Ultrafast Soft Actuators


 The quest for an advanced soft robotic actuator technology that is fast and can execute a wide range of application-specific tasks at multiple length scales is still ongoing. Here, we demonstrate a new design strategy leveraging the concepts of miniaturisation and fibre-reinforcement to realize high-speed inflatable actuators exhibiting diverse movements. To fabricate the designs, we employ a class of additive manufacturing technology called melt electrowriting. We demonstrate 3D printing of microfibre architectures on soft elastomers with precision at unprecedently small length scales, leading to miniaturised composite actuators with highly controlled deformation characteristics. We show that owing to their small dimensions and deterministically designed fibrous networks, our actuators require extremely low amounts of fluid to inflate. We demonstrate that actuators with a length of 10 to 15mm and an inner diameter 1mm can reach their full range of motion within ~ 20ms without exploiting snapping instabilities or material non-linearities. We display the speed of our actuators by building an ultrafast, soft flycatcher.


Background
The eld of soft robotics proposed the development of versatile actuators as one of the rst marks on its roadmap to next-generation robotics, due to the integral role of these technologies in the function and performance of robots. [1][2][3] It is known that actuators determine the size, cost, power source, control mechanism, and general design of any robotic system, 4 therefore strong emphasis has been placed on the advancement of these components. Although a wide range of actuator designs have been proposed, due to their ease of operation, low cost and ability to achieve a large range of deformations, in atable actuators have been the primary subject of interest. 5 However, these actuators are often considered too slow for most applications as their speed is limited by large in ation volumes that are needed to create deformations and the consequent large viscous forces needed to let this volume pass through narrow tubes. Several design strategies leveraging snapping instabilities, 6 material non-linearity, 7 stored elastic energy 8 , as well as explosive chemical reactions 9 have been proposed to overcome this limitation.
However, the functionality of the resulting in atable actuators is highly limited as very speci c considerations have to be taken into account in their design and manufacturing. Combining high actuation speeds without compromising functionality has been a major challenge and a high-speed in atable actuator concept that can execute an extensive range of application-speci c tasks is yet to be demonstrated. In this work, we aim at developing highly-functional and modular actuators that achieve high speeds.
To accomplish this goal, we investigate mechanisms that lay at the basis of nature's fast-acting structures that rely on the transportation of uids for actuation. It has been shown that these uid-driven actuators harness miniaturisation to achieve fast movements. 10 For instance, the Aldrovanda can close its leaves in 20ms, which is ~10 times more rapidly than the Venus ytrap, due to its signi cantly smaller size (approximately 1/10 th of Venus ytrap). 10 Miniaturised designs in uence both the required volume of uid (Δ Volume ) that is needed to be displaced, as well as the distance it needs to travel, enabling rapid movements. Thus, we hypothesise that an analogues miniaturisation strategy can be applied to in atable actuators (see Figure 1A for the schematic illustration of the concept).
In addition to miniaturisation, it is essential to improve the e ciency of actuators in converting delivered uids into fast and predictable movement. As the transportation of uids is a fundamental problem in these systems, available volume in ux has to be e ciently converted towards desired deformations by avoiding unnecessary volumetric expansions that do not contribute to the overall desired deformation ( Figure 1A). To determine how design can in uence this e ciency, we performed Finite Element (FE) simulations (see Supplementary Text for further information) on three common bending actuator designs (eccentric, 11 corrugated membrane 12 and bre-reinforced 13 ) and measured the in ation volume required to obtain the same degree of bending. To eliminate the effect of size, we normalised the in ation volume by L 3 , where we have taken the length 'L' of the actuator as the characteristic length scale. From this analysis, we verify that the design of actuators has a major in uence on bending performance. The same bending angle is reached at lower input volume for those designs that limit parasitic expansion and cross-sectional deformations. As shown in Figure 1B, the actuator with an eccentric design 14 rst has to be in ated substantially to start bending. Then, more than 5 times Δ Volume has to be delivered to achieve 100° bending when compared to the bre-reinforced actuator design. Similarly, the formation of major bulges can be seen in the corrugated membrane actuator design, which is the hallmark of compromised performance. Based on these ndings, we conclude that deterministically designed high-modulus bre architectures are effective in converting uid volume in ux into the desired deformation. In addition to their e ciency, which is largely overlooked and yet to be exploited in the literature, bre-reinforced actuators are proven to be highly versatile with their ability to achieve tailored motions, 1315 making them the ideal choice in our application.
