Electrostatic bellow muscle actuators and energy harvesters that stack up
The development of electromechanical devices that are mechanically soft or compliant is expected to lead to robotic systems that can interact safely with humans and other living creatures (1). A key component of these robots is the actuation system, which is required to contribute to different motoric tasks, including soft joint motion/stretching, similar to mammalian muscles, or interaction with objects through inflatable/bendable interfaces (2, 3).
In response to this need, the past decade has seen a huge effort to develop fluidic actuation systems (FASs) (4, 5) and linear artificial muscles (AMs) (6–8) for soft robots. Robotic FASs are based on soft actuation structures capable of smooth interactions with the environment, but they require bulky compressors or pumps. Several works have been conducted to develop battery-based microcompressors (4) and lightweight fully polymeric pumps based on smart materials (5, 9). The first have been successfully demonstrated in some robotic applications but have limited efficiency and scarce controllability, and they are inherently stiff and noisy. The latter rely on less conventional operating principles such as electroosmosis (10), thermo-pneumatic force (11), and charge-injection electrodynamics (5) and are suitable for very small–scale applications with flow rates below a few milliliters per minute, but they struggle to reach intermediate scales required for centimeter-scale robots.
In parallel, the past decade has also seen a huge effort to develop AMs able to produce displacements and forces in the ranges of 10−3 to 10−1 m and 10−3 to 102 N, respectively. Traditional multipole electrical motors struggle to reach these scales because of the complexity in miniaturization, whereas microactuation systems (12) cannot be easily scaled up. Although thermally driven actuators (13, 14) have been identified as promising options, their response is limited by slow heat transfer dynamics.
Electrostatic actuators are an interesting option for actuation of robots owing to their simple design (relatively small number of components), lightness, high efficiency, ease in control, self-sensing capabilities, and bidirectional operation (i.e., they can work as actuator and as generator in the passive phase of motion). Electrostatic actuators that take advantage of Maxwell pressures within an air gap are the most effective solutions in the length scale from 1 to 10 μm (i.e., for microelectromechanical systems) but do not effectively scale up in the millimeter to centimeter range due to the decrease of the dielectric strength in large air gaps. Dielectric elastomers (DEs) (15–17) have been introduced as a possible solution for electrostatic actuator upscaling. However, they require complex layouts with prestretched functional membranes (18), and their useful force is limited by the polymer mechanical stiffness.
In 2009, Najafi and coworkers (19, 20) introduced the electrostatic hydraulic microactuator, which relies on a combination of deformable dielectrics and a dielectric liquid gap. Compared with microactuators with air gaps, these systems can bear larger electric fields. Compared with DEs, they present little or no force limitation due to the elastic stresses. The full potential of this concept was later proven at larger scales by Keplinger and colleagues (21) with the development of the HASEL (hydraulically amplified self-healing electrostatic) actuators. In parallel, Shea and coworkers (22) introduced the idea of zipping electrostatic actuators, i.e., a device in which two electrode-coated dielectric polymeric films come into contact through progressive increases in their contact surface, in response to an applied electric field. However, they obtained nonoptimal performance because of the use of air as the dielectric fluid. Later on, taking advantage of dielectric liquids, our group (23) demonstrated the possibility to revert the zipping actuation principle to perform electrical energy generation.
Among the most recent actuator concepts based on the zipping kinematics and a liquid dielectric, Peano-HASEL (21, 24) and electro-ribbon AMs (25) demonstrated impressive results in terms of energy densities, on the order of 102 J/kg, despite the use of simple off-the-shelf low-cost materials such as polypropylene or other flexible polymeric films and dielectric oils. However, these devices were only demonstrated as AM actuators, and no proof of bidirectional actuator-generator operation was delivered.
Here, we present the electrostatic bellow muscle (EBM), a lightweight electrostatic transducer that combines fluid dielectrics, flexible electroactive films, and stiffening elements to form a deformable unit that contracts and pumps the dielectric fluid in response to an electrical stimulus. Unlike previously proposed concepts, an EBM device can alternatively work as: (i) a hydraulically coupled actuator (which exploits the fluid pressure to produce work on the external world), in the same fashion as HASELs (21); (ii) a purely electrostatic actuator (without pressurization of the dielectric liquid), in a similar fashion as electrostatic ribbons (25).
