This article has been accepted for publication in IEEE Robotics and Automation Letters. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/LRA.2023.3337702

IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED NOVEMBER 2023

1

Robotic Skins with Integrated Actuation, Sensing, and Variable
Stiffness
Dylan S. Shah1 , Stephanie J. Woodman1 , Trevor L. Buckner1 , Ellen J. Yang1 , and Rebecca K. Kramer-Bottiglio1∗

Abstract—Soft robots are often designed to accomplish a single
function and cannot be repurposed for other tasks. In an effort
to create multi-functional robots, researchers have proposed
robotic skins, which are flexible, planar substrates with embedded
actuation and sensing that can be applied to different soft bodies.
By “roboticizing” otherwise inert bodies from their surface,robotic skins can be repurposed to create bespoke soft robots
as needed. However, current robotic skins are unable to support
their own structure and can only attain a single function in
the absence of a host. Here, we present a variable stiffness
robotic skin (VSRS), a concept that integrates stiffness-changing
capabilities, sensing, and actuation into a single, thin modular
robot design. Reconfiguring, reconnecting, and reshaping VSRSs
allows them to achieve new functions both on and in theabsence of a host body. We demonstrate how a single set ofskins with PneuFlex-style pneumatic actuators, a geometricallypatterned polyethylene terepthalate (PET) jamming membrane,
and liquid metal-based capacitive sensors can operate as closedloop locomotion robots while being able to support weight duringlocomotion, as well as stiffen to hold complex shapes. To highlightthe generality of the concept and illuminate the design space, we
also test a second embodiment with McKibben actuators anda woven-mesh jamming membrane that can be reconfigured toserve in a manipulation context. We see VSRSs having application
as adaptable linkages in larger robots, smart reconfigurable
garments, and reconfigurable active structures, thereby allowing
the robotic system to adapt to time-varying task requirements.
Index Terms—Soft Robot Materials and Design, Cellular andModular Robots, Biologically-Inspired Robots

I. I NTRODUCTIONM

OST robots can execute a fixed range of rigid-body
motions and are unable to adapt to unexpected changes
in performance needs, limiting their use to a finite number
of applications or environments. In contrast, many biologicalsystems thrive across a wide range of tasks and environments,
leveraging incredible cognitive plasticity [1], and an ability toadapt in stiffness to perform both forceful and gentle tasks [2].
By taking cues from nature on matters of mind and body,biologically inspired soft robots leverage new approaches tofunctioning in unpredictable environments [3]. Foundational
Manuscript received: July 11, 2023; Revised October 18, 2023; Accepted
November 12, 2023. This paper was recommended for publication by Editor
Xinyu Liu upon evaluation of the Associate Editor and Reviewers’ comments.
This work was supported by a National Science Foundation (NSF) EFRI
Grant (EFMA-1830870). DSS was supported by a NASA Space Technology
Research Fellowship (grant 80NSSC17K0164). SJW was supported by aNASA NSTGRO Fellowship (80NSSC22K1188).
1 D. S. Shah, S. J. Woodman, T. L. Buckner, E. J. Yang, and R. K. KramerBottiglio are with the Department of Mechanical Engineering & Materials
Science, School of Engineering and Applied Science, Yale University,
New Haven, CT 06520, USA. (dylan.shah.50@aya.yale.edu,
stephanie.woodman@yale.edu, ellen.yang@yale.edu,
rebecca.kramer@yale.edu)
Digital Object Identifier (DOI): see top of this page.