While the previous analysis pointed that bre reinforced design has the highest potential to achieve high speeds, it did not provide any information regarding the in uence of the materials and/or geometry on the performance of the actuators. To investigate the dependency of in ation volume on these two factors, we conducted a series of FE analyses. We designed and simulated a bre reinforced bending actuator consisting of double-helical bres (both clockwise and counterclockwise) with a pitch of 390µm as well as 3 longitudinally placed bres on one side that create bending, surrounding a hollow cylinder with an internal diameter of 1mm, a wall thickness of 0.2mm and length of 10mm. In our simulations (which were conducted using the commercial code Abaqus/Standard), we discretised the cylinder using secondorder hybrid tetrahedral elements (element type: C3D10H and the bres with 3-node quadratic beam elements (element type: B32) and actuated the models supplying incompressible uid to the internal cavity via a uid-cavity interaction. We modelled the material of the cylinder as incompressible neo-Hookean with the initial shear modulus m 0 , while the bres are assumed to be linear elastic with Young's modulus E and Poisson's ratio of 0.3. To begin with, we considered m 0 =15kPa and E=160MPa and found that both the bending angle and pressure vary more or less linear with in ation volume ( see Figure 2A).
From the graphs of Figure 2A, we can identify three actuator characteristics: the in ation volume that is needed to achieve a bending angle of 90° (ΔV 90 ), the corresponding pressure (p 90 ) and the needed energy (ΔE 90 ), which can be calculated as the area under the pressure-volume curve. For this particular actuator, ΔV 90 =2.35µl, p 90 =5.4kpa and ΔE 90 =0.0064mJ. Next, we tested different initial shear moduli values ranging between 7.5kPa<m 0 <120kPa for the elastomeric matrix and Young's moduli values ranging between 80Mpa<E<1.28Gpa for the bres. As these two parameters directly in uence the bending stiffness of either the cylinder (EI=3m 0 · π/4·(r o 4 -r i 4 ), with r o and r i being the inner and outer radius of the cylinder) and the bres (EI=E·π/4·r 4 , with r being the bre radius), we can use them to assess the in uence of both geometrical and material parameters on the performance of the actuators. In Figure 2B-D, we display these in uences by plotting respectively ΔV 90 , p 90 and ΔE 90 for different bending stiffnesses of either the cylinder or the surrounding bres, where stars indicate the previously reported values. Regarding the pressure that is needed to achieve a 90° bending angle ( Figure 2B), we can conclude that a higher pressure is needed when the bending stiffness of the cylinder increases. Surprisingly, the bending stiffness of the bre does not have a large in uence on the required input pressure levels. Regarding the in ation volume ( Figure 2C), we found that a combination of a stiff tube with compliant bres and a combination of stiff bres with a compliant tube lead to higher in ation volumes than when both are stiff or compliant. We can thus conclude that there is an optimal ratio of bending stiffnesses, where bres need to be ~15 times stiffer than the elastomeric matrix, which has been indicated by a dotted line on the gure. Lastly, The energy that is needed to bend 90° ( Figure 2D) is dominated by and follows the same trends as the pressure dependency, which is logical since the relative pressure variation is larger than the relative volume variation while varying stiffnesses.
To create these highly dynamic bending actuators with an optimal bre composition, we cannot rely on production processes described in the literature, as they either are incompatible with small scale production processes, 13,[15][16][17] or lack control over bre placements [18][19][20] . Therefore we developed a new manufacturing strategy that facilitates the fabrication of miniaturised composite soft actuators with precision at small length scales. We use melt electrowriting (MEW) technology, 21,22 a class of additive manufacturing system, which combines the capability of electrospinning systems to produce ultra-ne bres ( bre diameters between 1-50µm) with the design freedom of 3D printing. In this automated process, we apply a thin layer of uncured soft silicone-based elastomer on the rotational collector of our MEW system. By using a rod integrated into our MEW device, we move the stage in x-direction back and forwards with an elastomer and create a thin, uniform layer of the silicone-based tubular structure. We then start melt electrowriting of brous network designs on this partially-cured silicone tube to achieve enhanced bonding between the bres and matrix material. (see Figure S1 and Movie S1 for the schematic illustration and video of the fabrication process, respectively). After the completion of the 3D printing process, we allow the silicone to fully-cure and connect the actuators to a pressure source after sealing their tip.
