2021 IEEE 4th International Conference on Soft Robotics (RoboSoft)
April 12-16, 2021, Yale University, USA

Rapidly Reconfigurable Inextensible Inflatables

2021 IEEE 4th International Conference on Soft Robotics (RoboSoft) | 978-1-7281-7713-7/20/$31.00 ©2021 IEEE | DOI: 10.1109/RoboSoft51838.2021.9479435

Robert L. Baines, Sree Kalyan Patiballa, and Rebecca Kramer-Bottiglio

Abstract— Inextensible material inflatables, such as thosemade from heat-sealable fabric or Mylar, are lightweight, robust, and easily packed into compact spaces and self-deployed.
They are commonly made by heat-pressing two sheets together
to seal them along a desired curvilinear path. Upon inflation,
the sheets wrinkle about the constraints imposed by the seals,
giving rise to fascinating and functional shapes. In previous
literature, once an inflatable has been manufactured, it can
only attain a single inflated shape. Changing task demandsof the real world motivate adaptive inflatables that are not
fixed to a single deformation. Herein we present a method
for creating inflatables that rapidly switch between multiple
deformation modes. By patterning conductive fabric on thesurface, we bestow the ability to locally form or remove
seals during real-time operation. Namely, pulling a vacuum
to supply compression force and locally Joule heating regionsof the conductive fabric mimics the action of a heat press.
Furthermore, we present a finite element model to aid in theanalysis and inverse design of inextensible inflatables. Together,
the reconfigurable inflatables and inverse model unlock a vastarray of programmed inflated shapes with a single enclosed
volume.

Fig. 1.
Example R2I2: a single inflated volume rapidly transitions
between different bending directions and out-of-plane expansion, enabled byreverseable on-board seal formation. There are two diamond heaters, placed
on top and bottom in opposite orientations, that form the seals needed forbi-directional bending. Arrows indicate possible state transitions.

I. INTRODUCTION
Inflatables are transforming the field of robotics. They
have been used to generate actuators mimicking the dexterityof human musculature [1], to create mechanical camouflage [2], lift objects many times their own mass [3], andreplicate bio-inspired locomotion modes [4]. Elastomericinflatables, including McKibben artificial muscles [5] andfiber reinforced actuators [6], until recently have been preprogrammed and fixed to a single deformation trajectory. The
introduction of removable unidirectional laminae enabledmanual reconfigurable deformation of volumetrically inflating hyperelastic bodies [7]; switchable-elasticity siliconeFields Metal composite allowed for coarse deformation
changes without manual intervention [8].
The class of inflatables made from high stretching modulus(quasi-inextensible) sheets, such as heat-sealable fabrics or
Mylar, can often produce higher forces than their stretchable
material counterparts. As such, they are compelling alternatives for making high force-density actuators or standalone
deployable structures. Creating an inextensible inflatable
generally involves heat-sealing two sheets together along
a desired outer contour. Seals can be made inside of theouter contour as well. The geometry of these seals governs
the equilibrium shape assumed by the inflatable. Althoughcomplex topologies may be elicited upon inflation [9], after
manufacture, reported inextensible inflatables undergo onlya single deformation. Ou. et al. stacked multiple sealed
volumes on top of one another and gave each its own pressure
input to switch between bending modes [10]. However, theirapproach does not lend itself to switching between numerous
drastically different deformations. The aforementioned technologies enabling reconfigurable deformations in stretchable
elastomeric systems rely on surface strain limiting, and thus
are not transferable to systems composed of sheets that barely
stretch at operational pressures.
In this paper, we introduce rapidly reconfigurable inextensible inflatables (R2I2), systems that can autonomously
change deformation, on the order of seconds, via localized
on-board heat sealing operations. R2I2s are enabled byconductive fabric, which is laser-cut into the desired pattern
and adhered to an inflatable’s surface. When the fabric is
Joule-heated and a vacuum applied, a seal forms that causes
the inflatable to deform in a programmed way. The process
is also reversible: by merely heating the fabric again, theseal weakens and the force of inflation separates the sheets,
restoring the inflatable to its original state. We showcase
the concept of an R2I2 by modulating between two bending
modes and out-of-plane inflation with a single volume (Fig.
1 and Supplementary Video part 1).
The proposed reconfigurable inflatable paradigm can generate a diverse array of shapes with a single inflatable
volume. Crucially, R2I2s can reconfigure both their extrinsic
bending and intrinsic curvature (metric) as a function of theapplied heater pattern. As a complement to the vast design

Department of Mechanical Engineering & Materials Science, Yale University, 10 Hillhouse Avenue, New Haven, CT 06520, USA. (email:Rebecca.kramer@yale.edu
978-1-7281-7713-7/21/$31.00 ©2021 IEEE

