT-b-PMMA, 25/75 wt %, Mn = 24 kDa, polydispersity index of 1.25) micelle as a conductive filler. The micelles had a spherical morphology with a poly(3-hexylthiophene) core and a poly(methyl methacrylate) shell. Films of 50 μm thick with different filler content (from 1 to 2 wt %) were obtained by pouring from a dimethylformamide solution and slowly drying at 25°C. The resulting films were deformed to 300% under uniaxial tension and annealed at 80°C for 12 h to fix the sample. The degree of crystallinity of the films increased from 15.5 (pure matrix) to 22.2% (P3HT-b-PMMA content was 2 wt %) with an increase in the filler content. In this case, the crystallite size decreased from 39 to 20 nm, respectively. Pulling led to a change in the structure of the material, which was shown by the X-ray-diffraction method: after stretching and annealing, the paraelectric phase dominated and the ferroelectric phase almost completely disappeared in the sample compared to the initial film. A change in the composition of the crystalline phase led to a corresponding change in polarization in an electric field. We note that growth of the paraelectric phase led to the faster polarization of permanent dipoles in the composite material under the action of an electric field compared to the initial material due to loss of the ferroelectric phase. The ferroelectric domains caused polarization hysteresis due to cooperative coupling between them. Thus, stretched films could quickly return to zero polarization after the applied electric field was removed, resulting in a fast mechanical response of the material. By the example of films with a P3HT-b-PMMA content of 1.5 wt %, the change in their structure during deformation under the action of an electric field was studied. The structural data of the film without an electric field showed the predominance of the paraelectric crystalline phase. The content of the ferroelectric phase gradually increased with an increase in the electric-field strength with a corresponding decrease in the paraelectric phase. The phase transition of crystals from the paraelectric phase to the ferroelectric phase was observed at an electric-field strength of 5.5 kV/mm. The polar segments of P(VDF-TrFE-CFE) in the crystalline region of the film were oriented in the direction of the electric field, which ultimately led to rearrangement of the film volume and affected the transverse strain. Thus, structural studies have shown the effect of the stretching process and related changes in the structure on the electromechanical properties of the films. The addition of P3HT-b-PMMA to P(VDF-TrFE-CFE) led to an increase in the fraction of the crystalline ferroelectric phase and a decrease in the size of crystalline grains compared to the native polymer. Filled films exhibited improved electromechanical properties associated with homogeneous dispersion of the filler and, as a result, uniform distribution of the local field, which, in turn, affected the rearrangement of polar groups in polymer chains and led to volumetric changes in the film under the action of an electric field.

The use of electrospinning technology in the preparation of electroresponsive materials based on PVDF copolymers also made it possible to increase the electrostrictive response [73]. For example, a nonwoven fabric made from a poly(vinylidene fluoride-trifluoroethylene-chlorotrifluoroethylene) ternary copolymer (P(VDF-TrFE-CTFE); 63/28/9 mol %) showed a force-to-weight ratio 65% higher than that of a film; therefore, it exhibits a greater electrostrictive effect. The nonwoven material was obtained from 30 wt % solution of the copolymer in a mixed solvent acetone/dimethylformamide (55/45 wt %) at a stretching potential of 26 kV and a distance to the receiving roll of 14 cm. The thickness of the obtained mats was 80 and 60 μm and the diameter of the fibers in the mat varies from 200 to 1000 nm, with the main fraction of 400–500 nm constituting ~23%. The increased electrostrictive response is associated with the method of obtaining a nonwoven material: mechanical shear stresses, which are codirected with the electric field during electrospinning, lead to the orientation of polymer chains. Nanofibers have dipoles with self-induced orientation, and polarization during electrostriction leads to their reorientation. In addition, nanofibers have a larger surface-area-to-volume ratio compared to a film, which also increases the dielectric permitivitty of the material. It was assumed that nanofibers provide better alignment of dipoles in an electric field: in a film, the orientation of dipoles was statistically affected by a larger amount of material than in a mat of nanofibers. Figure 4 shows a diagram of the electrostrictive effect in a nonwoven material compared to a film. Beyond the electric field, a preliminary orientation of the dipoles in the nanofiber is observed in comparison with the random distribution in the film. When an electric field is applied, dipole reorientation occurs and the nonwoven material exhibits greater contraction compared to the film Δ1 < Δ2 thanks to the greater mobility of the material.