studies on automated gait adaptation [4], adaptive morphogenesis [5], and variable stiffness materials [6] are beginningto yield synthetic systems with life-like adaptive capabilities.
With an eye toward the design of specifically multi-purpose
soft robots, one common approach is the use of modular,
reconfigurable robots [7]. For example, Robertson et al.
proposed soft cylindrical modules that can be reconfigured
between locomotion and manipulation tasks [8]. More recently, Li et al. proposed meter-scale modular soft robots forlocomotion and manipulation [9]. Our own prior work includes
modular soft robotic skins: two-dimensional (2D) elastic membranes with embedded actuators and sensors, which, when
attached to the surface of a host three-dimensional (3D)
soft object, can impart controlled motion onto that objectand “roboticize” it [10]. Robotic skins have previously been
applied, removed, and re-applied to different host objects toachieve multiple tasks including locomotion, manipulation,
grasping, wearability, and shape-change [10], [11], [12].
However, soft modular robots bring challenges common
to all soft robots, including reduced payload capacity. To
allow soft robotic modules to gain some of the advantagesof rigid materials, numerous variable-stiffness materials havebeen proposed (as reviewed by Manti et al. [6]), including stimuli-responsive materials [13] and antagonistic actuators [14]. Variable-stiffness in thin systems has been achieved
by applying a vacuum to thin membranes filled with layers of
inextensible material to achieve “layer jamming” [15], [16]. To
apply layer jamming to modular robotic skins and allow themto lock into general biaxially-curved shapes, the skins need tostretch while unjammed [17]. Recent studies have begun toinvestigate stretchable variable stiffness solutions, including
jamming skins made by cutting intricate patterns in polyethylene terephthalate (PET) [18], and jamming meshes [19].
Here, we build upon this body of work by introducing theconcept of a variable stiffness robotic skin (VSRS), a soft
robot module that integrates actuation, sensing, and variable
stiffness. VSRSs retain the benefits of prior robotic skins andintroduce adaptive stiffness to achieve additional functions
such as shape-locking and load-bearing (Fig. 1). Throughtwo embodiments that illuminate the trade-offs of this design
space, we demonstrate how modular VSRSs can be used indifferent configurations to locomote while carrying a payload
and form a continuum manipulator with a tunable workspace.
II. VSRS OVERVIEWA VSRS has three primary functional components: a variable stiffness mechanism [6], actuators [20], and sensors [21].
Additionally, an inert substrate provides spatial organization

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This article has been accepted for publication in IEEE Robotics and Automation Letters. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/LRA.2023.3337702

2IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED NOVEMBER 2023

Fig. 1. A variable stiffness robotic skin (VSRS) is a reconfigurable, modular sheet containing sensors, actuators, and variable stiffness components. Afteruse in one task, each VSRS may be reconfigured into a different shape and (un)joined with other VSRSs for use in a different task, such as locomotion andmanipulation. Multiple embodiments of VSRSs are possible. Here, we show a design with pneumatic actuators, capacitive stretch sensors, and a stretchable
vacuum jamming variable-stiffness core.

and a way to attach to other skins. Important performancetrade-offs to consider when selecting components include
thickness, weight, the stiffness-switching ratio of the variable
stiffness materials, actuator performance, and sensor resolution. In this work, we sought to achieve sensors with longterm stability and low noise, actuators with a high strengthto-weight ratio, and fast-acting variable stiffness mechanisms
to enable real-time shape transitions.
The VSRS concept is independent of specific component
choices, which we demonstrate by realizing two VSRS embodiments, each square-shaped with nominal edge length of
13 cm, but varying in their selected components. The first
embodiment, “PET VSRS,” was made using fiber-reinforced
pneumatic actuators (similar to PneuFlex [22]), capacitive
stretch sensors (with oxidized liquid metal [23] electrodes),and jammed PET sheets [18] (Fig. 2). The second VSRS
embodiment, “mesh VSRS,” uses McKibben actuators [24],the same capacitive stretch sensors, and jammed woven meshsheets [19]. While both embodiments satisfy our definitionof VSRS, component choices yield unique advantages andcorresponding suitabilities to different use cases. Specifically,
we found that the PET VSRS had higher stiffness and payload
capacity, but couldn’t wrap into a continuum manipulator
configuration. However, by integrating actuation, sensing, andvariable stiffness capabilities into a single modular design, all
VSRSs including those demonstrated can serve as multifunctional, planar soft robots without requiring a host body, incontrast to equivalent single-stiffness skins.
III. PET VSRS R ESULTS
A. Manufacturing
We used a layer-by-layer method to manufacture the VSRS
while minimizing thickness (Fig. 2). First, silicone (Dragon
Skin 10, abbreviated as DS10, Smooth-On, Inc.) was rodcoated to make a thin layer and cured at room temperature.
Next, an oxidized liquid metal paste was created by shearmixing eutectic gallium-indium (EGaIn) with a laboratory
stirrer (IKA EuroStar 20 digital) at 400 rpm for 2 hr at 150 ◦ C,

