RESEARCH ARTICLE
www.afm-journal.deUntethered, Dynamic Robotic Fabrics Enabled by
Actively-Rigid Variable Stiﬀness Fibers
Trevor L. Buckner, Xiaonan Huang, and Rebecca Kramer-Bottiglio*
ﬂexible, lightweight, and adaptable to diverse applications. A wide variety of classic
and technical ﬁbers drives fabric usage as
ﬁreproof clothing, weather-protective barriers, and strong sails at sea. As a form factor, the ﬂat, planar geometry of fabrics poses
unusual challenges but also intriguing possibilities for robots that can be twisted, bent,
and folded on the ﬂy, changing shape toadapt to the task at hand, or simply for compact storage and later deployment.
Robots primarily made of fabric—or
robotic fabrics—face an inherent challengeof overcoming the instability and nonlinear responses of a soft and ﬂexible structure, which is exacerbated by the lack ofa third dimension to be leveraged for geometric stability. A stabilizing structure
is often provided by a variable stiﬀness
mechanism, such that the robot can remain nominally soft but activate stiﬀ regions when needed for load-bearing or
to guide actuation paths. For robotic fabrics, these variable stiﬀness components
are ideally implemented in a ﬁber-likeform factor to retain the properties of theneat ﬁber architecture.[1] Components in a ﬁber format can be
integrated smoothly into the base fabric substrate by weaving[2]or couching.[3,4] The change in stiﬀness can then be triggered via some stimulus, which could include an applied temperature change,[2,5] electrical current,[3,4,6] vacuum, or positive pressure,[7–16] mechanical tension,[17] or a variety of othermeans.[1,18]
Our prior work introduced an implementation of robotic fabrics with integrated functional ﬁbers—actuation, sensing, andvariable stiﬀness ﬁbers—which enabled closed-loop control ofcommon lightweight and breathable fabrics.[3] However, theprior robotic fabric suﬀered from key limitations that constrained
the demonstrations to tethered and quasi-static (move-and-hold)motions. We attribute these limitations to our use of a passivelyrigid variable stiﬀness ﬁber, which only becomes soft upon actuation (a common approach in the literature[2,4,5] ). Our speciﬁcvariable stiﬀness ﬁber selection in prior work[3] was also slow toswitch between stiﬀness states (on the order of minutes), suchthat local stiﬀness tuning could not be used as part of a dynamic control policy. Finally, the prior variable stiﬀness ﬁbers had
no neutral conﬁguration (i.e., the ﬁbers would stiﬀen in whatever position they were cooled in), which meant that co-locatedactuators were required for variable stiﬀness ﬁber positioning.

A robot that uses fabrics as its core body material can be lightweight,
compact, and highly ﬂexible. Ideally, the robot’s actuation, sensing, andstructural support are provided by ﬁber-based components, designed tointegrate with the fabric’s soft and conformable nature while preserving its
ﬁber architecture. Typically, variable stiﬀness ﬁbers are used for the structuralelements, functioning as “bones” that can be turned on and oﬀ as needed.
However, many variable stiﬀness ﬁbers are passively-rigid, only allowing the
fabric to become soft when powered, while some require bulky external air or
power supplies, making them untenable for untethered robotics. In this work,
an electrically-driven variable stiﬀness ﬁber is presented that performs a
ﬂat-to-curved geometry transition, providing a rigid load-bearing structure
when powered but remaining ﬂexible otherwise. Design principles for pairing
the actively-rigid variable stiﬀness ﬁber with a materially compatibleﬁber-based actuator are presented, and the actuator performance in diﬀerent
conﬁgurations is characterized. The variable stiﬀness ﬁber can be arranged
into sturdy legs, stable enough for a robotic fabric to lift and hold its own
battery pack and onboard electronics. This capability is demonstrated with aﬁrst-of-its-kind fully-untethered locomoting robotic fabric using two diﬀerent
quadruped gaits.

1. Introduction
Fabrics are not commonly associated with robots. However, consider a scenario in which an advanced piece of clothing autonomously folds itself in the laundry, a smart camping tenteﬃciently packs itself away, or an intelligent parachute adjusts
its descent trajectory, and upon landing, crawls like an inchworm to its ﬁnal designated location. While these examples may
seem fanciful at ﬁrst, pondering them suggests that, perhaps,
robots need not be limited to the traditional steel-and-rivets vision that has occupied the public perception for so long. In fact,
fabrics oﬀer a unique and relatively underutilized design spacefor robotics. As a material, the interlaced ﬁber structure of fabrics carries a centuries-long reputation of being highly resilient,
T. L. Buckner, X. Huang, R. Kramer-Bottiglio
School of Engineering & Applied Science
Yale University
New Haven, CT 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/adfm.202404431

DOI: 10.1002/adfm.202404431

Adv. Funct. Mater. 2024, 2404431

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www.afm-journal.deFigure 1. Robotic Fabric. Passively-soft and actively-rigid beams allow this robotic fabric to support its own battery pack and onboard circuitry stably
enough to stand up and walk. The fabric is a 120 mm square.

Because separate actuators were required for both positioning
and behavior, our prior robotic fabric instantiation suﬀered from
hardware and energy bulk that constrained the overall capabilities of the robot.
Herein, we present a robotic fabric implementation that uses
an actively-rigid variable stiﬀness ﬁber, enabling passive system compliance and dynamic motions. The actively-rigid variable
stiﬀness ﬁber is a patterned shape memory alloy (SMA; Nitinol)
beam, which when heated naturally increases in stiﬀness as it
undergoes a state transition from martensite to austenite, andfurther exhibits a ﬂat-to-curved geometry transformation to yield
a compound increase in the beam’s stiﬀness. This variable stiﬀness SMA (VS-SMA) is also electrically-stimulated (i.e., boasts
rapid stiﬀness switching) and self-straightening (i.e., does not
require an antagonistic component to reverse deformation,[2–5]reducing part count), and so can be actuated with miniaturized
onboard electronics and power, therefore lending to integration
into untethered, dynamic robotic fabrics.
Below, we will cover the design and performance characterizations of VS-SMA, as well as include details of how VS-SMA canbe used in conjunction with actuators and the necessary electronics to develop a thin, untethered, fabric-based locomotion robot(Figure 1).

2. Results
2.1. Design of VS-SMA
Our variable stiﬀness shape memory alloy (VS-SMA) beam is designed to achieve a signiﬁcant change in stiﬀness after undergoing the shape-memory transition. At room temperature, the Nitinol we used is fairly ﬂexible for a metal, (ﬂexural modulus ≈66
GPa[3] ). However, when heated above its Austenite Finish Temperature (Af = 80 °C), Nitinol undergoes a state transition frommartensite to austenite, causing an increase in modulus, up to
3× greater,[19] although this depends on processing and loading
conditions.[20] On its own, this small increase in stiﬀness is not
suﬃcient to act as a supportive beam, although it is a good start.
To multiply this eﬀect, we also program the VS-SMA to arch into ahalf-pipe when heated. This transition from a ﬂat sheet at room
temperature, to a 3D structure at elevated temperatures grants

Adv. Funct. Mater. 2024, 2404431

the beam a geometrical stiﬀness advantage that can be tuned byadjusting the beam shape and programming parameters.