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A. Fabric heaters
Laser-cut fabric heaters are able to create a wide variety ofinternal seal geometries, and consequently, inflated shapes.
Resistance R of a heater influences the power P it dissipates
as heat by P = I 2 R, where I is the current. Suddenchanges in heater trace width augment R and thereby P ,causing unwanted hot-spots. Fortunately, with laser-cutting
it is easy to ensure smooth changes in width. Heaters withproximate traces, like the circular (Fig. 3B top left) andserpentine (bottom left) heaters, can entirely seal areas,
though the contours of the sealed areas can be imprecise.
We found that individually heating straight sections, as withthe diamond shape (top right), results in more precise seals,
likely due to less resistance variation across the span of
the material. Heating straight sections requires a lead wireat each junction; multiple lead wires can be connected tocreate a quad-diamond (bottom right) network heater withdozens of possible seal patterns. Yet, adding more leads canbecome unwieldy as desired seal patterns scale in complexity.
This fact highlights an inherent trade-off between burdening
the R2I2 with additional electrical leads and desired seal
precision.

Fig. 2. Fabrication of R2I2s consists of four steps. First, two heat-sealable
fabric sheets are bonded together in a curvlinear path with a heat press todefine the contour of the inflatable. Second, conductive fabric is laser cut
to desired pattern. Third, the heater is bonded atop the inflatable. Lastly,
electrical lead wires are attached to the heater with liquid metal encapsulated
in silicone, and the pneumatic inlet is inserted.

space opened up by R2I2s, we present a finite element
analysis (FEA)-based inverse model that takes as input adesired array of inflated shapes and outputs conductive fabricpatterns that will create seals necessary to modulate between
those shapes—the first model of its kind for inflatablesystems.

B. Heat-sealable fabric
To determine the strength of seals formed along joined
sheets of heat-sealable fabric, we conducted t-peel tests on
an Instron Materials Tester at both room temperature (23°)
and 180° (above the melting temperature of the thermoplastic
resin). A peel test subjects the material to a shear condition
highly similar to that which seals experience under inflation.
The 23° average peel force from 20 mm to 80 mm is seventimes that of the heated specimens’ (Fig. 3C).
An optical micrograph juxtaposes delaminated sections ofa representative t-peel specimen at each temperature. Notabletexturing on the room temperature specimen confirms thatthe mode of delamination fractures thermoplastic resin bondsites between the two sheets, consistent with the elevatedforce required to peel them. On the other hand, the heatedspecimen has a relatively unmarred surface, suggesting thatbonds may be formed and removed without compromising
the sealing mechanism. We take advantage of the ability tocleanly remove seals when transitioning between different
shapes with a single inflatable.
We quantified how many times a seal could be formed andremoved before it failed to create a stable bond under inflation (Fig. 3D). A test was conducted on a square inflatableof side length 60 mm with a single heater in the center ofdimension 30x4 mm, consisting of cycles of 1) Joule heating
while applying a -80 kPa vacuum to apply a local seal, 2)
inflating to 7 kPa, and 3) Joule heating again to remove
the seal. For more than 50 cycles no seal failed, testifying
to the fact that the seal formation mechanism is highly
reversible. Granted, the exact geometry of the inflatable,
operating pressure, and heater pattern will influence results.
This study was merely intended to provide an estimate of
R2I2 reconfiguration repeatability with a representative seal
geometry.

