Hydraulically amplified self-healing electrostatic actuators

[0001] The present application is a national phase application filing under 35 U.S.C. § 371 of PCT/US18/23797 entitled “HYDRAULICALLY AMPLIFIED SELF-HEALING ELECTROSTATIC TRANSDUCERS” filed Mar. 22, 2018, which claims benefit of priority to U.S. Provisional App. No. 62/613,322 entitled “HYDRAULICALLY AMPLIFIED SELF-HEALING ELECTROSTATIC ACTUATORS WITH MUSCLE-LIKE PERFORMANCE” filed Jan. 3, 2018 and U.S. Provisional App. No. 62/474,814 entitled “HYDRAULICALLY AMPLIFIED SELF-HEALING ELECTROSTATIC (HASEL) TRANSDUCERS” filed Mar. 22, 2017, each of the foregoing being incorporated by reference for all each disclosure teaches and discloses.

[0002] The present invention is directed to soft actuators and, more particularly, to muscle-mimetic actuators for use in robotics and the like.

[0003] Historically, human-made machines have tended to rely on rigid components (e.g., such as metals) and typically have finite degrees of freedom. In contrast, nature makes extensive use of soft materials (e.g., mammalian muscle, cephalopods, muscular hydrostats, etc.) that are capable of large deformation and can easily conform to their environment. Soft robotics is a rapidly growing field with many potential applications including collaborative robots that safely interact with humans, transducers for biomedical applications, and soft grippers capable of handling delicate and irregular objects. Actuators and sensors that closely mimic properties of natural muscles are key components that will enable the next generation of soft robotic devices.

[0004] Existing artificial muscle transducers include pneumatic actuators, electroactive polymers (EAPs), shape memory polymers, and other thermally-activated systems, and each has various limitations. Currently, soft robots predominantly rely on pneumatic or fluidic actuators, which limit speed and efficiency. Such actuators are versatile and prevalent, but they have specific challenges. For example, because they are connected to storage systems of pressurized fluids or pumps via channels and valves, they tend to experience fluid drag, which can limit bandwidth and efficiency. Further pneumatic actuators can experience significant trade-offs between actuation speed and portability, with the response speed of untethered devices being low, and such actuators can often rely on additional sensors to control parameters of actuation.

[0005] Dielectric elastomer actuators (DEAs), a specific type of EAP, exhibit performance metrics that resemble biological muscle. DEAs are hyperelastic capacitors that consist of elastomeric layers sandwiched between compliant electrodes. When voltage is applied across the two electrodes, Maxwell stress causes the dielectric to reduce in thickness and expand in area. Continuous measurement of electrical impedance of the hyperelastic capacitors provides information on the state of actuation, giving DEAs self-sensing capabilities.

[0006] However, such electrically powered muscle-like actuators tend to have their own challenges. Being driven by high electric fields, DEAs can be prone to failure by dielectric breakdown and electrical ageing. DEAs can also be difficult to scale up to deliver high forces, as such applications typically rely on large areas of dielectric (e.g., in stack actuators), which tend to be much more likely to experience premature electrical failure, following the Weibull distribution for dielectric breakdown. Previous work has attempted to mitigate damage from dielectric breakdown, but these approaches have tended to present their own challenges. In one such approach, self-clearing electrodes have been used to isolate dielectric breakdown sites, but the dielectric itself remains damaged, which degrades the performance of the device. Another such approach utilizes a dielectric layer consisting of a silicone sponge that is swelled with silicone oil, and the oil locally redistributes after failure from electrical or mechanical damage; but this approach tends only to be useful at low actuation strain.

[0007] In view of at least the foregoing, embodiments described herein include a novel class of soft actuators (e.g., for soft robotics applications and the like), and methods for use and manufacturing of such soft actuators. The novel soft actuators are referred to herein as Hydraulically Amplified Self-Healing Electrostatic (HASEL) transducers (or actuators), and such HASEL transducers can provide high-performance, reliable, self-sensing, muscle-mimetic actuators that can overcome important limitations of current soft actuators. HASEL actuators use an electro-hydraulic mechanism to combine the advantages of fluidic and electrostatic actuators. Use of liquid dielectrics can allow for harnessing hydraulic principles to scale actuation force and strain. A wide range of different modes of actuation can be achieved by pressurizing and displacing a hydraulic fluid inside of deformable structures. HASEL actuators can be designed to linearly elongate or contract upon application of voltage, and can feature three-dimensional mobility. Mechanical and electrical properties can be tuned independently. Additionally, HASEL actuators can be fabricated from a variety of materials and can be compatible with a large number of fabrication techniques.

[0008] In one aspect, an electro-hydraulic actuator disclosed herein includes a deformable shell that defines an enclosed internal cavity; a liquid dielectric contained within the enclosed internal cavity; a first electrode disposed over a first side of the enclosed internal cavity; and a second electrode disposed over a second side of the enclosed internal cavity, where electrostatic forces between the first and second electrodes upon application of a voltage to the first and second electrodes draws the first and second electrodes towards each other to displace the liquid dielectric within the enclosed internal cavity.

[0009] In another aspect, a method of using an electro-hydraulic actuator includes applying a voltage to first and second electrodes of the actuator to generate electrostatic forces between the first and second electrodes; drawing the first and second electrodes towards each other using the electrostatic forces; displacing, during the drawing, a liquid dielectric contained within a flexible shell and disposed between the first and second electrodes; and flexing a portion of the flexible shell with the displaced liquid dielectric.

[0010] In another aspect, a method of fabricating an electro-hydraulic actuator includes disposing a first electrode onto a first surface of a first elastomeric shell; applying a first encapsulating layer over the first electrode and the first surface of the first elastomeric shell to create a first elastomeric unit; disposing a second electrode onto a first surface of a second elastomeric shell; applying a second encapsulating layer over the second electrode and the first surface of the second elastomeric shell to create a second elastomeric unit; securing the first and second elastomeric units together with the first surfaces of the first and second elastomeric shells facing each other; and filling an internal cavity between the first and second electrodes with a liquid dielectric.

[0011] In another aspect, a method of fabricating an electro-hydraulic actuator includes creating a first plurality of spaced electrodes on a first surface of a first film; creating a second plurality of spaced electrodes on a first surface of a second film; placing the first film over the second film such that the first plurality of spaced electrodes are aligned over the second plurality of spaced electrodes; sealing the first film to the second film at each of a plurality of spaced sealing locations to create a plurality of pouches, wherein each pouch is defined by: one of the first plurality of spaced electrodes, one of the second plurality of spaced electrodes, a portion of the first surface of the first film disposed between the one of the first plurality of spaced electrodes and an adjacent of the first plurality of spaced electrodes, and a portion of the first surface of the second film disposed between the one of the second plurality of spaced electrodes and an adjacent of the second plurality of spaced electrodes; filling each of the pouches with a liquid dielectric via respective filling ports; and sealing each of the filling ports.

[0012] In another aspect, a method of fabricating an electro-hydraulic actuator includes creating a plurality of connected, flexible pouches; filling each of the pouches with a liquid dielectric; positioning a respective first electrode on a first side of each of the pouches, wherein adjacent ones of the first electrodes are electrically connected; and positioning a respective second electrode on an opposite second side of each of the pouches, where adjacent ones of the second electrodes are electrically connected, and wherein the liquid dielectric in each pouch is disposed between its respective first and second electrode.