2.1.1. Mechanical Design
The tighter the radius of curvature of the arch, the higher the
rigidity of the beam. This eﬀect is increased for beams with alarger width-to-thickness (w/t) ratio, as the transition from ﬂat
to “3D” becomes more dramatic. Assuming the material modulus E is constant, the change in beam ﬂexural rigidity EIy canbe described via an analytical model of the changing area moment of inertia Iy as the cross-section becomes curved into anarch (Figure 2A, Analytical Model for Arch Stiﬀness).
The arch design is constrained by a few parameters. To begin,
we must consider size and space limitations. As discussed, a very
wide and thin beam will provide the maximum stiﬀness change.
However, a larger beam consumes more real estate in the robot
and also requires increased current ﬂow to reach target temperatures.
A second constraint is that the beam must be designed suchthat it can be returned to a ﬂattened condition when stiﬀness is
no longer desired and the heating stimulus has been removed.
That is, attempting to bend the beam along its axis when cooled
should collapse the beam back into a ﬂat state. Unfortunately,
the solid cross-section of the arch will instead cause the beam topinch at localized sites rather than smoothly ﬂatten, which causes
stress damage at those regions (Figure 2B). To combat this, we removed material from the central portion of the arch, essentiallydividing the cross-section into two parallel struts, attached at theedge with a sparse bridge (Figure 2C). The remaining material in
the bridging pattern is still powerful enough to actuate the beam
into an arched conﬁguration and yet allows the beam to smoothly
bend when heat is removed (Figure 2B) at the cost of a reduced
variable stiﬀness range. The area moment of inertia Iy for the updated design was approximated analytically by treating the central bridge region of the arch as empty space (Analytical Model forArch Stiﬀness). Figure 2D plots these values for the case where
the w/t ratio is ﬁxed at 25 (the thick line from Figure 2A).
A ﬁnal constraint is that the maximum arch angle must be
somewhat less than 180°. Otherwise, attempting to bend the2404431 (2 of 14)© 2024 Wiley-VCH GmbH

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www.afm-journal.deFigure 2. VS-SMA Mechanical Design. A) Flexural rigidity of a beam with an arc cross-section, varying the arc angle and width-to-thickness ratio (normalized against a ﬂat beam of the same dimension). The thick line marks our chosen aspect ratio. B) Solid beams will pinch and kink. Split beams
bend smoothly with a gradual transition from arched to ﬂat. C) Key shape parameters for the split-beam design: strut width and bridge gap. D) Flexural
rigidity of a beam where the center portion of the arc has been removed (normalized against a ﬂat beam with the same portion cut out). The thick line
marks our chosen bridge gap. E) Various tested designs with diﬀering strut widths, bridge gaps, and arc radii. Lines are used to group related designs.
The circled point marks our chosen design. F) Representative force/displacement curves for a VS-SMA beam, demonstrating the diﬀerence in stiﬀness
when ﬂat and when heated to activate into an arch. The middle plot shows a beam that has been previously activated but has been allowed to cool, thus
only a very short displacement is required to locally collapse back into a ﬂat beam. G) The ﬁnal chosen VS-SMA design, showing a top-down view andtwo proﬁle views: ﬂat and arched.

beam to ﬂatten it may instead cause the arch to further compress
into a circle.
Given these constraints, and following the predictions from
our analytical model for maximizing the ﬂexural modulus ratio,
we experimentally tested a range of strut widths, bridge spacings, and arch curvatures (Figure 2E). Using a consistent materialAdv. Funct. Mater. 2024, 2404431

thickness of 140 microns, each sample was laser-cut into the desired shape, inserted into a small brass tube to constrain it into
an arched cross-section, and then heat-treated in an oven to set
the arch into the Nitinol’s shape memory. For each specimen, weused a three-point bending test to measure the ﬂexural rigidityof the beam in its cold-ﬂattened state, in its hot-arched state, and

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www.afm-journal.debeing bent back to ﬂat after cooling down (Figure 2F). The maximum beam width was limited to 3.5 mm (w/t = 25) in consideration of the size constraint, and arch curvatures were limitedby the tubing sizes available. Following experimentation, we also
found that a bridge gap of at least 40% was needed to facilitate
the return from arched to ﬂat upon bending without pinching.
In the end, we selected a design with parallel strut widths of 1mm, and a bridge spacing of 1.5 mm, which provided a usefulbalance between size, stiﬀness change ratio (≈ 8.8×), and ease of
manufacture. Our radius of curvature was selected as 3.17 mm,
giving an arc angle of approximately 126° (Figure 2G), safely below the 180° limit. We note that for these chosen parameters,
Figure 2D predicts a ﬂexural rigidity ratio of ≈25×; we attributethe diﬀerence to imperfections and nuances that the model does
not account for. For instance, the bridged region of the beam iseasier to bend than the struts, which causes a tighter localized
curvature at the arc center. Additionally, deforming the VS-SMA
away from its programmed conﬁguration (ﬂattening it), induces
internal stresses that cause the ﬂattened state to become morerigid than analysis of the geometry alone would predict.[21]2.1.2. Electrical Design
Our VS-SMA beam was designed to be activated with Joule (resistive) heating, which allows it to be powered by a portable battery
and easily managed via software. As long as the SMA is not physically damaged via plastic deformation, a target temperature of≈100 °C allows for prolonged actuation, tested up to a fatigue lifeof >1000 cycles with no visible degradation in performance.[1,21]
However, as with any resistive heating process, SMA is susceptible to cold regions that fail to activate, as well as hotspots andburnout, which anneals the material and reverts the programmed
state. Hence, consistent heating is highly desired for reliable
functioning of the VS-SMA component.
The VS-SMA bridging pattern has been structured such thatcurrent can ﬂow as evenly as possible from terminal to terminal to reach a consistent temperature throughout the volume of
the beam. Assuming a repeating 45° zig-zag bridge pattern, thebeam can then be broken into sections and chained end-to-end toachieve beams of arbitrary length (Figure 3A), which can be automated using a parameterized CAD model (OnShape). Conceptually, the VS-SMA beam can be visualized as three parallel electrical pathways: the left strut, the right strut, and a narrow center
zig-zag (Figure 3B). The two struts are of a constant width fromend to end, and so on their own will heat evenly. However, introducing the center zig-zag complicates the electrical circuit, potentially diverting current unevenly between the two struts eachtime the zig-zag connects. This is solved however by noting thatthe zig-zag can be broken down further into the segments thatrun parallel to the strut walls, and the 45° cross beams that musttraverse a longer length as they bridge the two struts (Figure 3C).
If the extra traversal distance is accounted for by simply multiplying the widthof the cross beam segments by a factor of√1∕cos(45◦ ) = 2, the electrical resistance per unit of axial length
down the beam will remain constant for every segment along theentire zig-zag path. The net eﬀect is that each of the two struts andthe center zig-zag will have a constant current down the lengthof the beam, equivalent to three parallel resistors that only touchAdv. Funct. Mater. 2024, 2404431