Fig. 4.
figure 4

Scheme of the electrostrictive response of a film and a nonwoven material. Randomly oriented dipoles in the material without an electric field (a). Orientational ordering of dipoles in an electric field leading to deformation (contraction) of the material (b). The nonwoven material shows more compression compared to the film Δ1 < Δ2. Adapted from [73] with permission from MDPI (Open Access).

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Thus, an analysis of published data shows that the magnitude of the electrostrictive response is primarily determined by the structural features of the material: the presence of easily polarizable segments or domains, as well as balance of the ferroelectric and paraelectric phases.

In conclusion of the section, it should be noted that when creating a soft-robotic device, not only the mechanism of functioning (Maxwell pressure and/or electrostriction), electrical sensitivity, deformation force and compliance of the material to an external stimulus, but also the engineering implementation of the actuator element become fundamentally important aspects. Therefore, we will further consider the main modern approaches to the design and creation of soft robots.

2 ON THE ROLE OF ENGINEERING DESIGN IN THE DEVELOPMENT OF SOFT ROBOTS

The functional materials discussed above can be used in various units and structural elements of soft-robotic devices, which often have complex geometry and require a special design approach. Some of these engineering problems can be solved by additive manufacturing technologies. There are many reviews devoted to this topic, but in this section we focus only on the main approaches used in soft robotics. Most technologies for manufacturing parts and structural elements of soft robots can be simplistically classified into three main groups:

(i) molding, i.e., manufacturing of parts by casting it in a specific form (mold);

(ii) subtractive manufacturing, i.e., making parts by removing material;

(iii) additive manufacturing, i.e., making parts by adding material.

In soft robotics, as a rule a combination of technologies is used: for example, a mold is made using a subtractive or additive method, and the necessary material is poured into it. In particular, using this approach, a flexible finger was made from silicone using a brass mold, the method of obtaining which is similar to a subtractive technology [74]. Another example is the manufacture of a flexible articulated drive using a mold obtained not by a subtractive, but by an additive method [75]. Similarly, to make a mold and obtain modular elastomeric actuators, 3D printing technology can be used, followed by assembly into a single structure of a caterpillar robot [76]. Elements, the properties of which are determined by an artificially formed periodic structure, are called metamaterial. Thus, rapidly developing additive technologies are increasingly used in soft robotics. This is explained by the fact that the use of additive technologies makes it possible to quickly and inexpensively manufacture products with desired properties and complex topology, which is common for nature [77, 78]. Thus, the additive technologies used today are briefly reviewed in this section.

2.1 Additive Мanufacturing Technologies

The extrusion printing method (or fused deposition modeling (FDM)), is a 3D printing process that uses a continuous filament of thermoplastic material to layer-by-layer melt material and solidify it upon cooling. This technology is a basic one and also one of the cheapest printing methods; therefore, it is widely used in soft robotics to obtain prototypes, molds and auxiliary structures. FDM printing is the most affordable due to the relative simplicity of the equipment and, accordingly, its simplified maintenance, as well as the ease of manufacturing the printing material (filament). In the study [79], the FDM-printing method was used to make molds to create a soft multi-legged robot. It was possible to develop a robot based on silicone in the form of a brush. The bristles contain iron powder as a filler and mimic the musculoskeletal system of biological systems controlled by a magnetic field. The advantage of this design is in the implementation of functions inherent in individual animals, for example, the adaptability of an octopus to various environments, overcoming obstacles by a caterpillar, etc. Shaping and adjusting the accuracy of the bristles is difficult without first creating molds.