[0013] In another aspect, a method of fabricating an electro-hydraulic actuator includes bonding a first surface of a first elastomeric sheet to a first surface of a second elastomeric sheet; injecting a gas into an internal cavity between the first surfaces of the first and second elastomeric sheets; curing the first and second elastomeric sheets together with the injected gas disposed between the first surfaces of the first and second elastomeric sheets; removing the gas from the internal cavity; filling the internal cavity with a liquid dielectric; securing a first electrode over a second surface of the first elastomeric sheet; and securing a second electrode over a second surface of the second elastomeric sheet.

[0014] In addition to the exemplary aspects and embodiments described above, further aspects and embodiments will become apparent by reference to the drawings and by study of the following descriptions.

[0086] Embodiments described herein include a novel class of soft actuators (e.g., for soft robotics applications), and methods for use and manufacturing of such soft actuators. The novel soft actuators are referred to herein as Hydraulically Amplified Self-Healing Electrostatic (HASEL) transducers (or actuators), and such HASEL transducers can provide high-performance, reliable, self-sensing, muscle-mimetic actuators that can overcome important limitations of current soft actuators. HASEL actuators use an electro-hydraulic mechanism to combine the advantages of fluidic and electrostatic actuators. Use of liquid dielectrics can allow for harnessing hydraulic principles to scale actuation force and strain. A wide range of different modes of actuation can be achieved by pressurizing and displacing a hydraulic fluid inside of deformable structures. HASEL actuators can be designed to linearly elongate or contract upon application of voltage, and can feature three-dimensional mobility. Mechanical and electrical properties can be tuned independently. Additionally, HASEL actuators can be fabricated from a variety of materials and can be compatible with a large number of fabrication techniques.

[0087] In some embodiments, HASEL actuators are implemented as laminated structures consisting of electrode layers and a combination of solid and liquid dielectric materials. The layers form self-healing capacitors, which deform when a voltage is applied. Embodiments can sense deformation via a change in capacitance when the electrodes are deformed or displaced. In some embodiments, use of liquid dielectrics inside the soft electroactive structures can confer self-healing capabilities to HASEL actuators, as liquid dielectrics return to an insulating state after electrical breakdown events. The ability of HASEL actuators to fully recover from dielectric breakdown can be important for certain applications, such as for scaling up for use in large devices and for delivering large forces.

[0088] Some embodiments extend the HASEL actuator concepts to provide a new type of linearly-contracting electrostatic actuator that operates similar to pneumatic Peano-artificial muscles, referred to herein as a Peano-HASEL actuator. The Peano-HASEL actuator can use electrodes to pump dielectric fluid into a pouch, creating a geometry change that produces linear contraction on the application of voltage. Peano-HASEL actuators can demonstrate the advantages of other HASEL actuators, while also being able to contract on activation. Some embodiments are compatible with common industrial production methods, which can permit quick adoption for various applications.

[0089] FIGS. 1A-1C show an illustrative layered structure 104 of a HASEL transducer 100 and the self-healing abilities conferred to the HASEL transducer 100 from the structure 104. As illustrated, the structure 104 includes a flexible shell 108 (e.g., stretchable or elastic, non-stretchable and inelastic but bendable) filled with a liquid dielectric 112 (e.g., oil). First and second stretchable, flexible, or rigid opposing electrodes 116, 117 can be placed on opposite sides of the shell 108. The first and second opposing electrodes 116, 117 may be any appropriate ionic or electronic conductors. The first and second opposing electrodes 116, 117 can be separated by the shell 108 and the liquid dielectric 112. The layered structure 104 forms a capacitor that is operable to store charge upon application of a voltage to the structure 104. In some arrangements, the shell 108 can serve as a solid dielectric of the capacitor. In any case, upon occurrence of a dielectric breakdown, the liquid dielectric 112 can refill a breach 120 caused by the discharge path, thus restoring insulating properties of the liquid dielectric 112. This property can allow the HASEL actuator 100 to self-heal from electrical damage, thereby increasing reliability and operational lifetime of the actuator 100.

[0090] Turning to FIGS. 2A-2E, a specific type of HASEL actuator 100 in the form of a donut-type HASEL actuator 200 is shown to illustrate conversion of electrical actuation to mechanical deformation. The donut-type actuator 200 includes a flexible shell or pouch 208 (e.g., elastically deformable) that defines an enclosed internal cavity 209, a liquid dielectric 212 contained within the enclosed internal cavity 209, a first electrode 216 disposed over a first side (not labeled) of the enclosed internal cavity 209, and a second electrode 217 disposed over an opposite second side (not labeled) of the enclosed internal cavity 209. For instance, the first and second electrodes 216, 217 may include respective first and second electrical leads 221, 223 to which a voltage (e.g., DC voltage) is configured to be applied. While the first and second electrodes 216, 217 are illustrated as being disposed on or over an outer surface (not labeled) of the shell 208 (e.g., the first electrode 216 being disposed over an upper or a first outer surface and the second electrode 217 being disposed over a lower or a second outer surface), other embodiments envision that the first and second electrodes 216, 217 could be disposed on or over an inner surface (not labeled) of the shell 208 (e.g., such that the first and second electrodes 216, 217 are in direct contact with the liquid dielectric 212). In a further embodiment, one of the first and second electrodes 216, 217 may be disposed over an inner surface of the shell 208 (e.g., on the inside of the internal cavity 209) and the other of the first and second electrodes 216, 217 may be disposed over an outer surface of the shell 208 (e.g., outside of the internal cavity 209). Regardless of whether the first and second electrodes 216, 217 are disposed inside or outside of the internal cavity 209, the first electrode 216 may be considered disposed over a first side of the internal cavity 209 and the second electrode 217 may be considered disposed over a second side of the internal cavity 209.

[0091] A surface area of the shell 208 over which the first and second electrodes 216, 217 are disposed comprises an active area 224 of the shell 208 and a surface area of the shell 208 over which the first and second electrodes 216, 217 are not disposed comprises an inactive area 228 of the deformable shell. While the active area 224 may be surrounded by the inactive area 228 as illustrated in the figures, other embodiments envision that the inactive area 228 may be surrounded by the active area 224. In any case, application of a voltage to or across the first and second electrodes 216, 217 (e.g., via the respective first and second electrical leads 221, 223) induces an electric field through the liquid dielectric 212 (e.g., and shell 208) to generate electrostatic forces that attract the first and second electrodes 216, 217 (where such electrostatic forces generally extend along a first reference axis 250). The generated electrostatic forces generate an electrostatic Maxwell stress on the active area 224 of the shell 204. Compare FIGS. 2A-2B. The electrostatic stress displaces the liquid dielectric 212 in the active area 224, thus generating hydrostatic pressure that acts on the shell 208 (e.g., in the inactive area 228) to urge the shell in one or more different directions so as to move the shell 208, stretch the shell 208, etc.

[0092] Stated differently, applying a voltage (e.g., high-voltage signal) across the electrodes 216, 217 generates an electrostatic force that causes the electrodes 216, 217 to attract or otherwise draw together, where the attraction displaces the liquid dielectric 212 in between the electrodes 216, 217 along a second reference axis 254 from the active area 224 into the inactive area 228, thus coupling electrostatic stress to fluidic pressure. The pressurized liquid dielectric 212 can deform (e.g., flex) the shell 208 (e.g., in the inactive area 228 in this embodiment) to perform mechanical work, such as lifting a load. For instance, the pressurized liquid dielectric 212 can, upon being forced into the inactive area 228, urge against the shell 208 to elastically deform the shell 208 in the inactive area 228, such as along a third reference axis 258 that is parallel to the first reference axis 250. Compare shape of inactive area 228 in FIGS. 2A, 2B, and 2D and also in FIGS. 2C and 2E. For instance, note how a thickness of the inactive area 228 increases while a thickness of the active area 224 decreases thus creating “out-of-plane” deformation of the structure. In one arrangement, the shell 208 may be inhibited from elastic deformation along at least a portion of the second reference axis 254 in any appropriate manner. For instance, note how the overall width of the actuator 200 remains constant in FIGS. 2A, 2B, and 2D.