at the ends. This can be veriﬁed by drawing the split segments
in a simple circuit diagram. First, we reduce the number of variables by constraining resistances in the same pathway to be scalarmultiples of each other (Figure 3C labels these scalars x and y.)Then, since we want each pathway to act as an independent resistor in parallel with the others, we add a further design constraintthat the contact nodes between the three struts have a net zerocurrent ﬂow. The circuit can be evaluated under nodal voltage
analysis to reveal the required resistance values of each segment(and hence, segment width) to achieve behavior that ﬁts withinthese constraints. It turns out that any segment width will satisfy
the equations generated by these constraints, as long as the scalarvalues x and y are equal. The resulting heating proﬁle is visualized in a ﬁnite-element simulation (Solidworks 2021), conﬁrming the lack of hot or severe cold spots in the struts (Figure 3D).
The widening of the zig-zag cross beams does cause the bridge
to receive a proportionally lower power density and hence it runs
a little colder than the struts, although this is preferable to overheating. This behavior is also veriﬁed in physical specimens via
a thermal camera (Fluke TiX 580) (Figure 3E).
Avoiding hotspots also requires a reliable electrical connection
to any power source. Given the low electrical resistivity of Nitinol(8.2 × 10−6 Ωcm, about 4.8× that of copper), a beam of VS-SMA
has a total resistance of < 0.017 Ωcm−1 , which makes the system particularly sensitive to any small source of resistance andsusceptible to hotspots and overheating. The wide and ﬂat terminal shape resulting from the above electrical design also does notlend itself well to crimping, so instead components must be soldered. This solder bond also provides a sturdy mechanical linkthat resists loosening or displacement due to motion in the overall robotic system.

2.2. Design of Larger VS-SMA Support Structures
VS-SMA beams can be connected end-to-end in series via thesame soldering approach mentioned above to achieve larger andmore complex support structures (Figure 4A). For our robotic fabrics application, we have applied this concept to two main use
cases.

2.2.1. Load-Bearing Limbs
A variable stiﬀness system is often most directly used as aload-bearing mechanism. For example, we can arrange VS-SMA
beams into a supportive “leg” with a triangular proﬁle, andsew them onto a piece of fabric (Figure 4B). The two verticalbeams are placed to share the load placed above, while the fabrictethers the beams together to prevent them from pulling apart(Figure 4C).

2.2.2. Rigid Frames for Force Application
When a chain of VS-SMA beams is used to circumscribe a section of fabric, it can act as a stabilizing frame. When activated,
this VS-SMA frame will hold the contained fabric taut, causing
the enclosed area to act as a rigid panel (Figure 4D). This rigid

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www.afm-journal.deFigure 3. VS-SMA Electrical Design. A) The VS-SMA beam can be lengthened to an arbitrary size by adding additional segments, without complicating
the electrical heating proﬁle. B) The VS-SMA beam is designed as three parallel electrical pathways, two thick struts, and a center narrow zig-zag. C)
A beam segment can be sliced further into smaller regions (top) to derive an equivalent circuit diagram (bottom). To aid in design calculations, someresistances are constrained to be multiples of others, scaled by variables x and y. Nodal analysis reveals that if the scalars x and y are equal, there will
be a net zero current ﬂow between the three pathways, equivalent to three independent currents in parallel. D) Joule-heating ﬁnite-element simulationshows the lack of hotspots. The bridge section is just slightly colder than the main struts. E) Thermal image of physical beam shows lack of hotspots.
The ends are cold due to conduction into alligator clips.

panel provides a large stable interface against which actuators canbe anchored to apply forces in a predictable direction. Several ofthese rigid panels can be placed in close proximity with edges parallel and separated by ﬂexible hinges, similar to an origami structure. When each panel in a series is activated, the fabric is transformed from a ﬂexible sheet to an articulated linkage (Figure 4E).

for fully reversible, bidirectional motion. We also noted in Ref.
[21] that stacking multiple thin ribbons can provide greater net
forces compared to singular large ribbons, especially when paired
against an opposing actuator whose stiﬀness must be overcome
to generate motion.

2.3.1. Actuator Shape and Design
2.3. VS-SMA Integration with Bending Actuators
The novel design of VS-SMA was created for compatibility withbending actuators as a key feature. As demonstrated in our previous work,[3] Nitinol can also be used as an actuator for bending
motion. In our prior work, we discussed a method for ﬂattening oﬀ-the-shelf Nitinol wires into thin ribbons, which increased
the reliability and actuating force when programmed to curl froma straight position. By placing those actuators back-to-back on afabric, they can form an antagonistic actuating pair, which allows

Adv. Funct. Mater. 2024, 2404431

In this work, we decided to use the same ultra-thin ribbon design found in Ref. [21], but instead of stacking, the ribbons arearranged side-by-side in parallel to more evenly distribute themover the surface of the robot for more uniform overall ﬂexibilityof the fabric. The actuating ribbons are connected in electricalseries in a serpentine pattern. A departure from earlier works,
rather than form the actuators from ﬂattened wire, we insteadchose to laser-cut them from a Nitinol sheet as a contiguous trace.
This added manufacturing precision eliminates many sources

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www.afm-journal.deFigure 4. Larger VS-SMA Structures. All scale bars are 20 mm. A) VS-SMA beams can be soldered end-to-end to create larger shapes. B) VS-SMA beams
sewn onto fabric. C) Supportive triangle easily ﬂexes when inactive (top) but straightens and becomes rigid when active (bottom). D) Standard fabricdraped over a gap collapses under a point load (top). An active VS-SMA frame pulls the whole region taut against pressure (bottom). E) A series oflinked VS-SMA panels (top). When inactive, the panels easily ﬂex and warp into an arbitrary shape (middle). When active, the panels straighten andbecome a rigid linkage (bottom).

of hotspots at junctures due to slight inconsistencies in crosssection, and also ensures even spacing between ribbons to avoid
the chance of accidental shorting during use.
When pairing serpentine bending actuators in an antagonistic
conﬁguration, it is important that they not overlap, which would
impose unnecessary resistance to motion, leading to losses in actuation force for both actuators by adding to the eﬀective area moment of inertia. Instead, the serpentines should be interleaved inparallel so as to retain as thin a proﬁle as possible (Figure 5A).
Further, no one actuator should dominate either side or the outerregion, else the actuation will become uneven with unintended
motion as a result (Figure 5B). That is, the interleaved serpentines should be symmetrical, with the outer edges limited to one
trace wide before changing actuators (Figure 5B). If one bending
direction will require higher forces than the other, e.g., lifting aload against gravity versus lowering a load with help from gravity, the two actuator serpentines can be designed with diﬀering
numbers of total traces to reduce the antagonistic resistance inthe high-force direction (Figure 5C), as long as the above rules

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are also followed. Finally, antagonistic actuators can be placed on
opposite faces of the fabric to mitigate thermal cross-talk. Notethat even through the fabric, opposing actuators should still beinterleaved to avoid overlapping.

