RESEARCH ARTICLE
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Stretchable Shape-Sensing Sheets
Dylan Shah, Stephanie J. Woodman, Lina Sanchez-Botero, Shanliangzi Liu,and Rebecca Kramer-Bottiglio*
kinematics[3]andaccompanying
dynamics.[4–7] However, an emerging classof robots comprises continuously deformable segments, rendering the rigid-bodyassumption invalid. Many approaches tosoft robot state estimation pair a modelwith several strain sensors, exploiting thefact that much of the surface area and interior volume of soft robots stretch duringuse. For example, researchers have proposed numerous schemes for sensor-based
closed-loop control of continuum robots,[8]including for medical applications.[9]Another particularly well-studied class ofsoft robots is soft grippers, where manymethods were used to sense shape,[10–12]
including a few demonstrations of closedloop control of soft grippers.[13,14] Thestrain sensors used include resistive
sensors made of liquid metal (eutectic
gallium-indium, or EGaIn)[10,11] or conductive polymer composites,[12] and multilayer
capacitive sensors using conductive
polymer composites.[15–17] Despite thesepromising advances, strain sensor-based
methods have some inherent limitations. For example, Caseet al. showed how several common silicones can change mechanical properties over time and even when deformed at different
rates, making modeling challenging.[18] Additionally, it is unclear
how to generalize these advances in strain-based shape estimation to reconﬁgurable soft robots[16,19–21] or robots whose resting
shape changes during their lifetime.[22,23] In both reconﬁgurable
and shape-changing robots, the resting shape dramaticallychanges, violating the basic assumptions utilized in strain-based
techniques, such as the constant-curvature or piecewise-constantcurvature models in widespread use with manipulators.[8]In a step toward decoupling shape estimation from themodeling and design of the robot, researchers have proposed
numerous sensorized surfaces. Several authors have proposedusing ﬂexible fabric or plastic sheets to connect several rigid,
sensorized elements, and then estimating the relative orientation between sections with known geometries (using, e.g., an
inertial measurement unit, or IMU), to determine the spatial
locations of discrete points within a sheet.[24–27] In a related but
different approach, Huard and Sprynski et al. proposed a continuously deformable, sensorized sheet to measure 3D spacecurves.[28,29] Other approaches to surface estimation use
machine learning and statistics to process sensor data andextract a continuous estimate of the shape of the target
surface.[30–32] For instance, Rendl et al. used 16 piezoelectricSoft robot deformations are typically estimated using strain sensors to inferchange from a nominal shape while taking a robot-speciﬁc mechanical model into
account. This approach performs poorly during buckling and when material
properties change with time, and is untenable for shape-changing robots that
don’t have a well-deﬁned resting (unactuated) shape. Herein, these limitations
are overcome using stretchable shape sensing (S3) sheets that fuse orientation
measurements to estimate 3D surface contours without making assumptions
about the underlying robot geometry or material properties. The S3 sheets canestimate the shape of target objects to an accuracy of 3 mm for an 80 mm long
sheet. The authors show the S3 sheets estimating their shape while being
deformed in 3D space and also attached to the surface of a silicone threechamber pneumatic bladder, highlighting the potential for shape-sensing sheets
to be applied, removed, and reapplied to soft robots for shape estimation. Finally,
the S3 sheets detecting their own stretch up to 30% strain is demonstrated. The
approach introduced herein provides a generalized method for measuring theshape of objects without making strong assumptions about the objects, thusachieving a modular, mechanics model-free approach to proprioception for
wearable electronics and soft robotics.

1. Introduction
Sensing our body’s shape is crucial for many, if not all, of ourdaily activities. When our proprioceptive feedback systems malfunction, the consequences can be dire, ranging from decreased
joint stability[1] to bodily damage including possible osteoarthritis.[2] In robotics, proprioception is equally as fundamental, playing an essential role in executing safe, controlled motions.
Numerous approaches to proprioception in robots have been
proposed. Rigid-link robots can estimate their shape accurately
by measuring the angles between the links, and applying forward
D. Shah, S. J. Woodman, L. Sanchez-Botero, S. Liu, R. Kramer-Bottiglio
School of Engineering & Applied Science
Yale University
New Haven, CT 06520, USA
E-mail: rebecca.kramer@yale.edu
The ORCID identiﬁcation number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/aisy.202300343.
© 2023 The Authors. Advanced Intelligent Systems published by WileyVCH GmbH. This is an open access article under the terms of theCreative Commons Attribution License, which permits use, distribution
and reproduction in any medium, provided the original work is
properly cited.