[0093] As illustrated, the actuator 200 can take a toroidal, or any other suitable shape. The ratio of the active area 224 to inactive area 228 can be adjusted for scaling force and strain according to hydraulic principles. It can be seen that as the applied voltage increases from V1 to V2, there is a small increase in actuation strain s. Compare FIGS. 2A and 2B and also FIG. 3. However, when the voltage surpasses a threshold V2 and increases to V3 for instance, the increase in electrostatic force starts to exceed the increase in mechanical restoring force (e.g., owing to the elasticity of the shell 208 and/or a load being applied to the shell 208), causing the first and second electrodes 216₁, 216₂ to abruptly pull together (see FIGS. 2D and 3); this is a characteristic feature of a so-called pull-in or snap-through transition. Pull-in transitions and other nonlinear behaviors are features of soft active systems that offer opportunities to improve actuation response or functionality and have been used to amplify the response of fluidic and dielectric elastomer (DE) actuators. After the pull-in transition, actuation strain further increases with voltage; this describes the pull-in instability that is shown in FIG. 3. Experimental data in FIGS. 6A and 6B reflects this behavior (e.g., that actuation strain is small until a sudden increase in strain occurs after a certain threshold).

[0094] FIGS. 4A-4B illustrate how implementations of the layered structure 104 of HASEL actuators 100 can form a capacitor. Changes in capacitance can be proportional to the amount of displacement or deformation, which can be used for sensing and control. This property can allow HASEL actuators 100 to self-sense their state of deformation, providing a feedback mechanism to control the state of actuation. For example, driving and control electronics can make use of circuits that add a low amplitude alternating current (AC) signal to the high-voltage, direct-current driving voltage, and from there, can obtain the impedance of the circuits containing the deformable capacitors. Impedance data can then be readily converted to provide real-time information about strain of actuation for further use in control of actuator kinematics.

[0095] FIGS. 5A-5B further illustrate self-healing behaviors of HASEL transducers 100 (e.g., as described in FIGS. 1A-1C). Specifically, FIG. 5A shows self-healing of a portion of a donut-type actuator 200 with PAAm-LiCl hydrogel electrodes. As illustrated, a voltage ramp of 1 kV/s is applied until dielectric breakdown occurs, with a 10 second wait period after each breakdown event. The inset figure shows the sequence of events during self-healing tests. FIG. 5B shows self-healing of a planar-type HASEL actuator (similar to the actuator described below with reference to FIGS. 16A-16C). A linear voltage ramp at a rate of 0.5 kV/s was applied until dielectric breakdown occurred. After 1 minute, another linear voltage ramp was applied until dielectric breakdown. This was repeated for 50 cycles to evaluate the self-healing performance of a six-unit planar HASEL actuator. Gas bubbles formed after dielectric breakdown occurred (upper-left image). These bubbles have a lower breakdown strength, and electrical breakdown occurred in the same location but at lower voltages (lower-left image). After the gas bubbles were removed, electrical breakdown occurred at a higher voltage and in a different location (top-right image). Electrical breakdown can also occur at a different location and at voltage higher than initial breakdown voltage and without removing any gas bubbles (lower-right image). For the illustrated case, gas bubbles formed during electrical breakdown may be trapped in the area between the stretchable conductors, which may result in a low breakdown voltage (˜5 kV). Removing the gas bubbles can restore the dielectric strength of the actuator. Some embodiments of the HASEL actuators may be fabricated with outer layers made from gas permeable elastomers, so that gas may be automatically purged from the liquid dielectric.

[0096] FIGS. 6A-6B further illustrate hydraulic behaviors of HASEL actuators 100 such as the donut-type actuators 200 described in relation to FIGS. 2A-2E. For the sake of illustration, two donut-type HASEL actuators 200 are shown in FIGS. 6A-6B, respectively, as fabricated with identical elastomeric shells and volume of liquid dielectric, but with different electrode areas relative to the diameter of the pouch (the shells, liquid dielectric, and electrodes not labeled in the interest of clarity). As shown, varying the electrode area in this way can tune the strain and force of actuation. FIG. 6A shows linear strain as a function of applied voltage under various loads for a first donut-type HASEL actuator with an electrode diameter of 2.5 cm. This actuator achieves relatively large strains, but generates relatively low force. FIG. 6B shows linear strain as a function of applied voltage under various loads for a donut-type HASEL actuator with 1.5 cm diameter electrodes. This actuator generates relatively large forces, but achieves relatively low strains. In both cases, an electromechanical pull-in instability can be observed, as indicated by a sudden jump in linear strain. This pull-in instability can be harnessed to create unique modes of nonlinear actuation in certain implementations.

[0097] Some embodiments use a laminated structure of liquid and solid dielectrics to independently tune mechanical and electrical properties of HASEL actuators 100 to suit particular applications. FIGS. 7A-7C illustrate tuning of HASEL actuator 100 properties in context of a HASEL actuator 100 designed to resemble a circular DEA, so that the two actuator implementations can be compared. The illustrated HASEL actuator 100 expands biaxially under an applied voltage. Both the illustrative DEA actuator and the illustrative HASEL actuator 100 may have the same total dielectric thickness (t) and comparable overall dielectric strength. However, as illustrated in FIGS. 7A-7B, about one third of the HASEL dielectric consists of a liquid dielectric (e.g., the HASEL actuator has a liquid dielectric thickness (t_liq) equal to one third of the overall thickness t). Because the liquid dielectric layer generally does not resist deformation (e.g., shear), the circular HASEL actuator is overall much softer at a comparable dielectric strength, and thus deforms at significantly lower voltages as compared to the circular DEA actuator. FIG. 7C shows a plot of area strain as a function of voltage for the circular HASEL and circular DEA implementations. For example, at 11 kV, the HASEL actuator 100 shows 46% area strain, while the DEA actuator shows 12% area strain. Varying the ratio oft to t_liq can achieve different amounts of stress and strain for a given voltage.

[0098] Different performance characteristics of the donut-type HASEL actuators 200 can be altered by varying the arrangement of the actuators 200; arrangement of the electrodes 216; geometry, material, and/or thickness of the shell 208; the volume of liquid dielectric 212 inside the shell 208; and/or other parameters. For example, the shell 208 can be made out of elastomers or flexible plastics to achieve specific actuation responses, and the frequency response of the actuator 200 can vary depending on the viscosity of the liquid dielectric 212, the overall size of the actuator 200, etc. As one example, FIGS. 8A-9B show that the overall stroke of actuation can be increased by stacking donut-type HASEL actuators 200 to create a stack 300. Specifically, FIGS. 8A-8C show the relaxed state (without an applied voltage in FIG. 8A) and an activated state (with an applied voltage in FIGS. 8B-8C) of a stack 300 of five donut-type HASEL actuators 200. As shown, the active areas 224 of adjacent actuators 200 in the stack 300 may overlap and the inactive areas 228 of adjacent actuators 200 in the stack 300 may overlap. In other embodiments, however, active and inactive areas 224, 228 of adjacent actuators 200 in the stack 300 may overlap or partially overlap.