II. M ATERIALS AND M ETHODS
The fabrication process for R2I2s is simple (Fig. 2).
An initial inflatable geometry is created by heat sealing
two pieces of fabric along a specific contour. R2I2s inthis paper are made from thermoplastic-impregnated nylon
fabric (200D, Seattle Fabrics). Uniaxial quasi-static tensile
tests reveal the high Young’s modulus of the heat-sealable
fabric at E = 510 MPa (Fig. 3A; this value is usedlater in the FEA model). Melting the thermoplastic of two
sheets pressed together allows the resin to flow between the
sheets, and when cooled, forms a contiguous seal (note withtraditional heat sealing, melting only the thermoplastic andnot the reinforcing fibers is desired for mechanical integrity).
Conductive fabric (copper Taffeta from Less EMF Inc. witha sheet resistance of 0.05 Ω/sq) is laser-cut to a desired
pattern (VLS 2.0 Lasers) and bonded to the surface of thefabric with Silpoxy (SmoothOn Inc.). Then, flexible wires
or conductive threads are connected to the conductive fabricwith eutectic Gallium Indium alloy encapsulated in silicone(Dragon Skin 10 Medium, SmoothOn Inc.), so that the fabriccan be tethered to an external power supply for Joule heating.
Lastly, a small slit is cut into the enclosed volume, and apneumatic inlet is inserted.
Owing to its low bending modulus, the fabric heater isable to conform to the wrinkle field that occurs locally atseals, and thus has a negligible impact on the shape assumed
by the inflatable. Similarly, the liquid metal and silicone
interface between the wires and conductive fabric can deformin the presence of a wrinkle field without losing continuityor shearing off, as would a brittle connection.
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Fig. 3. A. Uniaxial tensile test of heat-sealable fabric. A solid mean line, calculated from five rectangular samples, is surrounded by a cloud indicating
one standard deviation from the mean. The dashed line is a linear fit. B. Laser cut heater patterns at different scales. More precise or complex seals
require additional electrical leads. C. Standard t-peel test at room temperature and elevated past the melting point of the thermoplastic resin in the fabric,
revealing a seven-fold difference in peel strength. Clouds indicate one standard deviation from the mean for five samples. Inset is an optical micrographof a representative specimen exhibiting delamination. D. Snapshots from the cyclic reconfigurability test, wherein a single volume modulated between two
different deformation modes more than 50 times.

patterned (with a heat press) seals. For instance, we madea single volume capable of morphing between a saddle andan twisted anti-cone (Fig. 4B). The pre-patterned geometries
were adapted from work by Siéffert et al. [9]. The R2I2
was fabricated by stacking the two pre-patterned inflatables,
gluing them along their edges, and connecting them with atube to render a single volume. Rectangular fabric heaters
adhered on either side served as valves to selectively direct
air flow. Transitions between shapes took 35 sec (at 1 W)
because we needed to seal one valve when pulling a vacuum
and then open the other valve when inflating.

III. A PPLICATIONS
A salient application of R2I2s is to make dexterous
and reconfigurable actuators. We made an R2I2 capableof rapidly twisting in one of two directions or expanding
out-of-plane (Fig. 4A). A long, continuous fabric heater
adhered to the R2I2’s surface exploits varying trace width toproportionally dissipate power in areas of higher resistance(thinner sections). The same heater pattern is mirrored on
the backside, enabling on-demand seals at ± 45° distributed
along the length of the R2I2. Transitions from out-of-plane
inflation to handed twisting took 20 sec, limited mainly by
the cool-down period required for a seal to set. Transitions
from handed twisting to out-of-plane expansion took only
5 sec (when 7 W was applied).
Some seal patterns can be difficult to form with theproposed fabric heaters and vacuum mechanism, particularly
if the pattern requires many electrodes, or extremely highresolution and close-proximity features within 1 mm. Yet
such patterns are desirable because they distort the inflatables’ metric and can doubly-curve its midplane section.
Fortunately, there is a way to realize R2I2s that modulate
between said deformations: fabric heaters can be utilized
like valves that selectively open or close sections of a
volume, directing air flow between regions containing pre-Combining valving, pre-patterned seals, and on-demandseal formation further expands the R2I2 design space. As ademonstration, we fabricated an artificial flower (Fig. 4C).
The flower has two diamond heaters circumfrentially about
its “pedals”, one central spiral heater, and a valve at its“stalk” regulating air flow into a pre-patterned seal section.
The flower can morph between several distinct states. Shownare two bloom phases, the left in which the stalk is straight
and a portion of the pedals are unfurled. This is the default
state, without making seals or releasing the valve. The rightbloom is toggled by sealing the central spiral heater andperipheral diamond heaters, and opening the valve to thepre-patterned geometry within the stalk. The result is a non31

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Fig. 4. A. Long R2I2 rapidly changing twisting direction, made possible by a single heater with only two electrodes on either side. B. Fabric heaters usedas switches to modulate between complex pre-patterned topographies of drastically different Gauss curvatures. Design adapted from [9]. C. Combining
fabric heater valves to switch between pre-patterned deformations, and creating on-demand seal geometries with more complex fabric heaters, we madean artificial flower capable of distinct “blooms.”