DOI: 10.1002/aisy.202300343

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bend sensors on a polyethylene terephthalate (PET) sheet toapproximate the shape of the sheet as a combination ofseveral shape primitives.[30] Meerbeek et al. embedded an arrayof optical ﬁbers in an elastomeric foam, and used machine learning algorithms to identify the mode of deformation and estimate
the angle of deformation of the foam.[32] One drawback of thedata-driven approaches[30–32] is that it is unclear how the algorithms would generalize to shapes not seen during training.
Furthermore, these prior sensorized surfaces (both the datadriven and rigid-link approaches) could not stretch, making them
incompatible with many soft robots.
In this study, we introduce stretchable shape-sensing (S3)sheets (Figure 1). The sheets comprise acrylic adhesive, biphasic
gallium indium alloy (bGaIn) circuits,[33] and commercial integrated circuits (ICs) that provide orientation and strain measurements. We demonstrate S3 sheets reconstructing their shape infree space and on several static shapes with known geometry,achieving an estimation accuracy of 3 mm on an 80 mm sheet.
We also show the sheets applied to the surface of a three-chamber
pneumatic bladder, highlighting their ability to estimate dynamic
shape change of arbitrarily shaped soft robots, without knowledgeof the robot’s geometry or material properties. Finally, we characterize the stretch sensor response while straining the sheets to
30%. Overall, the S3 sheets can be applied to an arbitrary host bodyto estimate its shape and changes in shape, then removed andapplied to a different host to do the same, cumulatively achievinga modular and mechanics model-free approach to proprioception.

2. Results
2.1. Circuit Overview
We made S3 sheets using sensorized stretchable circuit board
assemblies and used an offboard PC to postprocess the sensor

data for shape estimation (Figure 1). To manufacture the sheets,
we painted conductive traces of bGaIn[33] on both sides of astretchable double-sided acrylic tape (0.5 mm-thick VHB 4910,
3M Inc.), and then placed commercial surface-mount electricalcomponents on the circuits, including absolute orientation sensors (BNO055, Bosch), capacitive sensing ICs (MPR121, Arrow
Semiconductor), resistors, and capacitors. To measure thestretch along the S3 sheets, we painted bGaIn traces on the
top in a rectangular strain-gauge rosette centered around each
MPR121 (Figure 2a), and painted ground traces on the bottom
layer directly underneath these electrodes, to form capacitive
stretch sensors.[15,17,34] To reduce the effects of cross-talk(intracircuit electromagnetic interference), we included bypass
capacitors on the supply lines and aligned the ground planesof the interintegrated circuit (I2C) communication lines with
their positive rails. External noise did not cause issues in our
experiments, but in noisier environments, it may be necessary
to protect signal integrity by including ground pours on the
top and/or bottom of the circuit. Further manufacturing details
are presented in the Experimental Section.
The orientation and stretch sensing modalities fulﬁll complementary roles. The absolute orientation sensors provide a relatively low-noise estimate of the surface normal at discrete
points, while also providing orthogonal vectors in the tangent
plane. Further, absolute orientations reduce the propagation oferror from sensors earlier in the serial chain, when compared
to relative orientations reported by an IMU. The BNO sensors’
three vectors specify a unique coordinate system at each location,
helping to remove orientational uncertainties that can arise fromapproaches relying solely on stretch sensors or relative orientation sensors, but they do not provide any explicit information
about the distance between points on the surface. Meanwhile,the stretch sensor rosettes give information about the sheets’
2D strain state, a feature that will be useful in future sheets that

Figure 1. Stretchable shape-sensing (S3) sheets can stretch and bend to measure the shape of complex surfaces. The S3 sheets (middle) can estimate
their shape while they are deformed in 3D space (left) or applied to objects (right), without requiring additional modeling or sensor fusion algorithms todeal with each different application or use case. Each sheet has a nominal unstretched length of 80 mm.