Another example of the application of the 3D printing method is the manufacture of pneumatic flexible actuators from thermoplastic polyurethane by photopolymerization [80]. Photopolymerization is a method of manufacturing parts by the layer-by-layer curing of a monomer under the action of ultraviolet (UV) radiation. There are two ways to implement the technology: curing the monomer in a bath according to a preprogrammed mask or sputtering the monomer onto the work surface with subsequent illumination. This technology, similar to FDM printing, is widely used in soft robotics due to the simplicity of the equipment, versatility of use, and relatively low cost. The advantage of using this technology to produce elements of soft-robotic devices is the ability to print both hard parts, such as mold making, and the production of flexible parts (such as actuators). Another application of this technology is so-called 4D printing [81]. In this case, the part manufactured using a 3D printer is subjected to external influence, for example, temperature, which leads to a structural change in the part due to the shape-memory effect. A detailed description of the application of the technology for curable polymers and elastomers can be found in reviews [82, 83].

Selective laser sintering (production of parts from powder materials by local heating and sintering with a laser) is also an additive manufacturing technology [84]. The implementation of this technology allows manufacturing of parts with a complex topology, for example, with internal channels for fluid supply or parts with a cellular structure. However, this technology requires high costs for equipment and materials, so at the moment its application in soft robotics is limited.

The technology of rapid liquid printing, a method of printing with silicones, which as a rule is used for the manufacture of soft pneumatic actuators, should also be considered. The technology compares favorably with traditional silicone molding and the additive manufacturing of elastomers due to wide design opportunities at high printing rate without compromising the properties of the material used [85]. Of particular interest in the field of additive technologies is printing with hydrogels and bioprinting [86]. These approaches are based on traditional 3D printing, but hydrogels or special bioinks are used as precursor materials. These technologies, similar to the previous one, make it possible to avoid the use of injection molds and open up the possibility of creating complex flexible structures with preprogrammed properties close to biological objects. In recent years, hybrid printing has been actively developed. This method consists of using materials that differ greatly in terms of their properties [87, 88]. For example, printing a flexible substrate followed by applying conductive layers.

In addition to the additive technologies described above, textile-industry technologies can be used in soft robotics [89]. In particular, textiles can be used as a reinforcing material to strengthen the matrix. However, despite significant advances, the efficiency and performance of textile actuators in practical applications is still unsatisfactory.

Thus, among the main technologies for the manufacturing of soft robots, additive technologies can be distinguished, which allow various structural and functional elements to be produced quickly and from a wide range of materials, including those with a complex geometry. The technologies that are most popular and under active development at the moment are FDM and photopolymer printing technologies, bioprinting, as well as hydrogel printing.

2.2 Application of Numerical Methods in the Development of Soft Robots

The components of soft robots are usually made of rubber-like materials that exhibit nonlinear mechanical properties under large deformations. Taking into account the complex topology of soft robots, often inspired by real natural objects, analytical calculation of the strength, rigidity, reliability, and efficiency is a difficult and sometimes unsolvable task [90]. In this case, the finite-element method (FEM) is widely used.

Currently, commercial software products are widely used, for example: Abaqus, Ansys and COMSOL Multiphysics software packages. The main advantages of commercial FEM software packages include a user-friendly interface, an extensive library of materials, the ability to solve coupled nonsteady-state and nonlinear problems, ample opportunities for postprocessing results, and the expansion of functionality through script implementation. Solution of the task using the FEM can be divided into several stages: the creation of a computational model (three-dimensional or plane), applying the properties of materials, meshing into finite elements, imposing of loads and displacement, calculation and postprocessing. To create models, both commercial computer-aided design systems (CAD) (SolidWorks, Catia, etc.), as well as CAD modules built into finite-element complexes can be used. The main components of soft robots, as mentioned above, consist of elastomers, which can be subjected to large deformations up to several hundred and even thousands of percent. To describe the relationship between stresses and strains in such cases, special nonlinear elasticity models are used (including Mooney–Rivlin, Ogden, Yeoh, and others) [90]. The unknown constants in these models are determined from the experimental results of mechanical tests for uniaxial and biaxial tension, as well as pure shear, with subsequent minimization of the error between the ordinates of the model and the experimental curves [91, 92]. The application of FEM to some practical tasks of designing soft robots both exclusively in commercial packages and in combination with computer algebra systems is considered further.