to encourage the formation of solid gallium oxide throughout
the liquid EGaIn (inspired by Wang et al. [23]). This oxidized
gallium-indium (OGaIn) paste was manually spread over alaser-cut paper stencil to make four strips that served as theground layer of the VSRS stretch sensors. Wires were added at
one end of each electrode. We then applied a layer of silicone(EcoFlex 00-30, Smooth-On, Inc.) as a dielectric, let it cure,added another layer of OGaIn electrodes and wires, and added
a final layer of EcoFlex 00-30 to encapsulate the sensors.
To integrate layer jamming capabilities, we added pneumatic tubing and 15 layers of stretchable, geometricallypatterned PET sheets (cut from 0.01” PET, McMaster-Carr).
Each PET sheet comprised a pattern of inextensible polygons joined by extensible serpentine springs (as in our priorwork [18]), thereby granting the aggregated sheets flexibility
and elasticity while unjammed, and rigidity when under vacuum. To aid in alignment, each PET sheet had a hole cut into
each corner. After stacking the sheets together, the alignment
holes were filled with SilPoxy, and small weights were placedon the layers to ensure they stayed close together. Then,
we folded and sealed the membrane with DS10. Utilizing
additional PET layers would increase the jamming ratio at
the cost of raising the unjammed stiffness, and we empiricallychose 15 layers to balance these two objectives.
PneuFlex actuators were made by casting and curing DS10
in a 3D-printed mold and subsequently placing the molded part
onto a piece of fabric impregnated with uncured DS10. Oncethe molded part and silicone-fabric cured together, we wrapped
the actuator in fiber-reinforced silicone [25] to encourage
uniaxial bending, and attached tubing with SilPoxy (SmoothOn, Inc.). Finally, we used SilPoxy to attach velcro, magnetic
snaps, and laser-cut acrylic feet.
We controlled the modules using a vacuum pump, pneumatic pressure regulators [26], and an Arduino Uno (ArduinoAG). The stretch sensors’ capacitances were measured using
an MPR121 capacitive sensing integrated circuit (Resurgent
Semiconductor) due to its excellent onboard noise rejection
features, and sent to a PC for recording.

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This article has been accepted for publication in IEEE Robotics and Automation Letters. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/LRA.2023.3337702

SHAH et al.: VARIABLE-STIFFNESS ROBOTIC SKINS

Fig. 2. Design and manufacturing of a PET VSRS. First, the jamming skinmembrane was made from successive layers of silicone and oxidized liquid
metal paste (steps 1-5). To make the membrane into a robotic skin, we added
PET sheets and tubing, sealed the membrane, and attached actuators, lowprofile velcro, magnetic snaps, and acrylic feet to the skin (steps 6-8). Below
the manufacturing schematic, we have included an isometric-view photographof the finished 13 cm square skin, a side view schematic, and a legend
corresponding to both schematics.

B. Mechanical characterization
To quantify the stiffness-changing capabilities of the PET
VSRS, we tested the skins in a flat, three-point bending
configuration using a materials testing machine (Instron 3345).
Three samples were tested five times each when unjammed
at atmospheric pressure and jammed at −80 kPa, with theflexure fixture’s test anvil (Instron 2810-400) oriented both
perpendicular and parallel to the actuators. This experimental
design allowed us to test how stiffness was influenced byboth the vacuum pressure as well as the skins’ anisotropic
properties introduced by the actuators. An upper loading anvil
was lowered at 60 mm/min to deflect the skins a total of 30 mm(plotted to 20 mm in Fig. 3A to highlight the transition fromlinear to nonlinear regions), with the span between the lower
anvils set at 80 mm.
The force vs. displacement data resulting from the threepoint bending tests suggest a relatively uniform behavior
within each sample (visualized as narrow error clouds in
Fig. 3A). In the jammed configurations, the skins exhibiteda linear regime until the jammed layers slip, after which theslope and linearity both decrease [15]. Observed variations between different samples may be due to the more manual steps
in the manufacturing process, such as attaching the actuators.