[0099] In one arrangement, all of the first electrodes 216 may be electrically interconnected in parallel and all of the second actuators 217 may be electrically interconnected in parallel. In another arrangement, all of the first electrodes 216 may be electrically interconnected in series and all of the second actuators 217 may be electrically interconnected in series. FIGS. 9A-9B show an experimental result of the arrangement of FIGS. 8A-8C (e.g., a stack 400 of five donut-type HASEL actuators, each having an electrode diameter of 2.5 cm). In one arrangement, the stack 400 achieved 37% linear strain, which is comparable to linear strain achieved by biological muscle and corresponds to an actuation stroke of 7 mm (FIG. 2B). Hydraulic pressure is generated locally in each donut-type actuators 200, and liquid dielectrics 212 (not labeled) are displaced over short distances, allowing for high-speed actuation. The stacked actuators readily showed large actuation response up to a frequency of at least 20 Hz. While not illustrated, one or more objects could be disposed on top of the stack 300 and moved upwardly and downwardly upon application of a voltage to the stack 300 and removal of the voltage from the stack 300.

[0100] FIGS. 10A-10B illustrate how two of the stacks 400 can be modified to create a gripping mechanism 500 (e.g., a “soft gripper”). As shown, the actuators within each of first and second stacks 400₁, 400₂ may be constrained in any appropriate manner on one side to produce a tilting motion. For instance, each actuator may be constrained so that liquid dielectric may only flow into one half of the inactive area upon application of the voltage. When a DC voltage was applied to the first and second stacks 400₁, 400₂, the device 500 grasped delicate objects such as a raspberry 500 (see FIGS. 10A-10C) and a raw egg 504 (see FIGS. 10D-10E).

[0101] As another example of impacting performance of the actuators by altering parameters, FIGS. 11A-11B illustrate two different shapes for donut-type HASEL actuators 200 that can exhibit different behaviors because of different electrode layouts. In particular, FIG. 11A shows an illustrative donut-type HASEL actuator 200′ with an asterisk-shaped electrode layout both without and with an applied voltage while FIG. 11B shows an illustrative donut-type HASEL actuator 200″ with an annulus-shaped electrode layout both without and with an applied voltage. In FIG. 11B, it can be seen how the active area 224″ may be surrounded by one portion of the inactive area 228″ while another portion of the inactive area 228″ may be surrounded by the active area 224″.

[0102] As another example of impacting performance of the actuators by altering parameters, FIGS. 12A-12F illustrate an implementation of a donut-type HASEL actuator 200′″ that can provide three-dimensional mobility. The illustrated donut-type HASEL actuator 200′ is configured to selectively redistribute a liquid dielectric 212′″ throughout a ring-shaped deformable shell 208′″, thereby conferring three-dimensional mobility to the actuator 200′. The ring-shaped volume of liquid dielectric 212 may be surrounded by an insulating skirt 211′″, with opposing electrode pairs (e.g., 216₁′″/217₁′″, etc.) spaced along the surface of the shell to create a plurality of active areas 224₁′″, 224₂′″, 224₃′″ spaced by inactive areas 228₁′″, 228₂′″, 228₃′″. While three active areas 224′″ and three inactive areas 228′″ are illustrated, it is to be understood that more or fewer such areas may be included.

[0103] By selectively activating electrode pairs, the actuator 200′″ may redistribute liquid dielectric 212′″ to different regions of the internal cavity 209′″ of the shell 208′″. For instance, displacing the liquid dielectric 212′″ from one side of the internal cavity 209′″ to the other may cause the actuator 200′″ to tilt (e.g., by displacing liquid dielectric from the active areas 224₁′″ into the inactive areas 228 and the active areas 224₂′″, 224₃′″). This tilting mechanism can be tuned by precise activation of the electrode pairs, for example. For example, FIG. 12B shows a rest state for the specific implementation having three electrode pairs. As illustrated in FIG. 12D, charging a given pair of electrodes (e.g., electrodes 216₁′″, 217₁′″) causes local compression which results in an overall tilt of the actuator 200′″ from the normal axis 270′″. A high-voltage connection may be made with electrode 216₁′″ and a ground connection may be made with electrode 217₁′″. In some implementations, all electrode pairs can be activated at once, causing a change in the overall thickness of the actuator 200′″. As illustrated in FIGS. 12C, 12E, and 12F, such donut-type HASEL actuators 200′″ can be stacked into a stack 600 to achieve further degrees of three-dimensional mobility. For example, as illustrated by the cross-section of the actuated stack 600 shown in FIG. 12F, electrical connections can be routed through the center of the stack 600. Again, different modes of actuation can be achieved by varying material selection and geometry, and/or other properties.

[0104] FIG. 13 shows an illustrative process for fabricating donut-type HASEL actuators 200, according to one embodiment. In Step 1, first and second sheets of elastomeric material (e.g., for use in forming the shell 208) may be provided. For instance, this step may include casting 0.3 mm thick Polydimethylsiloxane (PDMS) sheets using acrylic molds. One sheet may have a first diameter (e.g., 6 cm) and the other sheet may have a larger diameter (e.g., 8 cm). The larger sheet may act as an insulating skirt (e.g., skirt 211′″ in FIG. 12A) to reduce dielectric breakdown through air. In Step 2, each sheet may be aligned concentrically with a respective ring member (e.g., acrylic ring). A bonding agent (e.g., uncured PDMS) may be applied to the areas or portions of the sheets that overlap the ring members. For instance, the bonding agent may be applied over respective first surfaces of the sheets and then the first surfaces of the sheets may be placed together into contact. The two halves may then be clamped together, such as by clamping the ring members together. In Step 3, a gas (e.g., air) may be injected between the first and second sheets such as by inserting a needle of a syringe between the two halves to inflate the shell. The clamped sheets may then be cured together to cure the bonding agent (e.g., such as in an oven at 75° C. for 30 minutes). In Step 4, the ring members may be removed. In one arrangement, a patch (e.g., Ecoflex patch) may be applied to the sheets to serve as a fill port. In Step 5, the gas may be removed from the shell and the shell may then be filled with a liquid dielectric (e.g., via inserting a needle through the patch and injecting with the liquid dielectric, such as 4 ml of the liquid dielectric, e.g., Envirotemp FR3 transformer oil). In Step 6, flexible electrodes (e.g., circular flexible electrodes, such as Polyacrylamide-lithium chloride (PAM-LiCl) hydrogel on Kapton film) may be placed on either side of the shell (e.g., with the Kapton film facing outward).

[0105] In relation to FIG. 14, donut HASEL actuator 200 was actuated with 18 kV at 5 Hz using a reversing polarity waveform. Under an applied load of 150 g, the actuation strain of the device does not noticeably diminish over the course of 1.08 million cycles.

[0106] FIG. 15A illustrates a representative process for measuring closed loop electromechanical efficiency of HASEL actuators (e.g., donut-type actuators 200). FIG. 15B illustrates a representative experimental setup for measuring efficiency. As shown, a high-speed camera was used to record displacement, y(t) (e.g., change in thickness of the inactive area 228). A digital acquisition (DAQ) unit sent a control signal to the HV-amplifier and recorded voltage, V(t), and current I(t). Electrical energy was calculated using voltage and current measurements. FIGS. 15C-15I graphically represent various electrical measurements for the actuation cycle of FIG. 15A. In FIG. 15C, voltage was applied as a symmetric triangular pattern with maximum voltage of 21 kV and period of 1.5 s. In FIGS. 15D-15E, a sudden increase in current and a change in the slope of charge indicates pull-in transition of the donut HASEL actuator. In FIG. 15F, total electrical energy consumed was 2.88 mJ. In FIGS. 15G-15I, time histories of mechanical variables during actuation were recorded for the same cycle. Total mechanical work or energy output was 0.59 mJ. Electromechanical efficiency for the cycle was 21%.