As contractile muscles, EBMs offer (i) suitability to be combined in arrays to achieve large strokes and forces and (ii) contractions over 40%, comparable with those of natural muscles and exceeding those of several AM technologies (8, 26, 27). As hydrostatic pump for FASs, EBMs outperform state-of-the art soft pumps based on dielectric polymers (28). Compared with Peano-HASELs, which excel in strain rate and power density but require external rolling/translating mechanisms (such as pulleys) to achieve actuation strains over 20% (27), EBMs provide larger contractions and better ease of stacking. Compared with electrostatic ribbons, which are capable of huge contractions of up to 100% (25), EBMs reach larger strain rates and provide more stable encapsulation of the dielectric fluid. In addition, EBM contractile muscles can operate in generation mode, converting pulsating mechanical energy into electricity, without modifications to their layout and loading mode, reaching an efficiency of about 20%. Therefore, they could be effectively used to implement power recycling during the passive/breaking phases of actuation.
As it stands, the EBM offers an alternative perspective to enable direct-drive actuation of soft lightweight robots that combine the AMs and FASs. Switching from actuator to generator mode might offer further opportunities to improve energy efficiency and produce a drastic reduction in the required battery capacity of autonomous robots.
EBM working principle
The EBM is an electrostatic transducer that converts electrical energy into mechanical work (or vice versa), taking advantage of electrostatic forces between oppositely charged electrodes (29), and it bears the ability to work both as an actuator and a generator (16, 24, 30, 23). The EBM consists of a circular pouch made of two overlapped layers of compliant polymeric dielectric material holding opposite flexible electrodes on their external faces (Fig. 1, A to D). The dielectric layers are held together by annular frames attached along their perimeter. These frames have the role of maintaining the structural integrity of the EBM and constraining its deformation. The pouch has a single central opening on the top and contains a volume of dielectric liquid. The bottom of the pouch holds a rigid end effector for force application (Fig. 1B).
(A) Representation of the EBM. (B) Photograph of an EBM prototype (bottom view) with reinforcing rings. The diameter of the coin, introduced for comparison, is 24.25 mm. (C) Schematic of the EBM with integrated fluidic reservoir and phases of the actuation at three different voltages (V1 < V2 < V3). In the initial state, the pouch is completely open under the action of a load. At the intermediate voltage, zipping takes place, and the load is pulled up. At the maximum voltage, the device is fully zipped, and the liquid dielectric between the polymer layers is minimum. Blue arrows in the picture qualitatively represent electric field streamlines. (D) Modeling of an EBM with inner and outer radii ri and ro as a combination of two portions: a flat zipped portion with thickness t and area A and a conical fluid chamber with radius rc and height h. An external force F and an internal fluid pressure p are applied on the EBM.
In the free state, the electrodes are flat, and the polymeric dielectric layers are in contact. Once a load is applied, the membranes deform out of plane, originating a liquid-filled pouch with a shape similar to a double-truncated cone shell.
In the actuation mode (Fig. 1C), with the application of a voltage, charges on opposite electrodes attract, causing the polymeric layers to be pulled toward each other in a “zipping” motion (22). During zipping, the polymeric layers gradually come into contact (starting from the perimeter), and liquid is evacuated through a central opening toward a reservoir.
Because of its layout, the EBM can pursue two different actuation modes: as a contractile actuator that does work against an external force or as a hydrodynamic actuator that does work against the pressure of the fluid. In the first mode, Maxwell stresses (16) are exploited to produce work against a force applied at the end effector, whereas the dielectric fluid is evacuated toward a soft-walled variable volume reservoir, hence resulting in little or no variation in pressure with respect to atmospheric conditions. In the second mode, Maxwell stress is used to induce a substantial pressurization in the fluid chamber, and the fluid is delivered to a fluid utility. In the generation mode, similar to DE generators (31), external mechanical forces drive the pouch deformation, whereas the voltage is properly varied in a such a way that electrical energy is generated and supplied to the driving electronics.