As demonstrated in Figure 3, we successfully fabricated a miniaturised bending actuator with an internal void diameter of 1mm, length of 10mm and a wall thickness of 0.2mm using our manufacturing technique (see Figure S2 for the technical drawing). The scanning electron micrograph ( Figure 3A) shows the accurate placement of the bres as well as their good continuity and consistency (see Table S1 for the detailed characterisation of the dimensions of the fabricated actuator). We selected the constituent materials of this actuator in accordance with the established principles depicted in Figure 2. As our ndings indicate that the use of soft matrix materials reduces the required actuation energy, we applied the softest grade silicone within the product family of a widely used elastomer (Eco ex with a shore hardness of 00-10). For the fabrication of the bre phase, we preferred polycaprolactone (PCL) due to its excellent rheological properties and processability via MEW process as well favourable mechanical properties (elastic modulus of 320MPa), leading to an actuator with a bre-to-matrix bending stiffness ratio of ~7.5. Although this ratio is smaller than the identi ed ideal ratio, our simulations suggest that this actuator (internal diameter of 1mm, and length of 10mm) require Δ Volume of 2.3559µl to achieve 90°b ending, which is marginally higher than that of an actuator built with materials having a bending stiffness ratio of 15 (Δ Volume of 2.3143µl). Overall, this material combination yielded high performant bending actuators that are also easy to manufacture, handle and characterise as demonstrated in Figure  3.
After pressurizing the actuator, we indeed observed the intended large bending movements with minimum parasitic deformations (see Figure 3A) (see Figure S6 for a bending actuator without helical bres exhibiting large parasitic deformations). Figure 3B shows the magnitude of the deformations achieved by the actuator at given air pressure both experimentally and as computed by means of FE modelling (see Movie S2). By downscaling the dimensions to diameter 1mm we were able to fabricate bending actuators that reach full stroke (270°) when inputting only volumes of less than 7.5μl. Furthermore, by modelling the volumetric expansion of our actuator using FEM, we see radially restricted actuators are characterized by a linear displacement-volume relationship. This means that the input volume is e ciently redirected towards only one spatial dimension, giving a leveraging effect for fast actuation. To con rm this, we have tested our bending actuators under a high-frequency pneumatic input (on-off), where the input air pressure was adjusted such that a full stroke was reached at the end of the cycle (see Figure 3C and Figure S8 for details). We were able to achieve an actuation frequency reaching 30Hz, where complete bending and recovery to initial state takes place within ~30ms (see Movie S7). Further, we see that the dynamics are limited by the de ation part of the cycle. In contrast to in ation where we can adjust the input pressure to reach full stroke quicker, the de ation of the actuator is limited by an atmospheric backpressure, resulting in a maximum actuation frequency of 30 Hz.
The presented methodology of combining miniaturisation with a bre reinforcement design showed to be a highly successful pathway of creating highly dynamic actuators. However, this methodology is not limited to only bending deformations. Using the fabrication freedom of additive manufacturing, we can deposit bres at arbitrary positions and orientations, as displayed in Figure 4. The bre architectures that give rise to the unique deformation of these actuators are displayed using SEM images, where for twining we combined helical bres with three grouped eccentric bres, for extending we remove the eccentric bres, and for contracting we only use eccentric bres that are evenly spaced. Further, these actuators were dynamically tested, resulting in a maximum actuation frequency of 20Hz for twining, 30Hz for contraction and 30Hz for elongation actuators (see Movie SI8-10 for high-speed actuation videos, Figure  SI3-5 for technical drawings of the actuators and Figure SI7 for detailed characterisation results).