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Figure 2. Using S3 sheets to estimate the surface proﬁles of several objects. a) Coordinate systems and geometry for the S3 sheets. The positions Pi of theorigin of each coordinate system Oi are our primary values of interest. Additionally, we have used black boxes to indicate three strain sensors within asingle module. Note that O0 and O1 are coincident, but differ by a rotation R10 . Red lines show x axes, green lines show y axes, and blue circles indicate thatthe z axes point out of the page (toward the camera in this view). b–d) Representative results for shape estimation of known geometries. Black dots show
ground truth, gold dots show the rigid-link approximation, and blue dots show the slerp estimation. (b) A rectangular prism with dimensions
44.6  26 mm. (c) A sinusoid with equation y ¼ 10sinðx=10Þ. (d) A cylinder with diameter 42.6 mm. Scale bars, 1 cm.

are ﬁrmly embedded in biaxially stretchable surfaces, such as
shape-changing robots.[35]2.2. Shape-Estimation Algorithms
During use, the S3 sheet will be deformed into a shape, thesensors give data, and we must ﬁnd algorithms to minimize
the error between the estimated shape and the true
shape. Different interpolation methods and shape-estimation
algorithms may perform better under speciﬁc sets of motions.
For clarity and generality, we will focus on two fusion algorithms:
a rigid-link assumption and approximating the sheets as asmooth curve using spherical interpolation of tangent vectors
with discrete integration.
First, we must become more precise in our notion ofshape and error. Numerous methods exist to quantify differencesin shape, after minimizing rotation, scaling, and translation
errors,[35,36] including the elastic deformation energy required
to stretch and bend one shape into another without cuttingor puncturing it;[37] heuristics such as the “shape index”
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ );[38] and the sum of squared differences between(S ¼ Perimeter2 πarea
important landmark points along the two surfaces in
Procrustes analysis.[39,40] Here, we are interested in quantifying
the shape of a discretely sensorized stretchable sheet at an instantin time, and we can easily apply Procrustes analysis for evaluating our sheets and comparing performance to other(nonstretchable) shape-sensing sheets.
Starting with a base coordinate system O0, deﬁned at the corner of the leftmost orientation sensor (with gravity pointing in
the negative z direction), we can deﬁne a series of coordinate systems of interest Oi (i ¼ 1, 2, : : : , 6) that are located at the cornerAdv. Intell. Syst. 2023, 2300343

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of each of our orientation sensors, with the z axis oriented normal to their surface (Figure 2a). The 3D position of these origins
will be denoted as Pi, deﬁned in the base coordinate system O0
unless speciﬁed otherwise. This coordinate system notation is
analogous to the traditional Denavit–Hartenberg notation[3] usedin traditional robotics. However, in traditional robots, the local“joint frames” correspond to the robot’s degrees of freedom.
In the case of an S3 sheet, there are inﬁnite degrees of freedom,and potentially inﬁnite interesting local frames to use. To minimize confusion while retaining all available information, we haveincluded precisely one joint frame per orientation sensor. The
straight-line distances between them will be deﬁned as diþ1i ,while the distance between neighboring coordinate systems,
along the surface of the skin, will be deﬁned as liþ1i .
To estimate the shape of a series of rigid links connected byspherical joints (i.e., they can rotate about arbitrary axes), one simply
needs to determine the coordinate transforms between the bases ofeach link. We will apply this simpliﬁed model to our S3 sheet, inwhat we will call the rigid-link assumption. Speciﬁcally, we deﬁne
the y-axis of Oi (denoted as yi) to point toward P iþ1 , and we deﬁne
the distance between Pi and P iþ1 to be diþ1
i . Thus
P iþ1 ¼ P i þ diþ1
 yi
i

(1)

Note that the orientation sensors used (Bosch BNO055) areglobal orientation sensors, allowing each sensor to be truly independent and preventing error propagation as the sensor countincreases. This is in contrast to a typical orientation sensor, suchas an inertial measurement unit (IMU), which would only give
relative rotations. We can collect the coordinate frame axes foreach sensor into a single rotation matrix Ri, and express thetransformation Ti, in O0 coordinates, as© 2023 The Authors. Advanced Intelligent Systems published by Wiley-VCH GmbH