2.3.2. Actuator Placement and Performance
Actuator size and placement in relation to VS-SMA frames willinﬂuence the total output force, as well as the maximum deﬂection achievable. Further, we show that it becomes possible to generate two separate motion types, pitch and yaw, (Figure 5D) while
keeping all actuators within the plane of the fabric substrate.
The generation of force or displacement from a bending actuator can be characterized by its force-displacement curve, which
diﬀers depending on the actuator’s length. Each curve is determined by two values, the nominal displacement 𝜃 0 and the blocking tip force Fmax . The nominal displacement is the maximum
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www.afm-journal.deFigure 5. Actuator characterization. A) Antagonistic actuators stacked directly on top of each other will cause unnecessary stiﬀness in the system.
Interleaving them side-by-side results in increased net actuation force. B) Interleaved antagonistic actuators should be symmetrical and distributed as
evenly as possible to avoid unwanted force concentrations that result in undesirable motion. C) If one direction of motion requires higher forces, reducing
the number of antagonistic traces will increase the net force in the primary bending direction by reducing the opposing stiﬀness to be overcome. D)
Actuators (red and blue) and VS-SMA (yellow) can be arranged to generate both pitch and yaw motion. E) Force-displacement curve for sample bending
actuators. F) For a ﬁxed lever arm length, increasing the actuator length will proportionally increase the output bending tip force. G) For a ﬁxed leverarm length, increasing the size of the ﬂexible gap region will proportionally increase the output bending angle. H) When used for contraction, bending
actuator length does not appear to aﬀect the resulting blocked force.

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www.afm-journal.dea cantilevered ﬁxture, without any external load. In the case of
SMA bending actuators, this angle can be several hundred degrees as the actuator coils through several complete revolutions.
The blocking tip force is the maximum force generated by the actuator. This force is achieved when the displacement of the actuator is completely blocked, that is, it works against a load with an
inﬁnitely high stiﬀness. In practice, however, the blocked force
can be diﬃcult to measure directly from a free-standing cantilever, as the actuator will tend to buckle rather than maintain
zero displacement.
Instead, we can approximate the blocked force by following
Euler-Bernoulli beam theory via 𝜃 = FL2 /2EI, where I and L are
the area moment of inertia and length of the actuator, and E is
the ﬂexural modulus of the actuator while active. However, rather
than using F to deﬂect a straight cantilever, we begin with an active actuator that has already curled to achieve some tip angle 𝜃,
and F becomes the opposing tip force required to coerce the actuator back into its initial ﬂat state. For 𝜃 = 𝜃 0 , F = Fmax , and any
value in between the unloaded and blocked states will follow a linear trend (Figure 5E). Thus, a desired intersection of force output
and curvature can be achieved by adjusting the actuator length.
Note that in practice, the actuator will always deliver some force
value lower than Fmax , since achieving the blocked force would
require fully constraining the actuator from motion, such as byclamping the actuator ﬂat against a table.
Bending Actuators (Pitch): By attaching a bending actuator
across the fabric hinge between two adjacent VS-SMA frames,a fabric joint can be made to “pitch” up or down (Figure 5D,
Movie S1, Supporting Information). Any portion of the actuator extending into one of the active and rigid VS-SMA frames
will be unable to curl as it is held ﬂat by the taut fabric. However, this does not prevent the constrained portion of the actuatorfrom contributing to the bending force. On the other hand, only
the portion of the actuator spanning the gap between VS-SMA
frames will be able to bend, and thus the gap size will determine
the maximum bending angle of this “hinge.” A larger gap allows
a longer portion of the ribbon to bend, while a narrow gap will result in very little curvature. We experimentally characterized thebending angle for diﬀerent gap sizes by attaching bending actuators to pairs of acrylic tabs as stand-ins for the rigid VS-SMA
frames. We applied a current (2.0 A) to the actuators and visually recorded the total angular deﬂection. Neglecting the weightof the acrylic tabs themselves, we see that indeed, the resulting
bend angle appears to change approximately linearly with the gap
size (Figure 5F).
We also measured the blocked bending force at the tip of theacrylic tab, while varying the length of the actuator extending
into the rigid region. As expected, longer actuators result in ahigher tip force, although they contribute little to the bending angle (Figure 5G). Of note, these results inform us that in an antagonistic actuator pairing, it is only necessary to overcome the bending stiﬀness for the portion of the opposing actuator in the hingegap, as that is the only portion of the actuator that undergoes
bending. That is, additional net actuation force can be achievedby extending further into the rigid VS-SMA frame region without
also increasing the antagonistic stiﬀness. Note that by constraining the actuators against the table, we achieve blocked forces thatclosely match the approximated values in the force-displacement
curve for any given actuator length (Figure 5E).

Adv. Funct. Mater. 2024, 2404431

Bending Actuators (Yaw): When not in direct contact with arigid VS-SMA frame, a bending actuator can still be used to impart a curvature to a surface or pull two points on the fabric toward each other. One interesting application of this is the ability
to create a “yaw” joint within the plane of the fabric by using abending actuator to pull two lever arms together. This motion canbe pictured as the angle of a triangle becoming narrower as oneedge contracts to pull the other two together (Figure 5D, Movie
S2, Supporting Information). An actuator in this conﬁgurationacts as a linear contracting actuator, so we measured the blocked
contraction force for varying actuator lengths (Figure 5H). In thiscase, we could not ﬁnd a correlation between size and contraction
force, although a longer actuator will of course have a larger total
arc length, and hence can curl into a larger bend angle.

2.4. Application
Using VS-SMA as a viable thin, ﬂexible, structural component
and with accompanying compatible actuators, we designed acomplete robotic structure to enhance a piece of plain woven cotton cloth such that it can stand and locomote under battery power.
The robotic fabric is fully untethered and weighs 30.9 g.

2.4.1. Component Placement
Part of our aim with this design is that the base cloth should not
require any additional cuts or holes to function properly. That is,
the robot should rely on bending and folding rather than complex
kirigami cutting patterns. This decision is mainly to demonstratethat even simple fabric pieces can be roboticized. To this end, we
begin with a plain 12-cm square piece of woven cotton cloth. The
four corners of the cloth will act as “legs” to stand and walk ina quadrupedal gait, and so are framed with VS-SMA to become
triangular load-bearing limbs. The center of the robot body is also
framed with VS-SMA to provide a stable central platform to holdthe onboard electronics (Movie S3, Supporting Information).
Bridging across the “knee joint” gaps between the central VSSMA panel and each leg, we place “pitch” serpentine bending
actuator. In this case, there is no need for an opposing antagonistic actuator, since the weight of the battery will provide the reversing force. Any overlapping SMA components are placed on
opposing faces of the fabric, and any adjacent components arespaced at least 3.0 mm apart to reduce thermal cross-talk.[3]Two magnetic fabric snaps are placed inside the central VSSMA panel to act as an anchor for easy attachment and removal of
the rigid electrical components (onboard PCB and battery). The
rigid components are held in small 3D-printed (PLA) frames withcorresponding magnetic snaps on the bottom. Four acrylic feetangled to provide anisotropic friction are attached with a silicone
adhesive (Silpoxy, Smooth-on, Inc.) under the tips of all four triangle VS-SMA limbs (Figure 6A).