Finally, to demonstrate the performance of our actuators, we applied them in a setting where speed, small scale and compliance are of the utmost importance: catching of a y without killing it. Towards this goal, we developed a soft robotic ycatcher ( Figure 5B). The ycatcher consists of three bending actuators that are placed in a triangular pattern around a 3D-printed base with a central cylindrical target area (see Supplementary Text for further information and FigureS10 for the technical drawing). When a y is detected, we apply air pressure to the three bending actuators using a syringe, rapidly closing the trap, successfully catching the y in the process (see Figure 5B and Movie S11). Furthermore, by combining various actuator designs in a linear or parallel manner, a wide range of miniaturized compliant devices such as actuators that transform into very complex shapes (Movie S12) and endoscopic systems that are able to navigate through complex and constrained environments (Movie S13) can be developed.
In conclusion, by enabling the seamless implementation of the concepts of bre-reinforcement to control volumetric expansion and miniaturisation, we were able to create a wide variety of actuator deformations with the application of only a few microliters of actuation volume. As volume ux is typically the limiting factor for speed, we were able to create high dynamic motions (up to ~30Hz) using standard pressure regulators. Our additive manufacturing-based automated manufacturing platform allowed us to downscaling the dimensions of bre-reinforced actuators without compromising their functionality. Such actuators that operate with low-volume and -pressure uids and exhibit minor volumetric changes are also highly advantageous in applications where space of operation is limited. In the present study, we focused our investigation on in atable elastomers. Yet, in future studies, alternative actuation methods can be explored by incorporating different matrix materials that respond to alterations in osmotic conditions, pH, magnetic elds or temperatures. The deformation of this type of soft matter can be guided via our 3D-printed brous network, which may unlock new research directions towards the development of a new generation of soft smart materials, actuators and robots.

Fabrication of soft actuators:
The fabrication process of the actuators starts with the application of a viscous platinum-catalysed silicone (Eco ex 00-10, Smooth-On Inc., USA) onto the printing collector (rod) of the MEW device. First, Parts A and B of the silicon were mixed and stirred thoroughly for 2min (1A:1B by volume), drawn into a positive displacement pipette and applied to the rotating printing collector after 18mins until a volume su cient for a wall thickness of ~200µm is deposited. With the aid of a 0.5mm diameter metal rod attached to the print head of the MEW system that lightly touches the rotating printing collector, the partially-cured silicon was uniformly dispersed by moving the translational linear stage of the system back and forth along the main axis of the printing collector for ~3 mins while it was rotating.
Subsequently, the printing process of the brous network onto the partially-cured silicon was commenced (see Movie S1 for the fabrication process).
For the preparation of the MEW device, rst, medical-grade polycaprolactone pellets (Purasorb PC 12, Purac Biomaterials, the Netherlands) were placed in a syringe and heated to a temperature of 80 °C in the extrusion head of the device. After allowing the polymer to reach a steady molten state (~10 mins), air pressure of 1.5 bar was applied to the syringe using an electro-pneumatic pressure regulator (ITV0030, SMC, Japan) to extrude the molten polymer through a 23G needle. During the extrusion, a voltage of 4.9 -5 kV was applied to the needle that leads to the formation of a ne, stable polymeric jet. The printing collector-to-needle distance was set to 3mm, and the jet was deposited onto the collector at a speed of 165mm/min (combined translational (linear stage) and tangential speed (rotational stage)). MEW is a computer-aided manufacturing technique which utilises programs written in G-Code-based numerical controlling language (see Table S2). The brous networks were printed onto the partially-cured silicone to enhance the adhesion between the matrix material and bres. After the completion of the printing process, the silicone was left to fully-cure for 2 hours. The actuators were then peeled off the rods with ethanol aiding as a lubricant. The actuators were mounted to a pressure source after sealing their tip with air-curing silicone (Sil-Poxy, Smooth-On Inc., USA).
Characterisation of the soft pneumatic actuators:

Scanning electron microscopy
The micrographs of the actuators and brous networks were acquired using a Tescan MIRA3 scanning electron microscope (SEM). Samples were rst gold-coated for 75 seconds at 30mA (Leica EM-SCD005 gold sputter coater, Wetzlar, Germany) before imaging.