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0

iþ1
P iþ1 ¼ P i þ diþ1i Ri ½0, 1, 0, 1 ¼ P i þ T i ½0, 0, 0, 1

0(2)

where we have expanded the homogeneous coordinates for an
origin point, to make it explicit that we are expressing the location of an origin. We can then express each coordinate asP0
jþ1
P i ¼ ½0, 0, 0, 1  i þ i1
j¼0 T j ½0, 0, 0, 1 , where the ﬁrst term
½0, 0, 0, 1  i is introduced to ensure that the point is still
expressed in homogeneous form. This ﬁrst term is the main
modiﬁcation required relative to the traditional Denavit–
Hartenberg parameters,[3] wherein the use of relative orientation
sensors allows progressive homogeneous transforms to be multiplied together to make a new homogeneous transform.
If there is negligible stretch in the system, as in the case of afreely moving sheet, then the distances liþ1
are all constant.
iiþ1Additionally, for relatively small curvatures, di  liþ1i , allowing
the skin to operate entirely using the orientation sensors. For
increased accuracy, by premultiplying the initial (ﬂat,unstretched) lengths li0 ¼ di0 with their stretch factor γ i (obtained
from the stretch sensors), we can get an estimate of the current
length liþ1
¼ γ i li0  diþ1i
i . However, to fully estimate the curved
shape of the skin between the successive orientation sensors, weneed to introduce other nonlinear connecting arcs.
To demonstrate how smoothly-varying curves can be used forinterpolation instead of a rigid-link model, we use an approachinspired by the work of Saguin–Sprynski et al.[27] Speciﬁcally,
with tangent vectors given by the sensors as yi and yiþ1 , we ﬁrst
interpolate with spherical interpolation (shorthanded as “slerp”)
to get a smooth estimate ts of the tangent curves connecting thepoints, with known arc-lengths
ts ðyi , yiþ1 , sÞ ¼

sinðð1  sÞθÞyi þ sinðsθÞyiþ1sinðθÞ

(3)

where θ is the angle between yi and yiþ1 , and the arc-lengthparameter s ∈ ½0, 1 allows us to get an arc-length parameterization of the tangent vectors along the unit sphere. This guarantees
the tangent vectors will be unit length, while including the constraint that the tangents match the tangents of the orientation
sensors. Note that, in the limit when θ ¼ 0, this yields the classical linear interpolation. Finally, we can numerically integrate
the tangent estimates with constant step size li =n with n subdivisions of s (such that the total arc length is identically liþ1i ) to getsmooth estimates of the curves connecting our orientation sensors, as desiredP iþ1 ¼ P i þ

n
X

liþ1
i =n  ts ðyi , yiþ1 , j=nÞ

(4)

j¼0

By studying these base shapes, we can begin to quantify thestrengths and limitations of the current hardware, pointing tofuture opportunities and challenges.
Applying the sheets to a variety of geometrically distinct
objects allows us to estimate their surface contours (Figure 2).
Here, we conformed a sheet to the surface of a rectangular prism(Figure 2b), sinusoid (Figure 2c), and a cylinder (Figure 2d).
These shapes represent a complexly curved surface, a discrete
polygon, and a constant-curvature surface, respectively,
highlighting the generality of the approach. For each shape,
we recorded 5 s of data at 30 Hz for ﬁve independent S3 sheet
applications. After each application, the skin was laid ﬂat on atable, then reapplied to the shape for an independent measurement. The total error, including intrinsic sensor noise and errors
due to reapplication of the sheet (representing the envisioned use
case of reconﬁgurable S3 sheets), yielded a root-mean-squareerror (RMSE) of 3.5, 3.6, and 2.0 mm for the rectangular prism,
sinusoid, and cylinder, respectively, using the rigid-link model.
Using the slerp smooth interpolation, we achieved an RMSE of
3.04, 2.7, and 1.5 mm, respectively, suggesting that smooth interpolation is a better estimator than the rigid-link approximation.
Finally, we note that the “null algorithm” of assuming the sheet
was ﬂat would yield much higher RMSEs of 7.11, 12.3, and15.3 mm, respectively.
Note that the accuracy of these curves, in particular discrete
shapes like the rectangular prism, is dependent on where the six
origins are placed: the skin has no knowledge of where discontinuities may lie on the surface. Hence, the change in orientation between two origins could be due to an inﬁnite number ofcurves between the two origins. However, most objects are concave and do not have large, irregularly shaped protrusions, so
the error is often small. The Nyquist–Shannon sampling
theorem tells us that the S3 sheets can only accurately measure
variations in shapes that have a wavelength (or characteristic
length) that is more than double the spacing between
orientation sensors. Increasing the sensor density–and therefore, the number of origins of interest–can allow for the estimation of more complex surface proﬁles. However, current
semiconductor packaging technologies limit the sensing ICs(accelerometers, capacitive sensing chips, etc.) to a minimum
size of approximately 3 by 3 mm, introducing a tradeoff
between sensor density and the deformability of the circuit.
Additionally, the offset between the target shape and the orientation sensors represents a ﬁxed offset error and a slightsmoothing function, making it desirable to manufacture thesheets to be as thin as possible. Here, we used 0.5 mm VHB(sold as 0.02 inches thick), making substantial further improvements in this regard unlikely.
2.4. Estimation of 3D Space Curves

