Inflatable structures are not new to space, in 1960 and 1964 NASA launched a pair of large (>30 m diameter) aluminized mylar balloons into orbit, Echo 1 and 2 (Hansen, 1995). Echo 1 was successfully used as a passive communications satellite for several months. Recent interest in inflatable structures has increased due to the success of the Bigelow Expandable Activity Module (BEAM), a storage module for the ISS which completed its initial 2-years mission and has remained docked for extended usage (Valle and Wells, 2018). The majority of inflatables designed for space are structural, for habitation, storage, or large communication structures (antennae, reflectors). These designs are mostly intended to be inflated and rigidised to form inflexible passive structures. This rigidisation can be achieved in multiple ways, using hardening resins (UV, temperature, and etc) or strain-rigidising metal-polymer laminates (Schenk et al., 2014). However in this work we investigate the potential for inflatable robotic systems that are active and flexible.

The problems with using gas in space are primarily those of control, and storage. An early attempt to launch Echo 1 ended in disaster as small amounts of residual air deliberately left inside the balloons, intended to inflate it, expanded far more rapidly than planned, tearing the skin to shreds. The late 90s saw a similar incident with the L’Garde Inflatable Antenna Experiment, a test wherein a 14 m parabolic reflector supported by an inflatable torus and 3 inflatable struts was deployed from a satellite on-orbit. Small amounts of residual air caused rapid, uncontrolled inflation of the torus, and uneven deployment of the struts (Freeland et al., 1997). These experiments show that using residual gas for inflation is effective but dangerous; better methods allow for the controlled release of gas into the structure at a slower rate. This can be done with traditional compressed gas containers, as was the case for BEAM, but only for large scale structures. A more scalable method is the use of sublimating solids, the eventual method used by the Echo project. Although manual inflation was the only method used in the experiments described in this paper, alternatives will be the focus of a future publication.

Soft robots show great potential for space applications (Lin et al., 2013), and DETs could be an integral part of their development. To be completely soft, these robots would require soft actuators, and current inflatable designs typically use pneumatic actuators (for example the McKibben actuator or derivatives) powered by large tethered compressors. These compressors have considerable bulk, and make the use of these robots in space less practical. Our approach to this problem is to replace the pneumatic actuation with electrical. By integrating DETs into the skin of a robot we can selectively deform different sections to produce a desired motion. This allows for the production of untethered, lightweight inflatable robots.

The basic structure and function of a DET actuator (DEA) is shown in Figure 2. In its simplest form, it is a sheet of elastomer with compliant electrodes on either side to form a soft capacitor. These stretchy electrodes can be produced from a wide variety of materials (Rosset and Shea, 2013). Carbon based electrodes are the most common in literature, either as a loose powder, suspended in a grease, or as part of a conductive polymer matrix as in our case. When a voltage is applied, the subsequent Maxwell pressure causes the area to expand and the thickness to decrease (Pelrine, 2000). DEAs have been used to power a huge variety of different devices since their inception. When placed in antagonistic arrangements they can mimic biological structures like the human eyeball (Liu et al., 2008), jaw (Wang and Zhu, 2016), limbs (Kovacs et al., 2007) or other locomotory systems (Sun et al., 2016; Cao et al., 2018). Of particular inspiration for us were the multi-degrees-of-freedom spring roll actuators used by Pei et al. used to create a hexapod robot (Pei et al., 2004).

On Earth, DETs have proven to be excellent candidates for actuation, strain-sensing (the capacitance of DETs increases with strain), and energy generation (Anderson et al., 2012). For example, as strain sensors they have been used to monitor the human body in motion-capture gloves (StretchSense, 2020) and diver body kinematics with gesture recognition (Walker and Anderson, 2017; Nad et al., 2019). DETs have also been produced that can sense compression, and shear forces which have potential applications in fields as varied as health care and agriculture (Mahmoudinezhad et al., 2020; Kim et al., 2013).

For space, DETs have undergone testing as sensors for monitoring the structural health of inflatable structures (Litteken, 2017) due to their excellent strain-sensing properties, ability to undergo large deformations, and their ease of integration into fabric. There have also been some attempts to produce space actuators using DEAs including a robotic arm (Branz and Francesconi, 2016) and a satellite gripper (Araromi et al., 2015). These actuators used rigid structures to provide the agonist to the DEA antagonist. Where our actuators differ is the use of inflation, allowing them to be more tightly compacted prior to deployment and making them capable of forming entirely different structures to those comprised of rigid materials.

DET grippers have also been built which incorporate electro-adhesion, utilising electrical fringe fields produced by interdigitated electrodes to generate attractive forces in nearby objects or surfaces (Shintake et al., 2016). Though the forces produced by these electro-adhesive pads are small, this is not a major disadvantage when operating in a zero gravity environment. One area in which this adhesive mechanism excels where others do not is controllable adhesion to smooth, non-magnetic surfaces (or surfaces which should not be magnetised, e. g due to sensitive electronics), such as the exterior of man-made satellites. Electro-adhesive pads have been used in combination sensor/gripper configurations such as that published by Xiang et al. which are integrated into inflated polymer shells similary to those used in this work and use the softness of the structure to conform to, and then grip, lightweight objects of varying surface curvature (Xiang et al., 2019). Electro-adhesive pads are an excellent addition to an actuator, but here we will primarily focus on the mechanical movement.