FEM has been successfully applied to solve the problem of the topological optimization of a pneumatic gripper for a soft robot consisting of two fingers, according to the criterion of maximizing bending deformation [93]. To build a three-dimensional model of the gripper, the integrated Abaqus CAE (Computer-aided Engineering) module was used, and to solve the topological optimization problem directly, an algorithm was developed that combines the use of Abaqus and Matlab. This approach is required to completely control the process of topological optimization, since most of the similar modules in commercial FEM packages operate on the black-box principle. To solve the problem of the nonlinear deformation of a pneumatic gripper, the following material elasticity parameters were used: Young’s modulus is 1.585 MPa; Poisson’s ratio is 0.49. The optimized models were manufactured using an Object 750 3D printer from a rubber-like material. Experiments have shown that the pneumatic gripper can generate a force of 0.23 N at an actuation pressure of 0.06 MPa and hold a small balloon. In this case, the angle of rotation of the gripper during bending was 14.71°.

In the study [94], the design of soft vacuum actuators was proposed that imitated the structure of the sporangium of fern trees. Ansys Workbench and Matlab were used to predict the force generated and the angle of rotation of the actuator when generating vacuum. A 3D model of the actuator was created in SolidWorks and imported into the static-calculation module. To determine the mechanical parameters of the material, uniaxial tensile tests were carried out on standardized extrusion-printed samples made from commercial thermoplastic polyurethane (Ninjatek). The nonlinear relationship between the stresses and strains was approximated using hyperelastic-material models integrated into the Ansys Workbench. As a result, the five-parameter Mooney–Rivlin model was chosen as the best one for describing the experimental curve in the strain range up to 200%. Deformation of the actuator in a numerical experiment was carried out by applying negative pressure to the internal surfaces of the model, taking into account the contact between the segments of the actuator at large deformations. In this case, the angle of rotation and the force generated by the gripper were fixed. Close values obtained in numerical and full-scale experiments indicated the adequacy of the proposed model and the possibility of further improvement of the actuator design.

Materials that vary their geometric and mechanical properties in response to changing environmental conditions are increasingly being used in tissue engineering and soft robotics. It is known that upon the absorption of water, most of the existing soft materials, such as hydrogels, exhibit swelling, i.e., a positive change in volume. A negative change in the volume (contraction) of the material when immersed in water is much less common. The production of materials capable of negative swelling is an urgent and complex task, and FEM is becoming an indispensable tool for predicting the properties of such components. Thus, using the FEM, soft composite metamaterials with a network structure were developed, which made it possible to achieve large negative-swelling coefficients [95]. FEM has also made it possible to regulate and predict the relationship between stresses and strains. The fabricated metamaterial consisted of three layers: two elastomer ones including a soft layer made of exo-1,7,7-trimethylbicyclo[2.2.1]hept-2-yl acrylate with photoinitiators (Tangoblackplus, Stratasys) and a rigid layer made of exo-1,7,7-trimethylbicyclo[2.2.1]hept-2-yl, tricyclodecane dimethanol diacrylate, titanium dioxide, and photoinitiators, as well as a hydrogel layer (SUP705, Stratasys) composed of a mixture of poly(oxy-1,2-ethanediyl), α-(1-oxo-2-propenyl)-ω-hydroxy-1,2-propylene glycol, polyethylene glycol, glycerin, phosphine oxide, phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide, and acrylic-acid ester.

It is important to note that the swelling deformation of the hydrogel transforms into bending deformation, which is achieved by placing this sandwich panel in the area of the cell fillets. The nonlinear deformation problem was solved in Abaqus based on the assumption of the linear elastic properties of the gel and polyacrylate with the values of the elastic modulus and Poisson’s ratio equal to 65 MPa and 0.4 for rigid polyacrylate and 0.2 MPa and 0.5 for the hydrogel, respectively. The Mooney–Rivlin model was used to simulate the hyperelastic behavior of the elastomer. The implementation of FEM in conjunction with analytical and experimental studies provides a powerful tool for creating metamaterials with accurately predictable and controlled properties, which can be used in soft robotics. When developing soft robots operating in an aquatic environment, the solution of coupled problems of fluid-structure interaction (FSI) is used. This approach allows not only to analyze the stress-strain state of the robot, but also, by solving the problem of computational fluid dynamics (CFD), to plot the displacement, velocities and acceleration fields that occur in the fluid when the robot moves, to optimize its geometry, taking into account emerging vortex flows, and to reduce energy consumption [96, 97].