Characterization of the movement in response to pressure The actuators were driven with air using a custom-made syringe pump, and their static images, as well as their videos, were acquired using a handheld digital microscope (Dino-Lite Edge 5MP, AnMo Electronics Corporation). The pressure values within the system were measured using a pressure sensor (HSCDANN005PGAA5, Honeywell Sensing and Productivity Solutions), which is placed next to the actuators.

High-frequency and rapid actuation tests (dynamic)
For the high-frequency actuation tests, a pneumatic system (Performus VII, Nordson Electron Fusion Devices, Inc) controlled by an external microcontroller was used. The pressure of the delivered air was adjusted for each actuator type to enable their full range of motion within the duration of each actuation cycle (see Figure S8). At higher frequencies (> ~10Hz), high-pressure values exceeding the regular actuation requirements of the actuators was set as the response of the system was found to be slow to reach the desired levels in the given time if high-pressure values are not used. The pressure values were measured using a pressure sensor (HSCDANN005PGAA5, Honeywell Sensing and Productivity Solutions), which was placed at the actuator-end of the experimental setup.

Measurement of the volumetric expansion (static)
The volumetric expansion of the actuators after their actuation was quanti ed by measuring the amount of uid (H 2 O) that is delivered with a positive displacement pipette. The actuators were submerged in water during the tests to avoid the deformations caused by the weight of the supplied water. Simulations: The response of our actuators upon in ation was modelled using the Finite Element (FE) method, using the commercial package ABAQUS (2019/Standard). In the bre actuator analyses, the silicone rubber was modelled as an incompressible Neo-Hookean hyperelastic material model with initial shear modulus μ 0 of 30kPa. The bres were modelled as a linear elastic material with Young's modulus E of 320 MPa and a Poisson ratio n of 0.3. The cylindrical rubber tube was discretised using 3D tetrahedral hybrid solid elements (element code C3D10H), while the bres were discretised using 3-node quadratic beam elements (element code B32). The bres and cylindrical tube are meshed separately and connected to each other using a tie constraint that allows no slipping of the bres relative to the tube. We pressurize the actuators by supplying incompressible uid to the internal cavity while monitoring the pressure inside and simulate the quasi-static behaviour using a static solver. Figure 1 Design rationale for achieving high-speed soft actuators. (A) Schematic illustration demonstrating the concept of bre reinforcement and miniaturisation to reduce ΔVolume needed for actuation, which is critical for achieving high-speed actuation via regular pressure suppliers. (B) The in uence of actuator design on the performance (capability of converting volume inputs into desired deformations). The gure indicates that certain actuator designs exhibit less parasitic deformations when in ated and require less volume input to achieve the same degree of bending.  Air pressure values measured while characterising the actuation performance of the bending actuators at different actuation frequencies (5, 10, 20 to 30Hz). At frequencies > ~10Hz, pressure values exceeding the regular actuation pressure requirements of the actuators were applied to be able to reach the desired pressure levels within each actuation cycle (see Figure S8 for exact values). The duty cycle was kept constant (on-to-off duration ratio of 2) for all the experiments.

Figure 4
Miniaturised soft actuators exhibiting various movements. Representative twining-, elongation-and contraction-type actuators with their scanning electron micrographs. To benchmark these actuators, we have collected the dynamic data (time to complete an actuation cycle) of in atable actuators from the literature and plotted it against their length scale (see Figure 5A).11,12,31-37,23-30 As illustrated, research efforts towards miniaturisation have been focused on actuators with bending and extending deformations, due to a lack of advanced manufacturing techniques that are needed to create other more complex deformations.38 Actuators with other deformation modes are typically found at larger scales,3915 where limited dynamic data is provided for them. Whereas we showed that additive manufacturing can create pathways for high dynamic actuators, typically these technologies are not well suited for miniaturisations or combining multiple materials.39-45. Therefore, as shown in Figure 5A, the majority of the miniaturised actuators were fabricated via various moulding techniques and are limited to only one actuation mode. As demonstrated, our MEW-based fabrication method provides large design exibility, giving rise to an increase in the design space of miniaturised actuators. We identi ed that our actuators are not only among the fastest in their class (actuators based on forced in ation) but also outperform their counterparts with respect to achievable deformation diversity ( Figure 5A). Furthermore, the collected data also points to the same conclusion as Nature -smaller systems are able to reach higher actuation speeds. Supplementary Files