In this paper we focus on two designs in particular. The first design is a segmented ball-shaped actuator with three degrees of freedom, equivalent to a universal joint coupled to a linear actuator. The second is a wavy hemi-spherocylidrical design, only capable of moving in two dimensions. However it is capable of acting as a linear conveyor in the same way as a line of multiple instances of the first design. This was derived from the first design to accentuate one potential use (linear conveyance/locomotion) while sacrificing the ability to move in more than one plane.

Our inflatable structures with integrated DEAs, start with flat membranes inflated from one side. The basic design was an inflated dome incorporating segmented carbon electrodes capable of tilting the dome in any direction called MIDA (multi-directional inflatable dome actuator). Further iterations we have built include the addition of an electro-adhesive end effector (to allow it to grip nearby objects or surfaces) (Ashby et al., 2019) and miniaturisation to demonstrate more advanced production techniques (inkjet printing) (Ashby, 2019).

The latest version of MIDA took inspiration from the starfish podia, see Figure 3. As well as the dome with segmented electrodes it incorporated a second side, this one comprising a single large actuator, an artificial analogue for the biological ampulla (see Figure 4). When actuated this dome expands, causing the original MIDA side to contract, as illustrated in Figure 5. This gives the system a fully 3D range of movement. Figure 5 shows the parallels between the motion of the starfish podium and that of our actuator. A key difference is the operation of the “muscles;” actuation of the DETs causes an expansion as opposed to the contracting biological muscle.

In the starfish, a single podium cannot effect much force; many podia work in tandem to produce enough force to move the starfish. Rather than create an array of individual MIDA actuators, we produced the same functionality in a single model. To that end, we designed our Phased Inflatable Locomotory Actuator (PILA, see Figure 6). PILA is a hemi-spherocylinderical inflated conveyor system which uses an array of DETs, to provide similar functionality to multiple MIDA actuators using a single-sided structure (see Figure 7). In MIDA a simple 100 µm thick silicone membrane is used, in PILA it is instead two 50 µm thick silicone sheets bonded together using plasma treatment (see Figure 8), with one having patterned holes so as to produce regions of half thickness, see Figure 6B. When inflated, this becomes a naturally wavy structure, see Figure 6C. The “peaks” are the thinner and wider sections that produce the out-of-plane motion, similar to the ampulla of MIDA and the starfish podia, the “trough” actuators provide the horizontal displacement of the “feet” necessary for the walking motion. This walking motion is an approximation of a “metachronal wave” that is seen in nature not only for the motion of starfish legs but also some terrestrial multi-legged animals such as centipedes. In contrast to the looping gait of leeches and caterpillars (and robots based on them such as (Guo et al., 2020)) it is a more dynamic gait, capable of relatively fast locomotion.

The maximum theoretical speed of either walking or conveying a load (assuming perfect operation and ignoring weight in the case of walking), is simply the horizontal displacement of one foot during a cycle multiplied by twice the frequency (twice because one foot will pass the load immediately to the next at the mid-point of the cycle). At higher frequencies we see a decrease in conveyor speed as the DEAs do not fully actuate, and the length of each stride decreasing is not compensated for by the faster steps. This difficulty in predicting the motion can be understood through computational modelling.

DEAs can be modelled analytically for very simple geometries. For small actuation of an ideal, flat elastomer of constant volume (Adz + zdA = 0), the Maxwell pressure can be written as: P = ϵ r ϵ 0 E 2 (1) Where ϵ ₀ is the permittivity of free space, ϵ _r the relative permittivity of the dielectric, and E the applied electric field (Suo, 2010).

Using this we can estimate the induced strain in the z direction: S x = P Y = − ϵ r ϵ 0 E 2 Y = − ϵ r ϵ 0 V 2 Y z 2 (2)

Here we have used V z to define the electric field E across the actuator and Y as the Young’s modulus of the dielectric, which is assumed to be constant for small deformations. This very simplified model assumes a perfectly elastic material, whereas in reality most DETs must be modelled as hyper-elastic systems (Suo, 2010).

For predicting large deformation of materials with a non-linear stress-strain curve, different models of varying complexity have been developed. One of the first, the Neo-Hookean model for hyper-elastic materials undergoing large deformation (proposed in 1948) is based on the thermodynamics of cross-linked polymer chains. This model is simple however, and tends to be accurate only for low strains. Polymer chains have a maximum strain before they reach their limit whereupon a drastic increase in the Young’s modulus will occur, this effect is not seen in the Neo-Hookean model, but is in more recently developed models (Suo, 2010). Some modern models used for predicting the strains of hyper-elastic systems include the Arruda-Boyce, Ogden, Mooney-Rivlin, Yeoh, and Gent models (Rosset et al., 2014; Gu et al., 2017; White et al., 2014; Vertechy et al., 2012; Lampani, 2000; Wissler and Mazza, 2005b,a, 2007).