2.4.2. Controls
The robotic fabric can be teleoperated via Bluetooth from a laptop
computer. The robot has an onboard BMD 350 module (U-Box)

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www.afm-journal.deFigure 6. Robotic Fabric Design and Locomotion. A) The robotic fabric is a 120 mm square piece of fabric equipped with magnetic snaps for easy
detachment of the onboard PCB and battery, a friction-biased foot at each corner, four bending leg actuators, a VS-SMA frame on the bottom, andthe accompanying wiring to provide Joule heating current. B) The onboard PCB allows for teleoperation via Bluetooth and is capable of driving up to
15 separate SMA components at a time via an array of transistor switches. C) The SMA components include a single continuous VS-SMA chain, arranged
into ﬁve rigid panels, and four legs: Front-Left (FL), Front-right (FR), Back-Left (BL), and Back-Right (BR). D) The battery pack can power the robot for
approximately 20 min on a single charge. E) The ﬁrst gait makes an inchworm-like motion by activating pairs of legs simultaneously. F) A drawing of
the gait in (E). Active bending actuators are marked in red. G) The second gait makes another inchworm-like motion by activating diagonally opposed
actuators, causing the robot to walk at an angle. The remaining two actuators are used only for stability. H) A drawing of the gait in (G). Active bending
actuators are marked in red.

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www.afm-journal.dethat contains an nRF 52832 microcontroller and a Bluetooth antenna (Figure 6B). Bluetooth commands are sent from an nRF52
development kit that communicates with the laptop through
UART. Each SMA component is labeled (VS-SMA, Front-Left,
Front-Right, Back-Left, and Back-Right), and assigned to a different keyboard key on the laptop (Figure 6C). A pair of onboard
3.7V LiPo batteries (220 mAh, 5.9 g, 25 mm × 17 mm × 8 mm)
connected in series are used to power the robot (Figure 6D).
An external thermal camera (Fluke TiX 580) is used to monitor
the temperature of all actuators to avoid overheating and overcooling.
Two inchworm-like gaits are implemented on the robotic fabric to achieve forward locomotion. Both gaits start with the activation of all VS-SMA panels so the fabric robot can hold its bodyweight, and they remain active while other SMA actuators are being actuated. For the ﬁrst gait, we actuate the front two limbs topull the fabric robot forward. Then, the rear two limbs are activated to bend inward to have frictional contact with the ground.
Then, all SMAs and VS-SMAs are deactivated, which will cause
the VS-SMA legs to collapse and buckle under the weight of theonboard PCB and batteries. The anisotropic frictional feet prevent the fabric robot from sliding backward during this collapse.
Finally, the gait begins again by activating the VS-SMA, which
straightens the legs and causes the robot to lunge forward slightly
as it returns to its original ﬂat conﬁguration (Figure 6E,F, Movie
S4, Supporting Information). The second gait starts with the actuation of one front leg to pull the robot toward the diagonal direction. The rear leg on the diagonal is actuated right after lifting the
fabric robot up, which reduces friction and helps the robot pullforward. As the robot reaches its highest point, the two other legs
are then actuated, lowering them to help keep balance. Similar tothe ﬁrst gait, all four legs and VS-SMA panels are then deactivated, causing the legs to buckle. In this case, beginning the next
gait cycle does not seem to generate the same secondary lungeas the legs straighten out (Figure 6G,H, Movie S5, Supporting
Information).

2.4.3. Locomotion Results
Both the forward crawling gait and the diagonal crawling gait enable the robotic fabric (total mass of 30.9 g, 12 cm × 12 cm) to
crawl an average of ≈0.75 cmmin-1 , or ≈0.07 body lengths per
minute (BLPM) for 20 min, at which point the battery voltage has
dropped low enough that powering multiple actuators simultaneously becomes diﬃcult (825 J consumed, estimated by Coloumbcounting from a limited number of trials). This leads to an approximate cost of transport (COT) of ≈18, 100. The robotic fabrictranslates ≈2.5 cm (0.22 body length) during the ﬁrst gait cycle ofboth gaits. This is substantially larger than the remaining gait cycles since the robot starts from a fully ﬂat shape at the beginningof the ﬁrst cycle, while it cannot fully recover to the ﬂat shape in
the remaining gait cycles due to the absence of antagonistic actuators. However, it requires ≈50 s and ≈12 s, respectively, to fully
actuate all VS-SMAs and one SMA during the ﬁrst gait cycle dueto the larger thermal barrier between the room temperature andthe austenite ﬁnish temperature in the ﬁrst cycle. The remaining
gait cycles only require ≈70% of the actuation time comparedwith the ﬁrst cycle since softening the VS-SMA during the de-Adv. Funct. Mater. 2024, 2404431

activation step only requires cooling below the martensite ﬁnish
temperature, 40 °C.

3. Discussion
Designing a robot within the limitations of a fabric (extremely
thin body, highly ﬂexible, planar arrangement of components)
comes with unusual challenges, but also poses an opportunity
to push technologies toward new untested paradigms. The novel
VS-SMA “actively-rigid” structural component represents one
such advancement that may be used as a model for further technology developments, moving beyond the typically “passivelyrigid” variable stiﬀness that is not appropriate for every use case.
In addition to being “actively-rigid”, VS-SMA is highly compatible with untethered systems, as it only requires electricity tofunction. Finally, VS-SMA automatically springs into its required
shape, eliminating the need for a secondary actuator to move it
into position. Each of these behaviors becomes especially valuable for robotic systems with very small proﬁles or that are otherwise designed for compactness.
The VS-SMA, and actively-rigid ﬁbers in general, are preferable in many potential applications, as they allow a robotic fabricto remain ﬂexible even when unpowered. For instance, several
eﬀorts have been made toward the development of smart textiles
in wearable applications, the user should retain a free range of
motion.[22–28] Similarly, a dynamic or locomoting robotic fabricbeneﬁts by retaining ﬂexibility in its joints while only activating
the “bones” it needs at a given time. Actively-rigid fabrics can also
be folded or compressed for storage without ﬁrst being activatedfor softening. Further, using actively-rigid variable stiﬀness ﬁbers
can drastically reduce the manufacturing complexity of a robotic
fabric, as the ﬁbers can be woven or threaded through a particular path in their passively soft state (as opposed to being softened
and maintained in a soft state until placement of that component
is complete).
Naturally, there is room for further improvement on this concept, and the design of VS-SMA comes with drawbacks of its
own. Any thermally-driven mechanism like the VS-SMA tends
to be susceptible to damage from overheating, and sensitive toenvironmental conditions. Thermally-driven systems are also extremely ineﬃcient, as evidenced by our very high COT. A great
deal of heat is constantly lost, requiring constant re-applicationof current to maintain the VS-SMA in an active state. Further,while it is possible to leverage controlled straightening and subsequent collapse of VS-SMA beams to generate motion, as demonstrated in the locomoting robot inchworm gaits, this process isalso highly ineﬃcient and slow. We also note that in pursuit ofovercoming the obstacles described in the introduction, the total stiﬀness change ratio is somewhat low compared to other existing variable stiﬀness solutions.[1,29,30] However, our achieved
value of 8.8× is on par with joint stiﬀening from human skeletal muscle[31] and is suﬃcient for functional robotic action. We
believe that nascent material technologies may be able to overcome some of the above limitations, perhaps using the VS-SMA
concept as a benchmark for future “actively-rigid” mechanisms.
The ﬁber-based nature of VS-SMA may also limit the total
robot size. The scalability of ﬁber-based planar machines is inﬂuenced by factors such as the linear mass scaling of the robotic
fabric unit and the power requirements for full activation, which