3

From the stiffness curves in Fig. 3A, we obtained stiffening
ratios (γ), which quantify the differences in mechanical stiffness when jammed versus unjammed. First, we extracted thetangent modulus of elasticity [27]: EB = L3 m/4bd3 , where
L is the support span, b is the width of the beam tested (mm),d is the depth of the beam tested (mm), and m is the slopeof the tangent to the initial straight-line portion of the loaddeflection curve (N/mm). We then defined the stiffening ratio
as: γ = EBj /EBu , where EBj and EBu are the jammed
and unjammed effective bending moduli, respectively. Tangent
moduli EB were averaged across the five trials, and γ was
calculated for each sample. The reported stiffening ratio is theaverage of the stiffening ratios of the three samples. The skins
attained approximate stiffening ratios of γ = 13.0 when theloading anvil was loaded parallel to the actuators (similar to
the results reported our prior work on jamming skins in [18]).
When the anvil was oriented perpendicular to the actuators,
they resisted bending, lowering the jamming ratio to γ = 4.1.
We note that the stiffening ratio γ was substantially less thanthat predicted by commonly used Coulombic layer jamming
theory [15], [18], [16].Theory predicts the stiffening ratio is
equal to number of layers squared (γ = N 2 , so γ = 250 forour modules). We suspect that the discrepancy between experiment and theory derives from our assumption that the PET
sheets are uniform sheets. In our experiments, the serpentine
PET springs (introduced when we patterned the PET sheets toenable stretchability [18]) would occasionally buckle out-ofplane during bending, likely causing lower inter-layer friction
and a smaller second moment of area (I), relative to a systemof homogeneous sheets.
The PET VSRS can change their stiffness to lock into
structures of various shapes and to suspend payloads (Fig. 3B).
While the skins were designed primarily for dynamic robotic
applications, they could also serve as standalone structures.
For example, the skins can jam in an L shape or S shape asshown here, representing end-use cases including protecting
scientific instruments and supporting payloads. Finally, we
note that the minimum radius of curvature attained here wasapproximately 3 cm. Multiple lines of reasoning informedby our experiments with various VSRS designs suggest that
smaller radii of curvature could be attained by using fewer
jamming layers (since the lower bound of curvature for bent
multi-layer systems of thickness h scales with 3/2h [17]), at
the expense of lower payload-supporting capacity (since thejammed stiffness scales with h3 [15], [18], [16]).
C. Locomotion
By using the actuators to generate motion, the sensors todetect motion, and the layer-jamming material of some of themodules to toggle stiffness, VSRSs can locomote in a varietyof configurations and deliver payloads (Fig. 4 and Supplementary Videos 1 and 2). Here, we characterize the locomotion
capabilities of our VSRSs in several configurations, ranging
from single skins to several connected skins to achieve varied
shapes.
First, to characterize the robot’s arching motion independently of actual forward motion, we set a single VSRS on a

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This article has been accepted for publication in IEEE Robotics and Automation Letters. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/LRA.2023.3337702

4IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED NOVEMBER 2023

Fig. 3. PET VSRS can be mechanically stiffened upon application of vacuum
pressure. (A) Mechanical characterization of PET VSRS in a three-point
bending loading condition. The solid lines denote a single trial, while thedashed lines denote an average of five trials for a single sample, and the clouds
represent ±1 SD. “Perp.” means the testing anvil was loaded perpendicular
to the actuators, while “para.” means the anvil was loaded parallel to theactuators. (B) A trio of VSRSs leveraging their variable-stiffness capabilities
to create both open and closed structures. Left to right: Three modules jammed
in an L shape as a standalone structure. A load-bearing Ω shape capableof holding a 1 kg weight. An “S” shape with curvatures concave in both
directions. A closed cylindrical shape. Scale bars, 5 cm.