in the simulations, we verified that the kinetic energy of themodel was low in comparison to the strain energy. Moreover,because dynamic simulations in ABAQUS are conditionallystable, we verified that the kinetic energy was very small
relative to the internal energy at all steps.
To verify the FEA model in a simplified design space,
we simulated three rectangular bending R2I2s—inspired by
Ou et al. [10]—of dimensions (l × w) 120x60 mm. Eachactuator has a diamond-shaped fabric heater located at its geometric midpoint, with spanning segments axb of 14x28 mm,
28x28 mm, and 42x28 mm, respectively. The diamond shapemakes a seal that induces extrinsic bending, upon inflation,
through a buckling instability. The magnitude of bending iscontingent on the diamond’s aspect ratio (a/b). All actuators
were inflated to 15 kPa in experiment; an equal magnitude
distributed pressure load was applied in simulation.
Qualitatively, there is good agreement between wrinkles
in simulation and experiment, testifying to the high fidelityof the simulation (Fig. 5A). The percentage error between
actual (θ) and simulated (θs ) bending angles for designs 1,
2 and 3 is 3%, 10% and 8%, respectively, with simulationconsistently overestimating the angle. We suspect that a seal
formed by the conductive fabric heater might be slightly
thinner than the geometry of the heater due to convective
dissipation of heat around the edges, and that this decreased
thickness was manifested systemically through smaller bend
angles in hardware. A simulated parametric study in which
we held a/b of a design constant and swept over a range ofseal thicknesses t, recording θs (Fig. 5B), elucidates how θsis highly sensitive to t. Even a 1 mm change in t can resultin an 8° change in θs (per design 2, going from 2 to 3 mm).
Based on the findings of this study, we verified that subtleties
in seal geometry can radically change apparent deformationof an R2I2. Some level of discrepancy between projected
and actual deformations must therefore be expected due tothe variability of a formed seal’s thickness.

Euclidean undulation along the stem reminiscent of frustrated
elastic sheets [11] and all pedals curling inward about asunken center. Due to the multiple heaters and distinct
pressurization steps, transitions between blooms can takeabout 1 min.
IV. P ROGRAMMING R2I2 DEFORMATIONWith hardware that enables rapid reconfiguration between
multiple deformations, naturally the question arises whether
we can specify a set of shapes and use a model to generate the heater pattern(s) required to realize those shapes.
The equilibrium shape of a certain class of simpler, often
axisymmetric inextensible inflatables is well-studied, andcan be described with analytical solutions [12]. Numericalinverse design has also been demonstrated for more complex
3D inflatables, but has two significant limitations: it does
not provide a user with the option to inspect physicallymeaningful quantities post-simulation, and it has trouble
processing planar surfaces and sharper edges of deformed
geometries [13].
Seeking to predict the shape of R2I2s, we conducted nonlinear quasi-static analysis in ABAQUS/Explicit. Established
FEA software is attractive because it gives us: 1) a highresolution map of surface wrinkles for qualitative comparison
with hardware, 2) insight into the governing physics of
the inflatable system, and 3) the ability to simulate highly
complex designs (which we will touch on in a later section)that existing models cannot accommodate.
A. FEA model
The FEA model was formulated with material stiffness
data from Fig. 2A, using a linear elastic continuum modelwith Young’s modulus of 510 MPa and Poisson’s ratio of
0.38. The R2I2 in particular was modeled as an enclosed thinshell with its seals constrained using *TIE constraints. Fournode doubly curved shell elements (S4R) with an hourglass
control were used to define the R2I2 contours. To improvethe computational efficiency and limit numerical oscillations
during dynamic simulations, mass scaling and Rayleighdamping were performed. To ensure quasi-static conditions

B. Inverse design for reconfigurable deformations
Having validated the forward FEA model, we proceeded
to conduct inverse design. We reiterate that the scope of this32

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Fig. 5. A. Top row: schematics of bending R2I2s with three different aspect ratio diamond heaters, showing relevant dimensions. Bottom rows: validationof ABAQUS simulation with experiment, with different bending angles as a result of seal geometry. B. Results of the parametric study. A plot of bending
angle versus seal thickness, holding a design aspect ratio constant. Legend refers to designs labeled in A. C. Top: schematic showing optimization variables
for the inverse design experiment in the context of the pre-defined R2I2 contours. Bottom: model-generated heater pattern transferred to an R2I2. D. Bend
angle versus heater aspect ratio. Points are plotted for the desired bending angle, the angle attained by inverse design for the pattern it generated, and theexperiment. Schematic insets illustrate which of the three diamond heaters was used to reach that angle in the experiment. E. Simulation provides insight
into designs that may be difficult to prototype, such as this 3×3 grid. The schematic in purple and black shows possible seal geometry. Images from FEA
show three distinct topographies achieved by sealing all patterns along a unique direction.

portion of the present paper focuses on a simplified subset ofthe design space—namely bending actuators via a buckling
instability—to exhibit the R2I2 concept. For the inverse
design problem, one seeks to find the required geometry of aheater that elicits several desired bend angles from an R2I2.
Posed as a shape optimization problem, this objective is:pattern for an R2I2 to achieve three bend angles: 90°, 110°
and 130°. The model output three diamond shapes that when
united become a tri-diamond (Fig. 5C bottom). We proceeded
to Joule-heat and thereby seal each diamond individually andthen inflate the R2I2 to measure the bending angle. Despite
the overlap in heater trace edges for the a/b =1.5 and 2
cases, the experimental bend angles are very similar to thoseprojected by the inverse design and the original desired input,
boasting less than 4% error at each angle (Fig. 5D). Strong
agreement between the output heater pattern from the inverse
model and the physically realized R2I2 attest to its efficacy inthis simplified design space; furthermore, the accurate results
bode well for inverse design of more sophisticated R2I2s.