Thus, at present, individual researchers and laboratories are implementing an approach to develop FEM software for specific tasks [96–98]. The disadvantages of such software packages include limited functionality compared to commercial packages, the advantages are a relatively low cost and flexible approach to the development of new FEM, the optimization of numerical algorithms, and the export of calculation results, including using computer algebra systems.

3 APPLICATION OF ELECTRORESPONSIVE MATERIALS FOR ROBOTIC DEVICES

Despite the fact that researchers and developers have relatively recently begun to use electroresponsive materials in soft robotics, the number of created prototypes and successfully tested products is quite large.

One of the most well-known products where an electroresponsive material (dielectric elastomer) has been successfully applied is a robot designed to explore the Mariana Trench. The biological prototype for it was the deep-sea snailfish [99]. The material used in the manufacture of the muscle membrane was the triblock copolymer poly(styrene-b-butyl acrylate-b-styrene) in a stretched state. Preliminary stretching of the membrane was performed using a special multiaxial system. MG Chemicals 846 carbon-filled composite was used as an electrode.

In the study [100], another successful example of the making of a soft robot is presented designed with a dielectric elastomer. The developed caterpillar robot was able not only to crawl, but also to climb vertical planes due to the presence of two supporting flexible, independently controlled electroadhesive surfaces, which provided additional degrees of freedom (Figs. 5a and 5b). However, it was not possible to make it autonomous, the power supply and controls were located outside the main body.

Fig. 5.
figure 5

Demonstration of the multimodal movement of a caterpillar in nature with a large number of degrees of freedom (a). A soft robot imitating a caterpillar turns to the left under the action of an external stimulus, bending its body (b). The principle of operation of a robot imitating a jellyfish (c). The functional element (actuator) consists of two elastomeric layers that encapsulate the conductive fluid. When an electric field is applied to the internal liquid electrode, Maxwell pressure arises, leading to elongation and thinning of the dielectric membrane, as well as bending towards the inextensible layer (spacer). The swim bladder provides buoyancy control. Fluorescent image of the robot (d). Adapted from [100] (a, b) and [102] (c, d) with permission from Elsevier and Frontiers Media (Open Access), respectively.

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Another example of a floating soft robot whose driving element was a membrane made of an electroresponsive material was described in the study [101]. The robot imitated a leptocephalus, the larval stage of eels, but had limited autonomy, since the power source and controls were outside the main body. The feature of the work is in the liquid electrodes providing increased mobility of the robot. In the study [102], taking a jellyfish as a biological prototype, a fully autonomous robot were created (Figs. 5c and 5d), refusing to use a dielectric elastomer membrane prestretched and fixed in a rigid frame: instead, the required tension was achieved by molding onto a nonplanar rigid substrate.

In [103], an overland insectoid robot was developed using a dielectric elastomer material for the muscle of the organ of movement. It was possible to produce an autonomous machine with a length of only 40 mm, having all the control electronics and a battery on board. The key technology that made this degree of miniaturization possible was the use of a stimuli-responsive material at voltages below 500 V. A 23-µm-thick PDMS membrane, preliminarily stretched in two directions and fixed in a rigid frame, was used in the study.

Electroresponsive materials are widely used in the development of single robotic devices, for which placement of the power source and control electronics outside the main body is not critical. Thus, in the study [104], a manipulator for a microscope was made. For this, a three-layer composite (laminate) with an ion-conducting membrane sandwiched between two electrodes with electronic conductivity was used, i.e., a structure that simulated electrical two-layer capacitors. Using this material, it was possible to create three types of manipulators: a miniature gripper (tweezers), a probe manipulator, and a miniature pipette.