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www.afm-journal.dealso scale linearly with ﬁber length.[3] While driving forces from
SMA bending actuators also scale linearly, support structures like
VS-SMA ﬁbers experience bending moments that scale quadratically with beam length, making long cantilevered regions less feasible.
The robotic fabric tightly integrates SMA actuators, VS-SMA,
customized miniaturized electronics, and onboard power onto apiece of fabric, demonstrating fully untethered locomotion forthe ﬁrst time by a robotic fabric. This in and of itself is a notable feat, given the constraints of designing all components tobe extremely thin. The seamless combination of VS-SMA andprogrammed SMA actuators provides both stiﬀness and force required for supporting the body weight and propelling the robot
forward during actuation without sacriﬁcing the ﬂexibility of thefabric at room temperature.
For future work, we plan to integrate thermistors into thethermally-driven components of the robotic fabric, which can already be supported by our customized miniaturized PCB, capableof powering, controlling, and sensing the temperature of up to 15
SMA actuators. This may allow the robot to perform a locomotive
gait autonomously while also monitoring temperatures to avoid
burnout or damage. Further, we surmise that it may be possible
to modify the VS-SMA design such that it mechanically locks andunlocks into the arched position, requiring power only to toggle
between the soft and rigid states, thereby drastically increasing
the speed and energy eﬃciency. With the demonstrated locomoting fabric as a base, computational tools can also be used to guidethe design and control of future robotic fabric designs to generate
more eﬃcient gaits and perform more advanced tasks. In particular, we envision robotic fabrics that fold themselves into multiple
conﬁgurations of the same body, perhaps walking as a quadruped
over some diﬃcult terrain, then curling into a tube for peristaltic
motion through a small tunnel, before ﬁnally bending into a pincer to manipulate some object. Indeed, this work presents only aglimpse at the potential capabilities of robotic fabrics, with many
improvements to come as ﬁber-based variable stiﬀness and actuation technologies develop.

The cross-section must then be shifted via the parallel∑ axis∑ theorem
such that the beam is bent about the neutral axis ȳ = Ay∕ A, where
A is the area of the cross-section. The relevant components are found as
follows:∑

Asector y =

=

∫A

y dA
𝜃
2

r

∫− 𝜃 ∫0r cos 𝜃 ⋅ r dr d𝜃

2

=

𝜃
2

r3
cos 𝜃d𝜃∫− 𝜃 3

(
)
r3
𝜃
2 sin
3
2
∑
∑
∑
Asector,R y −Asector,r y
Aarch y ==∑=R3 − r3

Asector =

1 dA

=

∫A

𝜃
2

3(

2 sin

Iy,sector =

=

∫A

r

∫− 𝜃 ∫0(r cos 𝜃)2 ⋅ r dr d𝜃

2

=

=

𝜃
2

∫

− 𝜃2

∫− 𝜃 ∫0r dr d𝜃

2

=

𝜃
2

r2
d𝜃
∫− 𝜃 2

r2
𝜃
2
∑
∑
∑
Aarch =
Asector,R −Asector,r==R2 − r 2𝜃2Finally, these values can be fed into the parallel axis theorem Iy,neutral =Iy − Āy2 to arrive at the shifted area moment of inertia for the arch:

Adv. Funct. Mater. 2024, 2404431(∑)
Aarch y 2
∑
Aarch

(4)

At this point, given a constant beam width w and beamt=R
( thickness)− r, diﬀerent arc angles could be iterated using 𝜃 = w∕ R − 2t and plotȳ =∑Aarch =∑
Aarch,solid y − Aarch,bridge y∑
Aarch,solid − Aarch,bridge∑

Aarch,solid −∑Aarch,bridge(5)

Iy,arch = Iy,arch,solid − Iy,arch,bridge

Iy,arch = Iy,sector,R − Iy,sector,r𝜃𝜃𝜃 + 2 sin cos
2
2

Iy,neutral,arch = Iy,arch − Aarch

(1)

(
)
r4
𝜃
𝜃
𝜃 + 2 sin cos
8
2
2

4(

(3)

2

∑

r4
cos2 𝜃 d𝜃4R4 − r=8)

the change in area moment of inertia. Figure 2A demonstrates how theratio of w/t aﬀects the beam stiﬀness ratio increase normalized against a
ﬂat beam.
To account for the cutout bridge section, the analysis could be repeatedas above, using a narrower angle 𝜙 = 𝜃 ⋅ bridge%. The resulting values canthen be subtracted from those for a solid arch as follows:

y2 dA
𝜃
2

𝜃
2

r

4. Experimental Section
Analytical Model for Arch Stiﬀness: For a curved cross-section, the area
moment of inertia Iy, arch could be modeled as the area moment of inertia
of a circular sector Iy, sector of radius R with a smaller sector of radius r
removed, where 𝜃 is the angle subtended by the arch:

(2)

2

)

Iy,neutral,arch = Iy,arch − Aarch

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Aarch y 2∑
Aarch

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VS-SMA Manufacture: The Nitinol alloy was purchased as a thin,
0.14 mm sheet (Baoji Seabird Metal Materials Co., Ltd.). This sheet wasthen laser-cut (LPKF ProtoLaser U4) into individual beams of the desired
pattern, usually in a large batch (Figure 7A). The cut beams could then be
removed from the sheet (Figure 7B), and the holes from the inner bridging
pattern were punched out. Each beam was then manually bent along its
cross-section with pliers to achieve an arch (Figure 7C). Each beam wasthen inserted into a cut brass tube of the desired inner radius to constrain
the beam in an arch, leaving one of the electrodes protruding from thetube so that the beam could be easily pulled out later (Figure 7D). The
sleeved beams were then placed in an oven (Thermo Scientiﬁc, Lindberg
Blue M) at 390 °C for 20 min (Figure 7H), after which they were removed
and quickly quenched in room-temperature water (Figure 7I). The tubes
were then drained of any water and returned to the oven. This heating
and quenching process was performed a total of three times. The beams
could then be removed from their brass sleeves (Figure 7J) and ﬂattened(Figure 7L). At this stage, individual beams of VS-SMA could be soldered
together into a frame structure, or attached to ﬂexible silicone wire leads
for power.
VS-SMA Flexural Stiﬀness Measurement: The ﬂexural moduli of the various VS-SMA beam designs in Figure 2E were measured using a dynamic
mechanical analyzer (DMA Q800; TA Instruments). Specimens were sized
to a length of 50 mm and placed onto a three-point bending ﬁxture witha support separation of 15 mm. All specimens were held at a constanttemperature (23 °C or 100 °C) and then subjected to a strain ramp of 4
mm/min to a maximum deﬂection of 2 mm. Each specimen was tested
in three diﬀerent scenarios: Flattened at room temperature, arched at 100°C, and arched at room temperature (collapsed back to ﬂat).
Bending Actuator Manufacture: Similar to the VS-SMA manufacturing
steps, the bending actuators were laser-cut (LPKF ProtoLaser U4) froma sheet of 0.14 mm Nitinol (Baoji Seabird Metal Materials Co., Ltd.), including a surrounding rectangular frame to give the thin serpentine pattern some stability during processing (Figure 7A). The Nitinol rectangle
was taped over on both sides using cellophane tape to further prevent theserpentine cutout from coming loose and tangled (Figure 7E). The entire
rectangle was then coiled tightly into a cylinder using high-gauge roundnose pliers (Figure 7F). This cylinder was then inserted into a brass tube
of 6.35 mm (1/4 inch) inner diameter to constrain the serpentine in a coil
(Figure 7G). The tube was then placed in an oven (Thermo Scientiﬁc, Lindberg Blue M) at 390 °C for 20 min (Figure 7H), after which they were removed and quickly quenched in room-temperature water (Figure 7I). The
tube was then drained of any water and returned to the oven. This heating
and quenching process was performed a total of three times. The wrapped
serpentine SMA could then be removed from its brass sleeve (Figure 7J).
At this point, most of the cellophane tape would be melted away, and the
Nitinol rectangle could be uncurled and separated from the serpentine
actuator (Figure 7K). The actuator ends were soldered to ﬂexible silicone
wire leads for power (Figure 7M).
Actuator Force-Displacement Curve Approximation: Determining theactuator force-displacement curve required two values: the nominal displacement 𝜃 0 and the blocked tip force Fmax . Each specimen was made of
a 0.14 × 1.0 mm bending actuator cut into a long, 10 mm-wide U-shaped
path. The open end of the “U” was clamped to the table such that the remainder of the actuator length (20, 30, 40, or 50 mm) remains free to curl
upward when activated. Specimens were activated with 2.0 A under zeroload. 𝜃 0 was then measured from the diameter D of the resulting coil via
𝜃 0 = 𝜋D.
Fmax is determined by ﬁrst measuring the actuator ﬂexural modulus E. A
materials tester (Instron 3345) was used to perform a three-point bending
test on each specimen with a support span of 3 mm, and a loading rate of
0.1 mm/s, bending each specimen (six total specimens, measured onceeach) opposite its normal actuation direction. During the text, specimens
were activated with 2.0 A such that the modulus measured was that of
the activated austenite phase. The resulting E measured was 18.7 GPa,
STD 4.1. Then, Fmax can be approximated by following Euler-Bernoulli
beam theory via 𝜃 = FL2 /2EI, where I and L are the area moment of inertia and length of the actuator, as detailed previously in the text.