Modeling of EBM
The EBM can be modeled as a variable capacitor, using an approach similar to that presented in (29), introducing the following simplifications:
1) In a generic configuration, the EBM geometry can be ideally divided into two portions (Fig. 1D): a fully zipped outer region, in which two flat dielectric polymer portions face each other over an annular surface and a double-cone chamber in which the polymer layers enclose a volume of dielectric fluid. Further assumptions on the distribution of the strains in the dielectric polymer layers are discussed in the Supplementary Materials.
2) The electrical response is purely electrostatic; i.e., leakage currents through the dielectric layers are neglected. Similar to (29), the total capacitance of the device is about equal to that of the zipped annular portion, whereas the capacitance of the double-cone portion housing the oil is negligible.
The EBM kinematics is described through two independent parameters, i.e., the height h of the pouch and the radial distance rc from the cone axis of the inner perimeter of the zipped region (Fig. 1D). The EBM response is governed by the following equations (see derivation and validation in the Supplementary Materials)(1)where ro and ri are the fixed inner and outer radii of the device; is the volume of fluid in the double-cone chamber; Uel = Uel(h, rc) is the elastic energy of the deformed polymer layers; is the area of the zipped electrode portion; t = t(h, rc) is the thickness of a single polymer layer in the zipped region (it varies with h and rc due to strain); ϵp is the dielectric constant of the polymer; and E is the electric field in the zipped region, which depends on the applied voltage V: E = V/(2t). The two terms on the righthand side of both equations in Eq. 1 account for the elastic restoring forces due to the dielectric polymer elasticity and the contribution of Coulomb electrostatic forces. The latter contribution, in particular, holds a term ϵpE2 proportional to the Maxwell stress applied on the polymeric layers over the zipping region.
The response of the EBM in the different working modes can be described in terms of the different applied loads (namely, F or p in Eq. 1). When the EBM works as a contractile actuator, the fluid dwells at a pressure close to atmospheric value (p ≃ 0), and the force F, which makes work in the direction of h, represents the useful output load. When the EBM works as a pump, p represents the useful available pressure, and F is either zero or equal to a constant preload. As a generator, the EBM can take advantage of either the input mechanical work provided by the external force (reverse muscle) or by the fluid pressure (reverse pump) to produce an electrical energy output.
The pouch consists of two layers of dielectric polymer attached together with a thin annular layer of double-sided adhesive film. The top film has a circular opening serving as the fluid outlet. Stiff reinforcing annular frames are bonded on the outer faces of the dielectric films with the aim of preventing deformations at the outer diameter of the films. A reservoir is connected to the top opening and an end effector on the bottom side (Fig. 2A). The reservoir includes a manifold that generates a radial fluid flow from the axial movement of the EBM and a slack membrane that implements a (nearly) constant-pressure variable-volume sealed reservoir. Conductive paint is applied on each side of the pouch (Fig. 2B) to form the electrodes. The device is preloaded and filled up with dielectric oil through the central opening (Fig. 2C).
(A) Exploded view of the EBM. Red arrows show the bonding of two dielectric layers with a thin adhesive on a circular edge. Blue arrows show the bonding of structural annular frames on the two sides of the pouch. Yellow arrows represent the application of the end effector and the fluid reservoir. (B) Electrodes are painted on the external surfaces of the dielectric layers with conductive paint. Flexible copper-tape connectors are used to create the connection with the circuit wires. (C) The EBM is filled with dielectric oil through an opening in the reservoir. The opening is sealed after filling.