It is interesting to consider the use of actuators made of electroresponsive polymers in microfluidics. Such materials are in demand in the design of micropumps, microvalves, and micromixers [105, 106]. The first microvalve based on an ionic polymer–metal composite is presented in the study [105]. The proposed design was quite simple: an actuator made of an ionic polymer–metal composite was enclosed in a PDMS housing and, in the normal state, when the input voltage was turned off, it blocked the microchannel inside. When a voltage of the correct polarity was applied, the actuator bent upwards and opened the channel. In the study [106], it was proposed to use an actuator made of an electroresponsive polymer in the construction of a micromixer. The micromixer was designed for mixing liquids with low Reynolds numbers. The developed prototype of an active mixer was the second one in which an ionic-polymer converter was used as a mixing element. By applying some programmed periodic or varying voltage, such as a sequence of pulses, a sine wave, etc., a flexural oscillation can be produced allowing the actuator to act as a stirring element for laminar fluids.

The study [107] devoted to the development of a manipulator element, i.e., a rotary soft robotic system driven by actuators made of a dielectric elastomer, is of considerable interest. The tested design consisted of two cone-shaped membranes prestretched by 10% with a thickness of 50 µm, rigidly connected along the outer diameter and precompressed out of plane relative to each other using a stiffener. Carbon (soot) electrodes were sector deposited onto the surface of the membranes using screen printing and divided into four sections, controlled independently from each other, which provided a large number of degrees of freedom.

Thus, the use of electroresponsive polymer materials is associated primarily with the creation of various miniature self-propelled systems that imitate the behavior of natural organisms, as well as miniature manipulators and actuator elements for various purposes. The use of stimuli-responsive materials has been justified by several factors analyzed in [108], where, based on an analysis of several studies, it was concluded that when an electroresponsive material (dielectric elastomer) is used in the actuator design, the item can be produced in just four stages (in contrast, for example, from the production of various types of actuators that use compressed air to function, the production of which requires five or even eight stages). In addition, only one production unit is required for manufacturing (as opposed to eight pieces with other constructive solutions). The possible problems considered in the study [108] include increased (compared to other technical processes) requirements for the qualifications of personnel, which can make it difficult to quickly introduce into mass production. All these noted advantages will continue to contribute to the high popularity of electroresponsive materials in soft robotics.

CONCLUSIONS

In the present survey, a brief review of modern research in the field of soft-robotic actuators has been presented, demonstrating the key role of the development of new hybrid materials and composites, as well as the use of structural methods using mega-science equipment to identify the structure–property relationship and study the mechanism of the electrostrictive effect.

An increase in the dielectric constant of materials and a decrease in their thickness offer the prospect for developing actuators with a low response potential, less than 1 kV. The design of the actuator is of great importance: the creation of multilayer elements makes it possible to increase its efficiency. A significant challenge in the development of electroresponsive elastomeric materials is the low durability of their operation, associated with the weak adhesion of the conductive (electrode) layer to the material and its destruction during repeated operation. The use of ferroelectric polymer materials makes it possible to achieve essential deformation under the action of an electric field due to the additional effect of electrostriction, which can significantly exceed the contribution of the Maxwell pressure. In this regard, great research interest is associated with copolymers of polyvinylidene fluoride, which exhibits a giant electrostrictive response.

It is difficult to imagine the creation of elements of soft-robotic systems without the use of additive manufacturing technologies, which make it possible to design both auxiliary forms and structures for molding stimuli-responsive material, and directly individual parts of a robot. Analytical approaches to calculating the characteristics of materials and design geometries, implemented both in commercial and open-source software packages, perform a predictive function in the manufacturing of soft actuators and open up broad prospects for optimizing the design of new nature-inspired robots.

Despite significant progress in the development of soft robotics, the creation of fully autonomous robots capable of long-term functioning similar to a living organism is an urgent scientific challenge. The sensitivity of materials to an electric field can be used as the basis for the motor and perceptual elements of a robot, which opens up the possibility for wider application of the nature-likeness principle in the development of artificial systems. The systematization of relevant data on the properties and composition of promising stimuli-responsive polymer materials for soft-robotic actuators makes it possible to determine further directions for the development of this special branch of materials science.