slippery acrylic plate and inflated it to 120 kPa over 25 seconds
for 11 cycles. As the robot arched during inflation, the heightof the midplane of the center of the VSRS was estimated byextracting the location of a red marker placed on the sideof the robot using video (processed using MATLAB’s Image
Processing Toolbox). The results suggest an approximately
quadratic relationship between height and pressure (Fig. 4A),
while the small surface strains experienced by the stretch
sensors resulted in the change in capacitance ∆C being
roughly linear as a function of height h (Fig. 4B). Using
the empirical relation for our PET VSRS determined from
Fig. 4B (C = 42.95 − 0.20 ∗ h), we then commanded therobot to to achieve a series of maximum arched heights using abang-bang controller (Fig. 4C). After receiving a commandedmaximum arch height, the robot would inflate its actuators
until it reached the height, at which point the robot was
immediately commanded to deflate. The robot was able toachieve multiple controlled arching sequences, which gave us
confidence that the approach could be used to vary the archheight during locomotion.
Next, we used this closed-loop control to demonstrate

gait-based obstacle avoidance (Fig. 4D and Supplementary
Video 1). In many real-world environments, obstacles andeveryday objects will create overhangs that are smaller than
the robot’s typical arching height. Here, we simulated thiswith an overhang made of acrylic. The friction-biased acrylic
feet allowed the robot to grip the ground and move acrossthe surface by repeatedly arching and flattening. The robot
could locomote with a fully arched motion up to an impasse(Fig. 4D(1-2)), then the set point was lowered so the robot
could execute a flatter gait and pass below the overhang(Fig. 4D(3)). After clearing the obstacle, the robot could
resume its faster, highly arched locomotion gait (Fig. 4D(4)).
Similar locomotion gaits can be attained in configurations with multiple modules connected in various topologies(Fig. 4E-G and Supplementary Video 2). While unimpededby obstacles, a single module achieved an average speed of
2.70 BL/min. When carrying the 200 g payload in Fig. 4E,
the robot was able to move at 0.78 BL/min. When at its
destination, unjamming the top module allowed the robot to
deploy its payload. Next, we attached three modules together
serially and jammed the middle module upward to hold aweight (200 g) while the outer modules inflated their actuators
to allow the trio to locomote (0.55 BL/min; Fig. 4F). When the
middle module was unjammed, it could then assist the group to
locomote (1.65 BL/min; Fig. 4G). Thus, by building equivalentfunctionality into each skin—variable stiffness capabilities,
actuators, and sensors—each skin could be repurposed in situ
to improve the functionality of the overall robot.
IV. M ESH VSRS R ESULTS
To illustrate how the VSRS concept can be realized withdifferent components and component layouts, we instantiateda second VSRS design made with McKibben actuators andwoven mesh jamming layers. Our primary objective during
this design phase was to redesign the VSRS to be sufficiently
deformable to serve as a continuum manipulator (where the“PET VSRS” design was empirically found to be too stiff
for this function). We thus demonstrate the “mesh VSRS”
modules achieving two canonical robotic tasks: locomotion
and manipulation. For completeness, we also expanded thecharacterization of the mesh VSRS to include three-point
bending and axial compression, with the skins wrapped in acylindrical shape.
A. Manufacturing
To fabricate the mesh skins, we used a layer-by-layer
method similar to that of the PET skins (Fig. 2). The sensor
manufacturing process was nearly identical; however, to enable
layer jamming, we added 50 layers of stretchable polyester
tulle fabric mesh (Craft Forge) instead of PET. We then sewedon McKibben actuators made from latex balloons (Qualatex 260Q) that were inserted into polyester mesh sleeving(McMaster-Carr) and sealed with cable ties (McMaster-Carr).
To keep the outer membrane and jamming layers in contact,
we stitched through two points in the center and re-sealed
the holes using EcoFlex 30. Finally, we used SilPoxy to
attach velcro, add laser-cut acrylic feet, and improve the bond
between the actuators and the membrane.