[0107] Another category of HASEL actuators 100 is planar-type HASEL actuators 700 as illustrated in FIGS. 16A-16C. As shown, a planar-type HASEL actuator 700 may include an elastomeric shell 708 containing a liquid dielectric layer 712. First and second stretchable conductors 716, 717 may cover most or all of the region containing the liquid dielectric 712. When voltage is applied, electrostatic stress deforms the dielectric structure to achieve actuation modes including, for instance, uniaxial and biaxial deformation. As the first and second electrodes 716, 717 may cover the entire area of the liquid dielectric 712, the entire actuator 700 may contract in thickness and expand in length in response to an applied voltage. To achieve uniaxial deformation, the actuator 700 may be pre-stretched and constrained in the width direction and a load may be applied in the length direction as shown in FIGS. 16A-16B. When voltage is applied across the electrodes, the dielectric thickness (the dielectric thickness extending across the page in FIG. 16C) is reduced and the actuator 700 expands linearly, moving the load downwards. When the voltage is turned off, the stored elastic energy of the deformed shell 708 causes the actuator 700 to return to its original shape and length.

[0108] FIG. 17A illustrates quasi-static linear actuation of a six-unit planar HASEL actuator 800 (made up of six planar-type actuators 700 back to back) at 11.5 kV with a 500 g load. Lateral prestretch was fixed at 2.5 and there was an initial prestretch of 1.5 in the direction of the weight. The use of six individual planar-type actuators 700 made it easier to operate actuators in different orientations as change in hydrostatic pressure of the liquid dielectric may be small. In FIG. 17B, a single planar-type actuator 700 is driven by a sinusoidal signal with frequency set near resonance and achieved 107% linear strain under a 250 g load (actuation stress ˜32 kPa). The amplitude of the voltage was 13 kV, which corresponds to an applied field of 10.1 kV/mm (based on un-deformed thickness of the actuator). The actuation frequency was 4.6 Hz. In FIG. 17C, a two-unit planar HASEL actuator was driven by a sinusoidal signal with frequency set near resonance and achieved 124% linear strain with a 700 g load (actuation stress ˜114 kPa). Amplitude of the voltage was 14.5 kV, which corresponds to an applied field of 15.5 kV/mm (based on un-deformed thickness of the actuator), and the frequency. By tuning the relative thicknesses of the elastomer shell and liquid dielectric layer, different amounts of actuation stress and strain can thus be achieved. FIG. 17D graphically illustrates actuation strain of the planar-type actuator of FIG. 17B at various applied voltage levels. FIG. 17E illustrates a plurality of planar-type actuators without and with an applied voltage and 4 kg of weight hung therefrom.

[0109] FIG. 18A schematically illustrates an experimental setup of a planar-type actuator 700 with and without an applied voltage and a load hung therefrom. Gravimetric power and work were measured and the actuator 700 was driven by a sinusoidal voltage signal. Displacement was measured using a high-speed camera (Model Phantom v710, Vision Research). Velocity and acceleration were calculated from the displacement data. In FIG. 18B, time histories for displacement, velocity, and acceleration for a two-unit planar-type actuator lifting a 700 g load are graphically illustrated. FIG. 18C presents a plot of specific power during contraction for a two-unit planar actuator lifting a 700 g load while FIG. 18D presents a plot of specific power during contraction for a single-unit planar actuator lifting a 1 kg load.

[0110] FIG. 19A illustrates an exploded view of a planar-type HASEL actuator 700′ according to another embodiment, including a molded elastomer shell 708′, first and second stretchable electrodes 716′, 717′, respective encapsulation layers 719′, 721′ (e.g., spin-coated elastomer layers) to encapsulate the electrodes 716′, 717′, and a liquid dielectric layer 712′ inside of the elastomer shell. FIG. 19B shows an illustrative step-by-step process for fabricating the planar-type actuator 700′ of FIG. 19A. As illustrated, embodiments can mold two flat pieces of elastomer for an elastomer shell (e.g., shell 708′), and then bond hydrogel conductors (e.g., first and second electrodes 716′, 717′) to the surface. First and second encapsulating layers (e.g., layers 719′, 721′) can be applied (e.g., spin-coated) on top of the electrodes to protect and insulate them, and the two halves can be joined (e.g., glued) together. The chambers of the elastomer shell can be filled with liquid dielectric (e.g., using a syringe or other suitable device).

[0111] FIG. 19C illustrates an exploded view of a planar-type HASEL actuator 700″ according to another embodiment, including a molded elastomer shell 708″, first and second stretchable electrodes 716″, 717″ (e.g., hydrogel layers), respective encapsulation layers 719″, 721″ (e.g., spin-coated elastomer layers) to encapsulate the electrodes 716″, 717″, and a liquid dielectric layer 712″ inside of the elastomer shell. FIG. 19D shows an illustrative step-by-step process for fabricating the planar-type actuator 700″ of FIG. 19C.

[0112] FIG. 19E illustrates another process of fabricating the planar-type conductor 700″ of FIG. 19C. The process used the following specific materials: Ecoflex 00-30 for the elastomer shell and encapsulating layer, PAAm-LiCl hydrogels for the stretchable conductors, and Envirotemp FR3 transformer oil for the liquid dielectric. In Step 1, two flat rectangular pieces may be molded out of Ecoflex 00-30 for the elastomer shell. The elastomer surface was treated with a 10 wt % solution of benzophenone in ethanol. A mask was used to treat only the area that will be patterned with electrodes. A solution for PAAm-LiCl hydrogel was prepared. In Step 2, a thin plastic spacer was used that was cut out in the shape of the conductors as the mold for the hydrogels. The process continued by placing the spacer on the elastomer surface, pouring in the hydrogel solution, and placing a glass slide on top of the plastic spacer to squeeze out excess hydrogel solution in Step 3. In Step 4, curing was performed under 365 nm UV light for one hour. In Step 5, a layer of Ecoflex 00-30 was spin-coated on top of the conductors to encapsulate them. In Step 6, two elastomer sheets with conductors were bonded together with a thin layer of uncured Ecoflex 00-30. Uncured elastomer was not applied to sections of the shell intended to be filled with oil (those portions of the shell that are to form the internal cavity or pouch). In Step 7, the two sheets were clamped between pieces of acrylic that have cut-outs for the liquid dielectric pouches not to be bonded together. A syringe was used to fill these areas with air, preventing them from bonding together. The two halves were cured together with the air inside the internal cavity. Air was removed from the liquid dielectric pouches, and the pouches were filled with Envirotemp FR3 transformer oil. The actuator was then connected to external electronics.

[0113] FIG. 20A illustrates use of a planar-type actuator 700 to sense a position of an arm holding a tennis ball. Specifically, a robotic arm powered by a planar HASEL actuator 700 measured capacitance for different payloads. The actuation voltage signal was set to 0 kV while the sensing voltage signal was set to an amplitude of 0.08 kV and frequency of 2.5 kHz. Normalized capacitance measurements are plotted as a function of time in FIG. 20C, where normalized capacitance is the instantaneous capacitance value divided by the capacitance of the arm without any loading. A tennis ball (60 g) was dropped onto a holder at the end of the arm. The plot in FIG. 20C shows the under-damped free response of the arm which settles to an equilibrium capacitance value. In FIG. 20B, The tennis ball was removed and a baseball (125 g) was placed onto the end of the arm. At equilibrium, the normalized capacitance measured from the baseball was more than double the value for the tennis ball.