Adv. Funct. Mater. 2024, 2404431“Pitch” Actuator Blocked Bending Force Measurement: To characterize
the eﬀect of SMA length on actuation force, the blocked bending tip forcesof several simple actuators were measured using a materials tester (Instron 3345). Each specimen was made of a 0.14 × 1.0 mm bending actuator cut into a long, 10 mm-wide U-shaped path. The open end of the “U”
was clamped to the table such that the remainder of the actuator length(20, 25, 30, 35, 40, or 45 mm) remained free to curl upward when activated. After the ﬁrst 10 mm of this free length, a 15 mm × 40 mm × 1.5mm acrylic tab was super glued onto the remaining length. The acrylic tab
constrains the aﬃxed portion of the actuator from bending. In addition
to the 40 mm tab, the 10 mm of unconstrained actuator makes up a 50
mm moment arm. The distal tip of the acrylic tab was positioned beneaththe Instron probe such that the actuator was constrained ﬂat against thetable. Specimens were activated with 2.0 A, causing the actuators to press
the acrylic tip upward against the probe to measure a blocked force until
a steady state was reached. Each data point was the mean value of three
specimens, measured once each. Despite being constrained from bending by the acrylic, longer actuators continue to generate higher forces fora given moment arm length.
“Yaw” Actuator Blocked Contraction Force Measurement: To characterize the eﬀect of SMA length on linear contraction force, the blocked contraction forces of several simple actuators were measured using a materials tester (Instron 3345). Each specimen was made of a 0.14 × 1.0 mm
bending actuator cut into a long, 10 mm-wide U-shaped path, sewn onto
a cotton fabric strip. Actuators were sized to 10, 20, 30, or 40 mm long.
The specimens were held vertically using a gripper ﬁxture, clamped onto
the exposed fabric at each end and ﬂush against the top and bottom of the
SMA. Specimens were activated with 2.0 A, causing the actuators to pull
downward on the probe as they attempted to curl, measuring a blocked
contraction force until a steady state was reached. Each data point was
the mean value of three specimens, measured once each. In this case,there appeared to be no discernible relation between actuator length andoutput force.
Nitinol Soldering: Nitinol tends to form titanium oxide on the metal
surface rather quickly in the presence of air. However, assembly in a vacuum or an inert environment was not always feasible. Instead, it was possible to achieve a solder connection using aggressive ﬂux (LA-CO, N3 AllPurpose Flux) to etch away the oxide, and using silver solder (96.5 Sn/3.5
Ag, SRA Soldering Products) which had become the standard for Nitinol
soldering. The rapid formation of oxide also inhibits the usual expected
wicking ﬂow behavior of the solder. In order to attach two Nitinol segments
together, each segment was individually etched with ﬂux and tinned witha small bead of solder, after which the two ends could be pressed together
and heated, allowing the two solder beads to reﬂow and join.
Robot Assembly: The locomoting robotic fabric was assembled byhand. First, the cotton fabric was cut to the desired shape, and the edges
were given a light coating of a liquid fray check sealant (Dritz Fray Check).
Locations for each component were carefully marked with a felt marker
through a paper stencil. The prepared VS-SMA beams and bending actuators were then couched directly onto the fabric using a sewing machine,
making sure to follow the full trace of any serpentine patterns to ensure
the entirety of the actuator was ﬁrmly attached to the fabric. The sewing
step must be taken slowly to avoid accidentally punching into and buckling any SMA components. At this stage, all power leads could be routed
toward the eventual PCB anchor point, cutting small holes in the fabric topass wires through if needed. The V+ lines were soldered together, while
the V- lines were attached to a set of header pins to ease connection to the
PCB later. Any long loose wires could be sewn down.
With the core structure of the robot in place, the biased acrylic feet could
be manufactured. These were laser-cut into ﬂat panels with a protruding
hook. The hook was then ﬁled down to a point to create a pointed tooth,which grips in the hook direction, but could slide easily in the opposite
direction or to either side. One foot was attached at the tip of each fabriccorner using silicone adhesive (Silpoxy, Smooth-on, Inc.), and the teeth
were aligned with the bending actuators.
Finally, magnetic snaps were punched into the desired anchor points
for the battery and onboard PCB, for easy detachment.

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www.afm-journal.deFigure 7. VS-SMA and Bending Actuator Manufacture. A) SMA components are laser-cut from a sheet of Nitinol. B) VS-SMA beams are separated fromthe sheet. C) VS-SMA beams are bent into an arc. D) VS-SMA beams are inserted into a brass tube to maintain the arch during heat treatment. E) Bending
actuators are also removed, and covered in tape to keep thin traces in position. F) Bending actuators are coiled into a cylinder. G) Bending actuators
are inserted into a brass tube to maintain the coil during heat treatment. H) SMA components are heated in an oven 390 °C. I) SMA components arequenched in water and then returned to the oven. J) SMA components are removed from brass tubes. K) Bending actuators are ﬂattened and separated
from the remaining material. L) VS-SMA beams are ﬂattened. M) SMA components can be soldered together in a frame and attached to ﬂexible silicone
wire for power.