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SHAH et al.: VARIABLE-STIFFNESS ROBOTIC SKINS

5

Fig. 4. Locomotion of PET VSRS, both solo (A-D) and connected in various topologies (E-G). (A) By inflating their PneuFlex actuators, the skins can arch
upward, raising the center of their body relative to its initial starting height. (B) Sensor capacitance decreases as the robot curls, resulting in a roughly linear
relationship between capacitance and height achieved. Dashed lines denote the mean over 11 cycles, while clouds depict ±1 standard deviation. (C) Executing
a series of stepwise-increasing arched motions up to a desired maximum arch height, while the VSRS was stationary. After reaching the target height, therobot automatically deflated its actuators to return to a resting state. (D) A VSRS approaches an overhang and then executes a flatter gait to pass below theoverhang, followed by additional highly-arched locomotion. Top: sensor data. Bottom: screenshots of actual VSRS motion, corresponding to the times marked
in the top plot. The planar, rectangular overhang was reflective and has been highlighted with a red border in D1 for clarity. (E) One module locomoting withanother payload-carrying module on top. When the top module unjammed, the weight was released into the environment. (F) Three modules connected inseries, with the outer two serving as locomotors and the middle one jammed upward to hold a weight. (G) The middle module was then unjammed and used
to aid in locomotion. Scale bars in (D-G) denote 5 cm.

B. Mechanical Characterization
To quantify the jamming behavior of the mesh VSRS, we
conducted mechanical tests while the VSRSs were unjammed(at atmospheric pressure) and while jammed (at −80 kPa).We
characterized the mesh VSRS in two three-point bending
conditions while the skins were flat (with the test anvil loaded
both parallel and perpendicular to the actuators, to matchthe PET VSRS characterization), and also added three-point
bending and axial compression characterizations of the skins ina cylindrical configuration, since individual mesh skins could
attain a cylindrical shape.
In the first three-point bending orientation, the actuators
were aligned parallel to the loading anvil (with the supporting
anvils spaced 80 mm apart), resulting in a stiffening ratio
between jammed and unjammed states of γ ≈ 8.6 : 1. In
the second orientation, the module was rotated 90 degrees sothat the anvil load was applied to the actuators. The actuators
resisted bending, raising the unjammed stiffness and lowering
the stiffening ratio to γ ≈ 2.0 : 1. As a control study,
we also tested three membranes that did not have sensors or
actuators (under both loading conditions, at five repetitionseach), finding that the stiffness ratio was γ ≈ 6.5 : 1 when theloading anvil was aligned parallel to where the actuators would
be aligned, and γ ≈ 2.4 : 1 when rotated to be perpendicular.
We suspect that this asymmetric bending stiffness is partially

due to the mesh’s anisotropy. In this study, asymmetry allowed
the VSRSs to achieve tighter curvatures, but in situations
where isotropic behavior is desired, the mesh orientation could
be alternated between successive layers.
To quantify the stiffness-changing capabilities of individual
mesh skins in a cylindrical configuration, we first used a threepoint bending setup (Fig. 5B). In this test, the same sample wastested five times. The loading anvil was lowered at a constantrate of 60 mm/min to a final displacement of 30 mm (withthe supporting anvils spaced 80 mm apart). We observed thatthe module is roughly five times as rigid while cylindricalcompared to the flat configuration, at both pressures, resulting
in a moderate stiffening ratio of γ ≈ 3.0. The higher stiffness
can be attributed primarily to the greater moment of area whilein the cylindrical shape (rigidity K = EI, where E is theeffective modulus and I is the second moment of area).
Finally, three specimens were tested five times each in axial
compression, with the modules curled in a cylindrical shape(Fig. 5C). The cylinder was 15 cm in height and approximately
5.5 cm in diameter, and the same loading rate was used asabove (60 mm/min). To attain consistent vertical alignment, apolylactic acid (PLA) 3D-printed cylindrical base was attached
to an acrylic plate. The base was inserted into the bottom of thecurled specimen just deep enough that the base lined up withthe active portion of the jamming membrane (i.e., to the edge

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6IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED NOVEMBER 2023