EBM operated as a contractile actuator
An EBM unit can work as a contractile actuator achieving contractions of up to 20% its initial length (including the length of the fluid reservoir) against external loads in the range from 1 to 6 N (up to roughly 70 times the whole muscle and fluid storage weight) with input voltages in the range from 6 to 8 kV. At 1 Hz, the EBM unit produced strokes of 1.3 mm (Fig. 3A) corresponding to a contraction of 18.0% of the length before actuation, with a maximum applied voltage of 6 kV. Neglecting the contribution of the reservoir height, the stroke corresponds to a contraction of 44.7%. Figure 3A reveals that at 1 Hz, the device sweeps the whole available stroke and remains latched at the upper and lower positions for a finite amount of time. The EBM moves synchronously with the applied voltage: When voltage is low, concurrent polymeric layers are kept apart (unzipped) under the action of the mechanical load; as the voltage increases, electrostatic forces progressively overcome the external load and cause the electrodes to zip; at large voltage (roughly above 5 kV), the electrodes stay fully zipped against each other, and almost all of the liquid is moved into the reservoir. The EBM experiences a very limited reduction in stroke due to increased frequency (Fig. 3A), similarly to hydraulically amplified muscles (24) and in contrast with frequency-sensitive fluid-based electrostatic ribbons (25). The EBM stroke at 4 and 8 Hz is, respectively, 97.0 and 92.8% of the stroke at 1 Hz, with a load of 1.5 N. Increasing the peak voltage to 8 kV, the EBM reaches a total contraction over 20% with forces of up to 2 N. An overview of the EBM unit response under quasi-static conditions under different applied forces is shown in Fig. 3B. In the low-force range (1 to 2 N), increasing the applied load leads to an increase in the stroke as a result of the increased initial length of the muscle. A further increase in the load, which acts against the electrostatic forces, causes a decrease in the actual stroke. The EBM still generates contractions over 17% with loads of up to 3 N—i.e., an equivalent lifting capability of 35 times its total weight (including the weight of the fluid reservoir) and 50 times the EBM core weight. Increasing the peak voltage generates a modest increase in stroke at small loads, whereas it has a relevant impact at high loads. In effect, at reduced loads, a relatively low voltage is sufficient to cause a contraction close or equal to the whole geometrically available stroke. A larger voltage still produces larger strokes even at 1 to 1.5 N, because it enables better fluid evacuation and the permanence of a thinner trapped fluid film in the fully zipped configuration.
(A) Time series of the voltage V and actuator displacement x at 1 Hz (top), 4 Hz (middle), and 8 Hz (bottom) with a load of 1.5 N. The voltage modulus is shown for clarity, although in practice, its polarity is reverted at each cycle. (B) Force-stroke (top) and force-contraction responses at 1 Hz (bottom), with different applied forces F and voltages. (C) Frequency response at different voltages, with a 2.5-N load (top). Markers refer to tests with different voltage. Results of maximum-frequency test with a 2-N load and 8-kV voltage (bottom). The dashed line with markers refers to constant-frequency tests, whereas the continuous line refers to a test with chirp voltage input. (D) Blocking force test at different frequencies f with a voltage of 8 kV. Markers refer to constant force, whereas line extensions refer to tests with progressively increasing force. (E) Force-stroke response of three different EBMs: the base-case device (outer diameter do = 30 mm) and two versions with radial dimensions scaled by a factor sf = 2/3 (do = 20 mm) and sf = 4/3 (do = 40 mm), respectively. Markers represent constant-force constant-frequency measurements (4 Hz, 8 kV), whereas dashed lines represent theoretically scaled responses with respect to the base-case scenario.
In the range from 1 to 10 Hz, the EBM contraction weakly depends on the frequency even at relatively large applied loads (Fig. 3C). At 2.5 N, the contraction is nearly constant (close to 19%) at 8 kV in the range from 1 to 10 Hz, whereas it slightly decreases with frequency at 6 kV (with the stroke at 10 Hz still being 74.6% that at 1 Hz), because the electrostatic forces do not completely compensate viscous and hydraulic losses. The EBM provides actuation up to frequencies of at least 80 Hz (Fig. 3C) with 2 N of applied load, experimenting a reduction in stroke of 50% at a frequency of 37 Hz and of 80% at 80 Hz. The reduction in stroke at larger frequencies is ascribable to viscous losses due to the dielectric fluid motion.
The blocking force of the EBM (at which the stroke falls to zero) at 8 kV is close to 6 N (i.e., 98 times the weight of the EBM core), rather independently of the actuation frequency (Fig. 3D). The stroke at 5 N is roughly 65% of the maximum stroke, and it drastically falls in the interval of 5 to 6 N. The EBM unit achieves contraction rates of up to 1140%/s at 10 Hz (fig. S8), with power densities over 21 W/kg per EBM core mass (which still corresponds to 14.8 W/kg if the weight of the fluid reservoir is also considered).
The EBM has also achieved notable performance in terms of long-term cyclic operation. An EBM prototype subject to electric fields in the order of 120 kV/mm on the dielectric polymer layers was able to accomplish more than 0.1 millions of cycles at a 5 Hz operating frequency, with no visible reduction in stroke over time (fig. S11).