2.3. Surface Contour Estimation of 3D Objects
By applying the S3 sheets to the surface of objects, we can estimate the objects’ surface proﬁles. The sheets can stretch andbend to ﬁll the contours of the surface, allowing their orientation
sensors to get accurate readings of the surface normals. Here, we
explore this possibility by applying the sheets to objects withknown ground-truth shapes to estimate their surface contour.

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To test the limits of the S3 sheets under simultaneous bending
and torsion, we deformed the sheets using rigid bars, andestimated the sheets’ shape using both the rigid-link method(for ease of visualization) and the more-accurate spline method(Figure 3). While the shape-estimation appears accurate, thedense sensor spacing and occlusions during motion made it difﬁcult to obtain ground truth for the sheets’ shape. A complete© 2023 The Authors. Advanced Intelligent Systems published by Wiley-VCH GmbH

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Figure 3. Shape estimation of 3D space curves. Left, photos of the skin deformed in various shapes. Right, estimated shape using the rigid-link
approximation as well as the slerp interpolation, alongside the coordinate frame of each orientation sensor. a) Flat. b) Curved upward. c) Lifted in
the middle, making a concave downward shape. d) Bent around a wooden stick into a step-like curve. e) Bent and twisted simultaneously.
f ) Lifted in the middle and tucked in a highly contorted “Ω” shape. Scale bar in (f ) is 1 cm, and applies to all images.

video of the dynamic estimation of the sequence of motions
shown in Figure 3 can be found as Movie S1, Supporting
Information.
Moving sequentially through the subﬁgures, we haveattempted curves with increasing variations in curvature.
Initially, we can see that the orientation of the ﬁrst sensor, O1
is tilted downward slightly due to the grips lifting the sheet
off of the ﬂat surface (Figure 3a). However, the remaining
sensors are all aligned well, highlighting the global nature of
the orientation sensors. The curve was then lifted into a smooth
curve with a visually accurate sensor reconstruction (Figure 3b).
With the introduction of a rigid stick, two inﬂection points
were added to the curve, making it more difﬁcult for the sheets
to estimate their shape with the rigid-link assumption andincreasing the value of utilizing spline-based methods such as
slerp (Figure 3c,d). Next, we see how the orientation sensors
naturally detect torsion (Figure 3d), in contrast to stretch or
bend sensors, which can estimate at most a single degree of
freedom and require additional sensors to distinguish between
curvature and torsion. Finally, as the curvature increases
into a highly-curved “Ω” shape, the rigid-link assumption
results in physically unrealistic cusp nodes, while slerp approximates the curve but misses some of the nuances due to thecharacteristic length of the bend being of the same order of magnitude as the sensor spacing (Nyquist–Shannon sampling
theorem).

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Since S3 sheets can estimate arbitrary 3D space curves, they
can also be applied to the surface of soft robots to measure theirmotion. To illustrate this concept, we applied an S3 sheet to thesurface of a three-chamber pneumatic bladder (Figure 4 andMovie S2, Supporting Information). The estimated shape starts
ﬂat with the bladders (including the O1 sloped-down error as
noted previously), then as the bladders are inﬂated, the skindetects the motion and adjusts its estimation to be curved withthe bladders’ overall shape. Since the sheets could not detect theiroverall height, we have set the lowest estimated point at z = 0.
Using this baseline, the sheets successfully estimated the shapeand orientation of the surface, highlighting the generality of theprevious 3D space curves estimation.
2.5. Stretchability
The S3 sheets can also detect their stretch, using the capacitive
sensors emanating from the MPR121 ICs. Each MPR121 is connected to three sensors arranged in a rectangular rosette
conﬁguration, which, in theory, can detect the full 2D strainstate. However, we had difﬁculty getting all MPR121s
working simultaneously, thus we include this feature as a
proof-of-concept, and have not utilized the stretch functionality
for our shape-estimation experiments. To highlight thestretchability of the circuits, we stretched an S3 sheet along© 2023 The Authors. Advanced Intelligent Systems published by Wiley-VCH GmbH