[0114] Yet another category of HASEL actuators is peano-type actuators. Peano-type actuators are capable of fast, muscle-mimetic, linear contraction upon activation. This mode of actuation can exploit certain geometric principles free of relying on stacks of actuators, initial pre-stretching, rigid components, or other techniques. As illustrated in FIG. 21A, the structure of a peano-type actuator 900 can include a flexible, but inextensible shell 908 segmented into discrete pouches 909 that are each filled with a liquid dielectric 912. In other words, the internal cavity may be segmented into a plurality of sub-cavities. Each pouch 909 may not be in fluid communication with any of the other pouches 909. First and second electrodes 916, 917 may be disposed over the shell 908 of each pouch 909. The electrodes 916, 917 can be compliant or rigid, depending on the application. The portion of each pouch 909 covered by the electrodes 916, 917 may be referred to as the active area 924 while the uncovered portion (where contractile geometry change occurs as discussed below) may be referred to as the inactive area 928. To limit electrical arcing through the air around the device during operation, a skirt or an insulating layer can be added to cover the electrodes 916, 917.

[0115] In any case, the combination of each respective pouch 909, liquid dielectric 912, first and second electrodes 916, 917 may be referred to as a unit 904 and the peano-type actuator 900 may have any appropriate number of interconnected units 904 (e.g., such as units 904₁, 904₂, 904₃). When an increasing voltage (V) is applied to the electrodes 916, 917 of the interconnected units 904, electrostatic forces displace the liquid dielectric 912 causing the electrodes 916, 917 to progressively draw together and close; this forces fluid from the active areas 924 into the inactive areas 928 which causes a transition from a flat cross section to a more circular one and leads to a contractile force, F. See FIGS. 21A-21B.

[0116] When voltage is applied to the electrodes 916, 917, they attract due to electrostatic forces. This attraction is governed by the Maxwell pressure:
ρ=∈∈₀E²
where E is the electric field between the electrodes, ∈₀ is the permittivity of free space, and ∈ is the relative permittivity of the dielectric between the electrodes. As the electrodes attract, they redistribute fluid from the active areas 924 into the inactive areas 928. Because the shell 908 is inextensible (i.e., non-elastic), each inactive area 928 is forced to transition from a flat cross-section to a more circular one as shown. This transition may result in a theoretical linear contraction of up to 1−2/π, or approximately 36%, in the inactive areas 928, as seen through simple geometry changes (e.g., as illustrated in FIG. 21B). When a weight is attached to one end of the actuator 900, the increase in fluid pressure is converted to mechanical work performed on the external load. FIGS. 21A-21B show the conversion to mechanical force, as well as the accompanying deformation of the actuator pouches 909. FIG. 21C illustrates an experimental peano-type actuator 900 (with three units 904) as lifting a 20 g weight on application of 8 kV across the electrodes. This construction may use transparent hydrogels as electrodes and fiberglass-reinforced tape for mounting connections.

[0117] FIGS. 22B and 22C illustrate peano-type actuators 900 using hydrogel electrodes and aluminum electrodes, respectively while FIG. 22A graphically illustrates actuation strain of a peano-type actuator with different electrode types (hydrogel and aluminum) and supporting different loads. Specifically, a modified square-wave voltage signal with long rise and fall times (˜1 s) was used to ensure consistent actuation. The actuators were tested at 6, 8, and 10 kV; this corresponded to maximum electric fields of 140, 190, and 240 V μm⁻¹, respectively. The measured forcestrain curves are depicted in FIG. 22A and show little to no difference between aluminum- and hydrogel-electrode performance, demonstrating versatility in material selection and design. The highest load applied to the actuators was 10 N (1 kg), which corresponded to the blocking force for actuators activated at 6 kV and was less than the blocking force at 8 and 10 kV. The 1-kg load resulted in a maximum cross-sectional stress of 6 MPa in the actuator. A strain of 10% was achieved at 10 kV with a 0.02-N (20 g) load. The shape of the observed forcestrain relation is characteristic of Peano-fluidic actuators (12). Furthermore, the monotonic decrease in force with strain is also observed in skeletal muscle (20).

[0118] For most fluidic actuators, the limiting factor in mechanical response is the time required to pump the working fluid throughout the system. Because peano-type actuators 900 locally pump the fluid in each unit 904 (in each pouch 909 of each unit 904), the distance the fluid must travel is reduced which therefore reduces actuation time. In addition, viscous loss and design complexity are reduced by limiting or avoiding the need for regulators and valves.

[0119] FIG. 23A schematically illustrates a test setup for determining contraction characteristics of a peano-type actuator 900. In this setup, the minimum cross section of the actuator used for testing was (40 mm by 0.042 mm) corresponding to a maximum static stress of 2.9 MPa with a 500-g load. FIGS. 23B-23D graphically illustrate various electrical measurements taken during application of a voltage to the peano-type actuator. FIG. 23B shows how an 8-kV square wave was applied to the actuator. The resulting contraction response was measured, where t_s and t_e correspond to the time of initial contraction and equilibrium contraction, respectively. Underdamped oscillations were observed after initial contraction. The small oscillations observed after 0.3 s correspond to out-of-plane swinging of the load and are not part of the characteristic response. In FIG. 23C, peak strain rate during contraction as a function of load is shown. In FIG. 23D, peak and average specific power as a function of load are shown. FIG. 23E schematically illustrates a test setup for measuring a frequency response of the peano-type actuator. As shown, elastic bands were attached to the bottom of the actuator and tensioned to provide a constant 1-N restoring force. FIG. 23F presents frequency response curves for the peano-type actuator of FIG. 23E filled with liquid dielectrics of different viscosities. As shown, the actuator filled with FR3 liquid dielectric showed a nearly flat response up to 20 Hz. The lower viscosity Drakeol 7 allowed maximum actuation at higher frequencies.

[0120] FIG. 24A schematically illustrates a test setup for determining dynamic actuation characteristics of a peano-type actuator while FIGS. 24B-24E graphically illustrate various electrical measurements taken during application of a voltage to the peano-type actuator. Specifically, FIG. 24B is a zoomed view of initial portion of the contraction curve in FIG. 23B, with a 100 g hanging weight. A Savitsky-Golay filter was applied to position (contraction) data to provide smoothing; derivatives of the Savitsky-Golay fits at each point provided velocity (FIG. 24C) and acceleration (FIG. 24D) data. In FIG. 24E, specific power was calculated. Contraction time was treated as the time from the start of contraction t_s to equilibrium contraction t_e, ignoring the subsequent overshoot.

[0121] FIG. 25A demonstrates stack 1000 of peano-type actuators 900 in parallel to increase actuation force. Offsetting the units 904 of adjacent actuators 900 (e.g., so that active areas 924 overlap inactive areas 928 on adjacent actuators 900 or in other words by about half of the length of a unit 904) vertically allows the expanding cross section of one actuator 900 to nest within the pulled-in electrode area of adjacent actuators 900. Alternating electrode polarities ensures that adjacent electrodes are at the same potential. FIG. 25B shows a 1.4-cm-thick stack of six actuators in its inactive and active state, respectively, to visualize the offset configuration. As expected, the stack demonstrated an actuation force roughly six times that of an individual peano-type actuator 900, as shown in FIG. 25C. FIG. 25D shows this stack, which weighs 30 g, lifting 500 g over a strain of 4.6%.