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www.afm-journal.deOnboard Electronics: The PCB was designed to be small (28 mm × 26mm) and lightweight (5.8 g), yet must also be able to route high current(≈5 A) from the battery to each SMA component. The customized PCB
was composed of a BMD 350 module that contains an nRF 52832 microcontroller and a Bluetooth antenna, 15 N-MOSFETs (AO3416) that wereused as switches to control up to 15 SMA actuators, a voltage regulator(AP2210K) to pull down the voltage from 7.4 to 3.3 V to power the microcontroller, and a multiplexer (74HC4051) that could select analog input
signal for closed-loop control of the robotic fabric in a future iteration. A
pair of small and light 3.7V LiPo batteries (25 mm × 17 mm × 8 mm, 5.9 g,
220 mAh) were connected in series to power the robot.

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

Acknowledgements
T.L.B. was supported by the National Aeronautics and Space Administration (grant no. 80NSSC17K0553). X.H. was supported by the National Science Foundation (grant no. 1955225). R.K.B was supported by the National Science Foundation (grant no. 1954591). The authors thank Bilige
Yang for assistance with thermal imaging. X.H. is now with the robotics
program at the University of Michigan.

Conﬂict of Interest
The authors declare no conﬂict of interest.

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

Keywords
functional ﬁber, robotic fabric, variable stiﬀness
Received: March 13, 2024
Revised: April 29, 2024
Published online:[1] T. L. Buckner, R. Kramer-Bottiglio, Multifunct. Mater. 2018, 1, 012001.
[2] A. Tonazzini, S. Mintchev, B. Schubert, B. Mazzolai, J. Shintake, D.
Floreano, Adv. Mater. 2016, 28, 10142.
[3] T. L. Buckner, R. A. Bilodeau, S. Y. Kim, R. Kramer-Bottiglio, Proc. Natl.
Acad. Sci. 2020, 117, 25360.
[4] M. C. Yuen, R. A. Bilodeau, R. K. Kramer, IEEE Robot. Autom. Lett.
2016, 1, 708.
[5] H. M. Le, L. Cao, T. N. Do, S. J. Phee, Mechatronics 2018, 53, 109.

Adv. Funct. Mater. 2024, 2404431[6] J. Piao, M. Kim, J. Kim, C. Kim, S. Han, I. Back, J.-s. Koh, S. Koo, Sci.
Rep. 2023, 13, 4869.
[7] X. Liang, H. Cheong, Y. Sun, J. Guo, C. K. Chui, C.-H. Yeow, IEEE
Robot. Autom. Lett. 2018, 3, 2702.
[8] M. Brancadoro, M. Manti, S. Tognarelli, M. Cianchetti, Soft Robot.
2020, 7, 663.
[9] S. Jadhav, M. R. A. Majit, B. Shih, J. P. Schulze, M. T. Tolley, Soft
Robotics 2022, 9, 173.
[10] I. Andrade-Silva, J. Marthelot, Adv. Intell. Syst. 2023, 5, 2200435.
[11] Z. Zhang, Y. Long, G. Chen, Q. Wu, H. Wang, H. Jiang, Sci. Adv. 2023,
9, eadg1203.
[12] D. Quevedo-Moreno, E. T. Roche, IEEE Robot. Autom. Lett. 2023, 8,
3110.
[13] A. Bhat, S. S. Jaipurkar, L. T. Low, R. C.-H. Yeow, Soft Robotics 2023,
10, 923.
[14] V. Sanchez, K. Mahadevan, G. Ohlson, M. A. Graule, M. C. Yuen, C.
B. Teeple, J. C. Weaver, J. McCann, K. Bertoldi, R. J. Wood, Adv. Funct.
Mater. 2023, 33, 2212541.
[15] Y. Zhao, Y. Wang, IEEE Robot. Autom. Lett. 2023, 8, 3238.
[16] J. Xu, Y. Zhang, Y. Huang, L. Chang, T. Chen, T. Ren, Z. Cai, Int. J.
Mech. Sci. 2024, 264, 108840.
[17] T. M. Huh, Y.-J. Park, K.-J. Cho, Int. J. Precis. Eng. Manuf. 2012, 13,1255.
[18] L. Blanc, A. Delchambre, P. Lambert, Actuators 2017, 6, 23.
[19] K. Otsuka, C. M. Wayman, Shape Memory Materials, Cambridge University Press, Cambridge 1999.
[20] A. N. Bucsek, H. M. Paranjape, A. P. Stebner, Shape Mem. Superelasticity 2016, 2, 264.
[21] T. L. Buckner, R. Kramer-Bottiglio, in 2021 IEEE 4th International Conference on Soft Robotics (RoboSoft), IEEE, Piscataway, NJ 2021, pp.
579–582.
[22] E. T. Roche, M. A. Horvath, I. Wamala, A. Alazmani, S.-E. Song, W.
Whyte, Z. Machaidze, C. J. Payne, J. C. Weaver, G. Fishbein, J. Kuebler,
N. V. Vasilyev, D. J. Mooney, F. A. Pigula, C. J. Walsh, Sci. Transl. Med.
2017, 9, eaaf3925.
[23] T. H. Koh, N. Cheng, H. K. Yap, C.-H. Yeow, Front. Neurosci. 2017, 11,597.
[24] L. Rosalia, C. Ozturk, J. Coll-Font, Y. Fan, Y. Nagata, M. Singh, D.
Goswami, A. Mauskapf, S. Chen, R. A. Eder, E. M. Goﬀer, J. H. Kim,
S. Yurista, B. P. Bonner, A. N. Foster, R. A. Levine, E. R. Edelman, M.
Panagia, J. L. Guerrero, E. T. Roche, C. T. Nguyen, Nat. Biomed. Eng.
2022, 6, 1134.
[25] B. W. Ang, C.-H. Yeow, in 2019 2nd IEEE International Conference on
Soft Robotics (RoboSoft), IEEE, Piscataway, NJ 2019, pp. 577–582.
[26] R. Granberry, J. Abel, B. Holschuh, in Proceedings of the 2017 ACM International Symposium on Wearable Computers - ISWC ’17, ISWC ’17.
ACM Press, Maui, Hawaii, 2017, pp. 186–191.
[27] J. W. Booth, D. Shah, J. C. Case, E. L. White, M. C. Yuen, O. CyrChoiniere, R. Kramer-Bottiglio, Sci. Rob. 2018, 3, 22.
[28] V. Sanchez, C. J. Walsh, R. J. Wood, Adv. Funct. Mater. 2021, 31,
2008278.
[29] M. Manti, V. Cacucciolo, M. Cianchetti, IEEE Robot. Autom. Mag.
2016, 23, 93.
[30] T. L. Buckner, M. C. Yuen, S. Y. Kim, R. Kramer–Bottiglio, Adv. Funct.
Mater. 2019, 0, 1903368.
[31] J. D. W. Madden, N. A. Vandesteeg, P. A. Anquetil, P. G. A. Madden,
A. Takshi, R. Z. Pytel, S. R. Lafontaine, P. A. Wieringa, I. W. Hunter,
IEEE J. Oceanic Eng. 2004, 29, 706.

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