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Figure 4. Using S3 sheets to estimate surface proﬁles of a multichamber pneumatic bladder. The plots below each photo show the estimated shape of thesurface of the bladder. Since the sheets have no concept of elevation, we have deﬁned the lowest point of the skin to be z = 0. From top-left to bottomright: ﬂat, middle bladder inﬂated, middle and right bladders inﬂated, all bladders inﬂated, left and middle bladders inﬂated, and left bladder inﬂated. The
scale bar in t = 0 denotes 1 cm, and applies to all images.

the y direction to 30% strain (ε ¼ 0.3) cyclically, and plotted thesensor data from a complete module (Figure 5, with photos of astretched circuit presented in Supporting Information).
Due to their small size (6 mm long, 0.75 mm wide), the sensors have a relatively low capacitance, on the order of 10 pF(Figure 5). While each sensor has a different starting capacitance(likely due to variations in the trace width), the change in capacitance correlates linearly with stretch in the ideal case.[17,41]

In practice, viscoelastic effects and the sensors’ nonzero width
coupled with the Poisson effect lead to imperfect sensor behavior, complicating estimation of the 2D strain state with thestretch sensor rosettes. Despite these challenges, after the initialslack region of 08% strain, the response of each sensor
attached to a given MPR121 is distinct: the sensors aligned withthe stretch direction (sy and ty ) exhibited the largest response(0.12 μF), while the sensors at 45° exhibited a smaller response,

Figure 5. Stretchability of the shape-sensing sheets. Here, we stretched the sheets along the y direction to 30% eight times. a) Raw sensor data from two
MPR121 IC’s, with three stretch sensors each (oriented aligned with the x axis, angled at 45°, and aligned with the y axis). b,c) Change in capacitanceversus stretch, for two sets of strain sensors si and ti. Dashed lines denote the mean, while clouds indicate 1 standard deviation from the mean.

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and the sensors aligned with the x axis exhibited a slightly
negative response. This negative response could be due to theshortening of the sensors (contraction due to Poisson’s ratio, lowering capacitance) overpowering the effect of the sensor getting
wider (elongation in the y direction, increasing capacitance).
In this study, we found that small interfaces were the mostchallenging, with the quad ﬂat no-lead (QFN) packages used here
(pin width 0.2 mm and pin spacing 0.4 mm) beginning to fail atroughly ε ¼ 30%. To investigate whether corrosion was a likely
cause (since EGaIn is corrosive on many metals), we conductedscanning electron microscope/energy dispersive X-ray spectroscopy (SEM–EDS) analysis on MPR121 chips in three conditions:a pristine (unused) state; after being used in an S3 sheet circuit;after being used in an S3 sheet and cleaned (see the , Supporting
Information). We observed no noticeable change in compositionof the electrodes after being cleaned, suggesting that the EGaIn
was not corroding or otherwise alloying with the electrodesurfaces, which were primarily nickel and palladium.

3. Conclusion
In this manuscript, we introduced ﬂexible and stretchable sheetsthat can estimate their shape. This represents an advance toward
the estimation of surface proﬁles of soft robots, which could be
used to execute high-DoF closed-loop shape change. The removable sheets do not make assumptions about the underlying substrate, making it straightforward to apply, remove, and reapply theS3 sheets to the surface of soft robots with differing morphologies.
Limitations of the present S3 sheets could be overcome
through synergistic advances in stretchable circuits, materialinterfacing, and shape reconstruction algorithms. At strains over
30%, the ICs begin to lose connection and discontinue functioning. Potential routes to improve the IC interfacing include theuse of copper strain islands,[42] and the use of HCl vapor to
improve bonding with the liquid metal traces.[43] The use of
an automated pick-and-place machine could reduce componentalignment errors, and the use of purely elastic materials (without
viscoelastic effects) could prolong the S3 sheets’ lifespan by
reducing unwanted wrinkling. Increasing the sensor density
could yield higher-resolution estimates of shape. To apply theS3 sheets to larger surfaces, a multitude of sheets could be connected in a gridlike arrangement, and sensor fusion algorithms,
such as those proposed by Stanko et al.,[44] could be used to combine the information from each S3 sheet and estimate the shapeof large stretchable surfaces. We are currently working towardutilizing such a grid to measure the shape of shape-changing
robots[35] as they morph during locomotion, stretching in multiple directions. Finally, future advances in stretchable computing
could allow the S3 sheets to execute shape-estimation onboard inreal time.
Collectively, this work points to a new approach to shapesensing for soft robotics and wearables. Roboticists could fuseorientation and strain information to get estimates of curves
and surfaces on their robots without requiring extensive systemmodeling and mechanical characterization. This allows two
major design challenges to be decoupled—robot design canbe done more independently of the sensing design, thengeneral-purpose S3 sheets can be attached to the robots’ surfaces.