Fig. 5. Mesh VSRS were mechanically tested in three loading conditions. (A) Flat three-point bending, with the actuators pointing perpendicular (“perp.”) to
the loading anvil (as shown by the top illustration), versus parallel (“para.”) to the loading anvil (as shown by the bottom illustration). (B) Three-point bending
while in a cylindrical shape. (C) Axial compression while in a cylindrical shape. Note that the initial compression up to about 20 mm primarily corresponds
to compressing the silicone borders, while compression and buckling of the jamming fabric primarily happens after 20 mm. In all plots (A-C), the dashedcurves represent the mean over five trials of a single sample, while the solid curves denote a single representative load-displacement curve, and the clouds
represent ±1 SD.

of the silicone border). Two local force maxima were observed
during many trials: the first corresponding to the buckling of
the unsupported silicone edge on the top of the module, andthe second corresponding to the buckling of the main, jamming
portion of the module.
To evaluate the effect of jamming, we used the buckling
ratio (BR): BR = Fj /Fu , where Fj is the force just before
buckling of the jammed module (at the second peak), and Fu
is the unjammed force at the same location. The five jammed
and five unjammed force values were averaged separately foreach sample, and then the buckling ratio was calculated foreach sample. The average buckling ratio across three skins was≈ 2.4, similar to the ratios obtained in the other two loading
conditions where the actuators bent (flat with anvil rotated
90 degrees, and cylindrical bending). This similarity supports
what is predicted by taking the ratio of the Euler bucklingload (F b = nπ 2 EI/L2 ) while jammed and unjammed—mostterms drop out, leaving us with the observation that BR should
equal the ratio of the effective modulus, Ej /Eu .
C. Locomotion
By inflating their actuators to arch upward, Mesh VSRSs
can locomote in a variety of configurations and deliver payloads (Fig. 6 and Video S3), similarly to the PET VSRSs.
The friction-biased feet allow the skins to locomote, and thesensor data is captured in the same way. Moving over tautcotton muslin fabric, the single module was able to locomote
at 2.80 BL/min; two connected modules moved the fastest, at
4.82 BL/min; while three modules connected together moved
at 3.81 BL/min. Additionally, in the two-module configuration,
each module could switch between contributing locomotive
capabilities and holding a payload via jamming (Fig. 6C andVideo S3). That is, one module locomotes used the inchworm
gait, while the other gripped and held a payload, moving
with the payload at 2.42 BL/min. When the robot reached
its destination, the gripping module un-jammed to deliver its
payload (Fig. 6C). The different surface strains experienced by
all modules were captured in the sensory feedback for eachshape-gait pair as shown in the graphs next to each set ofphotos in Fig. 6A-C.

D. Continuum Manipulator
With the more flexible jamming mesh, mesh VSRSs canbe connected in series and curled into cylinders to create
a continuum manipulator (Fig. 7 and Video S4). The lower
module allowed the robot arm to lock into a given macroorientation, while the upper two modules used their actuators
to reposition the arm in further smaller-scale manipulation
actions.
A single module can be wrapped in a cylindrical shape tomake a segment that can reposition its tip (Fig. 7A-C). We
secured a module to a cylindrical foam base, with ≈ 3.5 cm
overlap. The foam was affixed to a piece of acrylic with four
motion-capture markers (for a PhaseSpace Improv motioncapture system) that defined a fixed local coordinate frame. A(fifth) motion-capture marker was placed on the top edge ofthe skin, to define the end-effector location. Then, we inflated
the actuators one-by-one in sequence, with overlap, to movethe segment around the perimeter of its attainable workspace.
Projecting the workspace onto the XY plane, we see that theworkspace is roughly a quadrilateral, with the corners attained
when two neighboring actuators were fully inflated to 100 kPa(Fig. 7B).
For a given configuration, the sensor feedback tends to berepeatable throughout the motion space (Fig. 7C). The sensor
with the highest observed capacitance change (sensor 3), forexample, consistently increased its capacitance the most when
actuators two and three were both inflated, while reading
almost no change (unstretched) when those actuators weredeflated. The other sensors showed unintuitive but repeatable
trends, suggesting that in situ calibration would be desirable
if precise motion within a workspace was necessary.
To demonstrate the capabilities unlocked through connecting multiple VSRS together in a multisegment manipulator
configuration, we wrapped three VSRSs sequentially around adeformable cylinder to form a three-segment continuum arm.
We then attached a motion-capture marker to the top VSRS. At
the start of each trial, the bottom VSRS was manually reshaped
and jammed to hold a new position. Then, the system inflated
the actuators of the top two (unjammed) skins column-bycolumn (i.e., actuator 1 of both skins, followed by actuator