[0122] FIGS. 26A-26B show a particular type of peano-type actuator 900′ for novel and useful modes of actuation such as bending and twisting applications. These applications may be useful such as for the construction of soft grippers for handling delicate and irregular objects. These peano-type actuators 900′ incorporate regions that have a greater bending stiffness relative to other regions to achieve such modes of actuation. This stiffening can be achieved through higher stiffness materials, semi-rigid or rigid materials coupled with soft joints, and/or in other suitable manners. The stiffened regions can be located along all or portions of the actuator shell to achieve various modes of actuation.

[0123] In FIG. 26A, the peano-type actuator 900′ achieves bending modes of actuation by configuring a first portion 908₁′ of the shell (e.g., a left or bottom side in FIG. 26A) to have a greater bending stiffness than a second portion 908₂′ of the shell (e.g. a right or upper side in FIG. 26A). Thus, the pouch 909′ of each unit 908′ is generally surrounded by the first portion 908₁′ of the shell on one side and the second portion 908₂′ of the shell on the other side. When a voltage is applied, inhomogeneous deformation of the pouches 909′ leads to preferential contraction on the right, and overall bending. FIG. 26B shows a perspective view, illustrating the deformation during actuation. Many other approaches are possible for varying actuation. For example, some implementations include twisting or torsional actuators, which incorporate strips of stiffened regions on either side to force a twisting motion on application of voltage. Other implementations include bidirectional bending actuators. For example, by placing two bending Peano-HASEL actuators back-to-back with the stiffened side in the middle, bending actuation can be achieved in either direction by applying voltage to one actuator or the other. Other implementations can achieve bidirectional bending actuation through a three-layer construction: a central stiff layer with incorporated electrodes, and two flexible outer layers (one on either side) that can be selectively activated by application of voltage.

[0124] FIG. 27A shows an illustrative process for fabricating peano-type actuators 900. In Step 1, a first plurality of spaced electrodes are created on a first surface of a first film and a second plurality of spaced electrodes are crated on a first surface of a second film. For instance, each film may be in the nature of a metallized, heat-sealable biaxially-oriented polypropylene (BOPP) film. For instance, the BOPP films may include a layer of vacuum-deposited aluminum on one side. An electrode pattern can be defined on the film by using a PDMS protective mask and submerging in a potassium hydroxide (KOH) etch. For instance, using a soft mask to preserve the electrode area, the aluminum layer may be etched using a 1 wt % KOH solution until excess metal is removed. In Step 2, the first film may be placed over the second film such that the first plurality of spaced electrodes are aligned over the second plurality of spaced electrodes, and then the first and second films may be sealed together at each of a plurality of spaced sealing locations to create a plurality of pouches. Each such pouch is defined by: a) one of the first plurality of spaced electrodes, b) one of the second plurality of spaced electrodes, a) a portion of the first surface of the first film disposed between the one of the first plurality of spaced electrodes and an adjacent of the first plurality of spaced electrodes, and d) a portion of the first surface of the second film disposed between the one of the second plurality of spaced electrodes and an adjacent of the second plurality of spaced electrodes;

[0125] For instance, the two films can be placed back-to-back and sealed together to form the discrete pouches using a heat press with a custom metal die. As shown, the heated brass die may seal the first and second films together at each of the sealing locations. Access ports can be left in each pouch for filling. In Step 3, each pouch can be filled with liquid dielectric (e.g., Envirotemp FR3 transformer oil via syringe or the like) and subsequently sealed (e.g., using a heated metal bar) in Step 4. FIG. 27B shows an illustrative final constructed actuator, which includes a skirt along the outside to prevent electrical arcing through air during operation. The shell materials can include: heat-sealable thermoplastics, reinforced elastomers, cast plastics, etc. A variety of dielectric fluids can also be used. Electrodes can be implemented with compliant materials, such as: carbon-based conductors such as conductive elastomers, fabrics, carbon grease; thin metal layers, such as vacuum-deposited metal layers or conductive tapes; ionic conductors, such as hydrogels and ionic liquids; etc. Other implementations can use rigid conductors for actuation.

[0126] FIG. 28 illustrates a process of fabricating a peano-type actuators, according to another embodiment. Section A illustrates basic components of a peano-type actuator 900 to be fabricated according to the process of FIG. 28. As shown in Section B, two BOPP sheets may be placed between two layers of Kapton film and sealed using a heated brass-rod die. The die may be designed to give pouches (e.g., 2 cm by 4 cm) with access ports (e.g., 2 mm) for filling with a liquid dielectric. A PDMS sheet may be placed below the Kapton as a load-dispersing layer. In Section C, the pouches may be filled with a liquid dielectric (FR3), such as by using a syringe. In Section D, a heated rod may be used to seal the filling ports. In Section E, PDMS-backed hydrogel electrodes may be placed on each side of the pouches. Section F shows a finished actuator.

[0127] FIG. 29 illustrates use of a planar-type actuator to power a robotic arm via an applied voltage and simultaneously sense a position of the arm via measuring a capacitance of the actuator. In other words, HASEL actuators can simultaneously serve as strain sensors. For instance, driving and control electronics may make use of circuits that add a low amplitude AC signal to a high-voltage DC driving voltage, thereby enabling obtaining of the impedance of the circuits containing the hyper-elastic capacitors. Relative capacitance can be recorded as a function of time to indicate the position of the arm. As shown, measured capacitance is low when the arm is fully flexed (on the left) and capacitance is high when the arm is extended (on the right). The bottom plot shows details of the applied voltage signal (solid line) and measured relative capacitance (dashed line), C/C_o, where C is measured capacitance and C_o is the minimum value for capacitance. Voltage and capacitance are ˜90° out of phase, which is typical for a driven damped oscillator. In one arrangement, a first capacitance of one of the first and second electrodes may be measured at a first voltage (or before applying a voltage) and a second capacitance of the one of the first and second electrodes may be measured at a second voltage, and the a difference between the first and second capacitances may be used to determine a strain of the one of the first and second electrodes relative to the other of first and second electrodes during displacement or pressurizing of the liquid dielectric.

[0128] FIG. 30A illustrates two peano-type actuators 900 in parallel for demonstrating fast and controllable actuation. As shown in FIG. 30B, by applying a 13-kV voltage step, these actuators contracted fast enough to throw a ping-pong ball 24 cm into the air. Labeled times are measured from the start of contraction. FIG. 30C shows how incrementing voltage allows for controllable actuation of the arm, as shown in the progression of images with increasing voltage from left to right. The horizontal lines mark the position of the top of the ball for comparison. The ruler to the left of each picture shows 1-cm increments for scale. Not all details of the actuators 900 are illustrated in FIGS. 30A-30C in the interest of clarity. FIG. 31 illustrates the full signal used in testing the lever arm setup of FIGS. 30A-30B. The three regions are meant to show the versatility of actuation for peano-type actuators 900. Section I demonstrates voltage steps of 1-kV increments from 0 to 12 kV with 0.75 s hold time at each voltage to show the accurate positional control with respect to input voltage. Section II is an offset sine wave constructed by reflecting every other cycle over the x-axis. This waveform is meant to demonstrate smooth and muscle-mimetic actuation. Section III is a 13-kV voltage step to demonstrate the high-speed operation of the actuators.