2

min : (θs − θs ∗ )Xi(1)

s.t : Lmin,i ≤ Xi ≤ Umax,iHere, θs is the bend angle from the FEA model and θs ∗is the desired bend angle. The design variables Xi ’s are
the X-coordinates of the points (Fig. 5C top). Lmin,i and
Lmax,i are the lower and upper bounds (enforcing realistic
heater dimensions), respectively. t is kept constant at 3 mm.
To ensure symmetry of a heater, we imposed an equality
constraint on the design variables as well.
The optimization was performed in a Python IDE withABAQUS scripting for the FEA model, post-processing, andresult validation. Due to the stationary nature of the bend
angle with small variations in the design variables, standard
gradient descent algorithms are ill-suited to solving thisinverse design problem. We thus employed basin-hopping[14], a stochastic global optimization algorithm.
We implemented our inverse model to generate the heater

C. Exploring novel R2I2s in simulation
To explore the design space for R2I2s even further, we
simulated a 3x3 square grid R2I2 (Fig. 5E, Supplementary
Video part 2). We specifically show the R2I2 taking on three
configurations, by activating all of the constraints in one orientation (Fig. 5E schematic shows possible configurations in
purple and black). The high-fidelity FEA model can capture
the wrinkling and buckling of the system, even in the context
of an intricate energy landscape arising from stretching andbending energy competitions between neighboring unit cells.
Rifts and valleys along the simulated R2I2’s surface exhibit
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a spectrum of curvatures. For R2I2s of size and complexity
rivaling this simulated 3x3 grid, it is pragmatic to simulate
such cases to validate feasibility before prototyping. As R2I2
manufacturing methods and hardware improve, we expect tobe able to realize these large-scale systems: reconfigurable
topography with unprecedented control of the metric.

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V. C ONCLUSION
With a simple concept we have presented herein—leveraging low-profile conductive fabric to locally create or
remove seals between heat-sealable sheets—we have showna glimpse of the rich spectrum of inflated shapes attainablewith a single volume. We demonstrated how R2I2s can
independently modulate both extrinsic bending and intrinsic
curvature along their surface. While the R2I2 concept holds
significant promise in the robotics space, it is transferable toother domains: in surgery, R2I2s with a lower sealing point
could be used for shape-morphing stents, in rehabilitation,
they could be applied to adaptive exosuits, and in architecture, R2I2s could be the foundation of smart structures.
However, R2I2s need further characterization and improvements before they are widely adopted. For the sametypes of deformations, R2I2s may surpass the speed ofreconfigurations in existing elastomeric systems [7], [8], buta primary bottleneck for R2I2 reconfiguration speed is cooldown time while seals form. Though the demonstrations
herein span a range of cool-down times based on heater
complexity—from 5 sec to minutes—implementing a heattransfer system or thermally isolating sections of heaterfrom the inflatables’ surface would certainly improve their
response times.
Additionally, exploring options for a heating material that
produces precise seals would help to seal distinct features<1 mm apart with fewer electrodes. Furthermore, it would
be prudent to electrically insulate the exposed heaters on
the surface of the actuator such that R2I2s could more
readily interact with an environment without the possibilityof shorting.
On the modeling side, our inverse pipeline finds fabricheater designs to realize desired bending angles; in the future
the objective could be augmented to more generic measures
like mid-plane Gauss curvature or surface normals. Overall,with this work we have taken a step toward the next generation of context-sensitive robotic systems by introducing areconfigurable actuator paradigm.
ACKNOWLEDGMENT
R.L.B. was supported by the National Science Foundation
Graduate Research Fellowship (DGE-1333468). S. P. was
supported by the Office of Naval Research under the Young
Investigator Program (N00014-17-1-2604).
R EFERENCES[1] F. Connolly, C. J. Walsh, and K. Bertoldi, “Automatic design of fiberreinforced soft actuators for trajectory matching,” Proceedings of the
National Academy of Sciences, vol. 114, no. 1, pp. 51–56, 2017.

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