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This article has been accepted for publication in IEEE Robotics and Automation Letters. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/LRA.2023.3337702

SHAH et al.: VARIABLE-STIFFNESS ROBOTIC SKINS

7

Fig. 6. Mesh VSRS can be reconfigured to adjust their functions. (A) A single VSRS executes an inchworm locomotion gait. Right: sensor feedback for all
four sensors during five actuation cycles (a subset of the full locomotion sequence). (B) Three modules linked together can locomote in the same fashion. One
sensor is plotted for clarity. (C) Two modules work together, one locomoting with an inchworm gait and one jammed on top to grip a payload. One sensor
from the gripping module is plotted for clarity. The payload-carrying module can be un-jammed to deliver the payload. In (A,B), the scale bars denote 5 cm.
In (C), an isometric view, the modules are identical to the other photos, with an edge length of 14 cm.

2 of both skins, etc.). A similar and approximately squaremotion path was attained for each trial, resulting in a series ofoverlapping local workspaces within the overall reach of themanipulator (Fig. 7E). The actuated skins reported repeatablesensor feedback across the trials, even though the bottom skin
was jammed in a variety of dissimilar shapes (Fig. 7F).
V. C ONCLUSION
In this manuscript, we introduced the concept of a variable
stiffness robotic skin (VSRS): a reconfigurable robotic platform incorporating sensing, actuation, and variable stiffness
materials in a skin-like form. We showed how VSRSs canbe connected in different configurations to achieve tasks inlocomotion and manipulation, while selectively stiffening to
improve their individual or collective functionality in theabsence of a host body. The actuators allowed the skins to
move, while the sensors enabled closed-loop control, andthe variable stiffness capabilities allowed the skins to be
re-shaped in a given connection pattern, allowing anotherlevel of dynamic task adaptability. Finally, we showed two
embodiments that highlight the richness of the design space,allowing mission constraints to be accommodated by selecting
appropriate actuators, sensors, and materials. In our particularembodiments—PET VSRS and mesh VSRS—the mesh VSRS
design traded a decreased maximum stiffness for increased
deformability, enabling it to better serve in a continuum
manipulation context.
In future work, we plan to improve the shape-sensing capabilities of VSRS by calibrating a data-driven shape estimation
algorithm, such as that proposed by Truby et al. [28], foreach new VSRS topology. Thin bending actuators, such as
SMA ribbons [29], could then be integrated to enable a
VSRS to autonomously achieve even more complex shapes.
Additionally, the trade-off between payload-carrying capacityand moldability could be overcome by utilizing variableelasticity materials to enhance the unjammed stretchability andthe jammed stiffness [30]. Finally, we note that for full proprioception, it would be useful to integrate vacuum sensors into
the VSRS to verify proper jamming was achieved. Paired withadvances in other areas—including actuation, sensing, variable
stiffness materials, and control—VSRSs could serve additional
applications, such as adaptable linkages in larger robots, smart
reconfigurable garments, and reconfigurable active structures.

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This article has been accepted for publication in IEEE Robotics and Automation Letters. This is the author's version which has not been fully edited andcontent may change prior to final publication. Citation information: DOI 10.1109/LRA.2023.3337702

8IEEE ROBOTICS AND AUTOMATION LETTERS. PREPRINT VERSION. ACCEPTED NOVEMBER 2023

Fig. 7. Mesh VSRS connected to form a continuum manipulator. (A) A single curled skin can reposition its end-effector in 3D. Insets show the manipulator
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(E) The resulting 3D workspaces for each pose in (D), along with other example poses (shown in gray), are combined in a single plot. (F) Sensory feedback
for the dominant sensor from the middle (most bent) module, corresponds to local motions about these jammed poses. Dashed lines denote the mean, whileerror clouds denote ±1 standard deviation, across 76 trials.

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