[0129] FIG. 32 is a plot of dimensionless capacitance and optically tracked position data for a single actuator under the influence of a varying voltage signal. Capacitance data is multiplied by a constant scale factor to provide agreement with position data.

[0130] FIG. 33A is a peano-type actuator 900 suspended in a colorful box. FIG. 33B is similar to FIG. 33A but with the box partially filled with a liquid dielectric. FIG. 33 C is similar to FIG. 33B but with the box fully filed with the liquid dielectric and without a voltage being applied. This figure shows how the actuator 900 is nearly or fully invisible. FIG. 33D is similar to FIG. 33C but with the voltage being applied.

[0131] FIG. 34 illustrates a process of fabricating a peano-type actuators 900, according to another embodiment, and using hydrogel electrodes. In Step 1, a PDMS pre-polymer layer may be spin-coated or cast onto a wafer (e.g., acrylic plate) and cured. In Step 2, the PDMS surface may be treated with a solution of benzophenone in ethanol (e.g., 10 wt %). A mask may be used to treat only the area to be patterned with electrodes. In Step 3, a solution may be prepared for PAAm-LiCl hydrogel, and a thin plastic spacer may be used that is cut out in the desired shape of the electrodes as the mold for the hydrogels. The spacer may placed on the PDMS surface, the hydrogel solution may be poured in, and a glass slide may be placed on top of the plastic spacer to squeeze out excess hydrogel solution. In Step 4, curing may be performed (e.g., under 365 nm UV light for one hour). In Step 5, the hydrogel/PDMS structure may be cut out (e.g., with a laser cutter) and set aside until needed. The shell may then be prepared using a heat press with a metal die to define pouch regions. Each pouch may be filled with liquid dielectric through access ports, and each access port may be heat stamped using a heated metal bar. The actuator may then be assembled by laying the hydrogel/PDMS electrode structure onto the pouch with the hydrogel side down and aligning them. The hydrogel may then be bonded to the surface using a cyanoacrylate glue. In Step 6, excess PDMS/hydrogel may be removed to expose completed electrodes.

[0132] FIG. 35 is a plot of cumulative failure probability versus electric field strength for peano-type actuators etched for different time periods. As shown, breakdown voltages of single-layer BOPP film with thin heat-sealing copolymer layer on one side are illustrated. One sample was etched for 4 minutes in 1.5 wt % aqueous KOH solution, while the other was etched for 60 minutes in the same solution. These conditions were meant to verify that the KOH etch did not degrade the breakdown strength of BOPP samples. Electrodes were PAAm hydrogels swollen with an 8 M LiCl solution. A voltage ramp of 500 V/s was applied until breakdown occurred, with 15 tests conducted under each condition. The data was fit to a two-parameter Weibull distribution to determine the characteristic breakdown voltages of 650 V/μm (4 minutes) and 685 V/μm (60 minutes).

[0133] Various embodiments can include various types of features and/or can address various design (e.g., operational) considerations. For example, pouches filled with liquid dielectrics can be segmented to control hydraulic pressure in specific regions. Segmented pouches can also mitigate the influence of gravity, preventing the liquid dielectric from flowing to regions of the pouch with lowest gravitational potential. Segmentation can allow actuators to operate in a variety of positions and orientations without loss of functionality. An example of segmentation is shown in FIG. 17E. By using designs that displace the liquid dielectric only over short distances, energy losses caused by fluid drag can be reduced, and maximum frequency of actuation can be increased. Additionally, the response time can be inversely correlated to the size of the actuator, such that scaling down the actuator can increase the maximum frequency of actuation. In some embodiments, electromechanical pull-in or snap-through instabilities (e.g., as described with reference to FIGS. 6A-6B) can give rise to actuators exhibiting actuation responses that are highly nonlinear and discontinuous (e.g., for use as “binary” actuators). In addition to their inherent ability to self-heal from electrical damage, some embodiments of HASEL transducers further include features for self-healing from mechanical damage, such as by incorporating mechanically self-healing ionic conductors and mechanically self-healing elastomers. Such embodiments can effectively be fully self-healing from both mechanical and electrical damage, which can yield highly durable devices with long lifetimes. The embodiments described herein, as well as modifications to those embodiments, can yield wide variety of HASEL actuators that can be fabricated, and/or arranged in arrays or other structures, to scale up force, increase stroke, achieve modes of actuation with higher complexity, etc.

[0134] The various techniques can be implemented with any suitable hardware and/or software component(s) and/or module(s), including, but not limited to circuits, application specific integrated circuits (ASICs), general purpose processors, digital signal processors (DSPs), field programmable gate arrays (FPGAs), programmable logic devices (PLD), discrete gates, transistor logic devices, discrete hardware components, or combinations thereof. For example, steps of methods or algorithms, or other functionality described in connection with embodiments, can be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in any form of tangible storage medium. Some examples of storage media that may be used include random access memory (RAM), read only memory (ROM), flash memory, EPROM memory, EEPROM memory, registers, a hard disk, a removable disk, a CD-ROM and so forth. A storage medium may be coupled to a processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. A software module may be a single instruction, or many instructions, and may be distributed over several different code segments, among different programs, and across multiple storage media. Thus, a computer program product may perform operations presented herein. For example, such a computer program product may be a computer readable tangible medium having instructions tangibly stored (and/or encoded) thereon, the instructions being executable by one or more processors to perform the operations described herein. The computer program product may include packaging material. Software or instructions may also be transmitted over a transmission medium. For example, software may be transmitted from a website, server, or other remote source using a transmission medium such as a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technology such as infrared, radio, or microwave.

[0135] The methods disclosed herein include one or more actions for achieving the described method. The method and/or actions can be interchanged with one another without departing from the scope of the claims. In other words, unless a specific order of actions is specified, the order and/or use of specific actions can be modified without departing from the scope of the claims. The various operations of methods and functions of certain system components described above can be performed by any suitable means capable of performing the corresponding functions.

[0136] Other examples and implementations are within the scope and spirit of the disclosure and appended claims. For example, features implementing functions can also be physically located at various positions, including being distributed such that portions of functions are implemented at different physical locations. Also, as used herein, including in the claims, “or” as used in a list of items prefaced by “at least one of” indicates a disjunctive list such that, for example, a list of “at least one of A, B, or C” means A or B or C or AB or AC or BC or ABC (i.e., A and B and C). Further, the term “exemplary” does not mean that the described example is preferred or better than other examples.

[0137] Various changes, substitutions, and alterations to the techniques described herein can be made without departing from the technology of the teachings as defined by the appended claims. Moreover, the scope of the disclosure and claims is not limited to the particular aspects of the process, machine, manufacture, composition of matter, means, methods, and actions described above. Processes, machines, manufacture, compositions of matter, means, methods, or actions, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding aspects described herein can be utilized. Accordingly, the appended claims include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or actions.

[0138] It will be readily appreciated that many deviations may be made from the specific embodiments disclosed in the specification without departing from the spirit and scope of the invention. For instance, some arrangements envision that different data item types may require different amounts of processing time by the processors and this may be taken account in the above discussion in any appropriate manner.

[0139] As mentioned, embodiments disclosed herein can be implemented as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a computer-readable medium for execution by, or to control the operation of, data processing apparatus (processors, cores, etc.). The computer-readable medium can be a machine-readable storage device, a machine-readable storage substrate, a memory device, a composition of matter affecting a machine-readable propagated signal, or a combination of one or more of them. In addition to hardware, code that creates an execution environment for the computer program in question may be provided, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0140] Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a sub combination.