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4. Experimental Section
Manufacturing: To manufacture the sheets, we made traces on doublesided acrylic tape (VHB 4910) using biphasic gallium-indium (bGaIn),[33]encapsulated using rubber cement (Elmer’s Products, Inc.) and mechanically placed commercial ICs (Figure 6). Speciﬁcally, we ﬁrst attached waxcoated paper (the backing of XFasten carpet tape) to VHB, and laser-cut
the outline and vias with a CO2 laser (ULS 3.0, Universal Laser Systems)(Step 1). Then, we used an ultraviolet laser (LPKF U4) to cut circuit outlines into the sticker paper on the top and bottom (Step 2). Next, we prepared an EGaIn suspension by adding EGaIn (1.8 g) to ethanol (11 mL),
followed by sonication using a probe sonicator (Qsonica, Q700) coupledwith a 1/4 inch diameter microtip (part number 4420) at 30% amplitude
for 2 h. To induce oxide formation and create bGaIn, the suspension waspoured into a crucible and baked in an oven (Lindberg Blue M, Thermo
Fisher Scientiﬁc) at 900° for 30 min. We then painted bGaIn on the bottomof the VHB, removed the bottom sticker paper, and encapsulated thetraces with rubber cement (Steps 3–4). After ﬂipping the circuits over,
we painted bGaIn on the other (“top”) side (Step 5). This completed
the substrate preparation.
To transform the traces into functional circuits, we then placed components with a 3-axis manual pick-and-place machine (custom made using
an Edmund Optics camera-positioning system, Step 6). Next, wires wereadded using silicone adhesive (SilPoxy, Smooth-On, Inc.), and the border
was encapsulated with rubber cement (Steps 7–8). Leaving the ICs
exposed during this step made it easier to debug and repair circuits when
they stopped working. Finally, we added SilPoxy on the border of each IC to
reduce shear strain at their interfaces with bGaIn (Step 9).

Figure 6. Manufacturing an S3 sheet. First, the traces were manufactured
using VHB, sticker paper masks, and rubber cement to encapsulate thebGaIn traces. Then, we added electrical components (ICs, resistors,
capacitors) and wires, encapsulated the border, added SilPoxy islands
around each IC, and attached motion-capture markers onto the orientation sensors to serve as ground truth.

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Supporting Information is available from the Wiley Online Library or fromthe author.

Acknowledgements
This work was supported by the National Science Foundation (NSF)
under grant no. EFMA-1830870. D.S.S. was supported by a NASASpace Technology Research Fellowship (grant no. 80NSSC17K0164).
S.J.W. was supported by a NASA NSTGRO Fellowship (grant no.
80NSSC22K1188). L.S.B. was supported by NSF grant no. IIS-1954591.

Conﬂict of Interest
The authors declare no conﬂict of interest.

Author Contributions
D.S.S. and R.K.B. conceived the project, planned the experiments, andmanaged the research. D.S.S., L.S.B., S.W., and S.L. designed and built
the hardware. D.S.S. wrote the algorithms. D.S.S. and S.J.W. performed
the experiments. All authors drafted and edited the manuscript. All authors
contributed to, and agree with, the content of the ﬁnal version of themanuscript.

Data Availability Statement
The data that support the ﬁndings of this study are available from thecorresponding author upon reasonable request.

Keywords
reconﬁgurable robots, robotic skins, soft robotics, stretchable electronics
Received: June 20, 2023
Revised: August 24, 2023
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