Analytical models however are not feasible for more complex structures, and so the implementation of Finite Element Modelling (FEM) as a numerical method is a useful tool for the design and prediction of DETs. The model used in this work is a based on that developed by O’Brien et al. in their 2009 paper (O’Brien et al., 2009), using ABAQUS FEA and custom subroutines UHYPER and USDFLD to simulate hyper-elastic behaviour and the applied voltage respectively. The primary difference is the form of the Strain Energy Function. For this the Yeoh model was used instead of the modified Arruda-Boyce as it has previously demonstrated excellent conformity to experimental results for Elastosil 2030 (Henke et al., 2017). The material constants were those identified by Kuhring et al. in their 2015 paper (Kuhring et al., 2015). The elements were M3D8R, 8-node quadratic membrane elements with reduced integration, which were generated in the deflated configuration. Inflation was simulated through application of a uniform pressure to the inside of the membrane surface prior to actuation. Other parameters are given in Table 1.

This model was used to optimise our design, by investigating the effect of changing parameters like the geometry of the electrodes (and the thin sections in PILA) without having to produce multiple physical prototypes. Another important factor in actuation is the level of inflation, an increase in actuation (assuming a constant voltage) is seen at higher pre-strains due to the thinning of the silicone and thus a higher electric field, but is counteracted by the strain-stiffening effect at higher inflations. The optimum inflation level can be found experimentally or by running simulations at different pressures and monitoring the level of actuation. See Figure 9 wherein the actuation (peak to peak displacement of the centre) of the ampulla was simulated at increasing pressures and voltage. The voltage used was a sinusoidal wave with a DC offset equal to half of the peak to peak amplitude, such that the voltage oscillated from 0 V to the maximum (2–5 kV). A local maximum can be observed for all curves at 1.3–1.4 kPa.

The production of the experimental prototypes is outlined in Figure 8, which shows the stages involved in producing the active membrane of a PILA actuator. We started with a pre-made silicone membrane (Wacker Elastosil^®2030, 50 µmfor PILA, 100 µm for MIDA) which was supplied on a roll with PET backing. From this we laser-cut a membrane of the desired shape. In the case of PILA, a second membrane was also cut, with gaps where thinner sections were desired. These membranes were then treated with a hand-held laboratory corona treater (Electro-Technic model BD-20AC) and pressed together to form the final bonded structure, this method was first published by Haubert et al. (Haubert et al., 2006). The treater was affixed to an acrylic holder which was set to maintain a 5 mm distance from the membrane at a 90°angle. Each membrane was treated for 45 s.

The electrodes used were a silicone-carbon black composite (Smooth-On EcoFlex™5 and Vulkan XC-72R respectively, 4.76% carbon black by weight after curing), which was thinned with heptane to reduce the viscosity. This was applied through a PET mask using an airbrush with a 0.2 mm nozzle (Harder & Steenbeck Ultra), at a pressure of 200 kPa. The final electrodes have a sheet resistance of around 100 k℧.

The membrane was affixed to a laser-cut acrylic support frame using an RTV silicone (Dow Corning 734) after stage VI in Figure 8 to allow the removal of the backing layer before the application of the second electrode layer. This frame was later attached to an acrylic support structure after stage VII which incorporates channels for inflation and cutaways to allow access to the electrode layers (see Figures 4, 7).

The silicone membrane used was gas-permeable, as is typical for PDMS compounds, albeit only to a small degree. However, maintaining a particular level of inflation over a long period was vital to the function of our actuators. To that end we applied a very thin coating of a less permeable polymer, SEBS-g-MA (maleic anhydride grafted styrene-ethylene-butylene-styrene). The SEBS-g-MA co-block polymer layer was applied in the final stage of manufacturing, using the same airbrush as the electrodes. For this purpose it was dissolved in Toluene at a concentration of 100mgmL⁻¹. This allowed the structure to maintain its inflated state for a timespan on the order of 10 s of hours rather than minutes.

We used two methods for measuring actuation. First, optical tracking of markers placed on top of the actuators. For this we used TrackMate, an ImageJ plug-in (Tinevez et al., 2017). However this was limited in terms of resolution and sampling frequency. Our second method utilised a laser displacement meter (Keyence LC-2400A with an LC-2440 diffuse reflective sensor head) to track the displacement to an accuracy of 0.1 µm. The drawback for this method was that it could only measure displacement in one direction, and the laser range restricted actuator configurations.

For measuring the blocked force produced by the actuation of the ampulla, MIDA was placed such that the end effector region (see Figure 3) was in contact with a bolt head (area ^∼76mm²) attached to a load cell (Interface SM-50N) whilst the ampulla was charged. The ampulla then had the voltage removed, pressing the end effector against the bolt.