2018 IEEE International Conference on Soft Robotics (RoboSoft)
Livorno, Italy, April 24-28, 2018

State and Stiffness Estimation using Robotic Fabrics
Jennifer C. Case1,2 , Joran Booth2 , Dylan S. Shah2 , Michelle C. Yuen1,2 , and Rebecca Kramer-Bottiglio2

Abstract— Robotic fabrics are planar, fabric-based systems
with embedded sensing and actuation functionalities. They area useful, reconfigurable tool which can turn passive structures into active robots through surface-induced deformations.
However, because of this flexibility, it is difficult to create
empirical models for all possible configurations and host bodymaterials that may be used with robotic fabrics. In this paper,
we focus on the widely-applicable case of a continuum joint
formed by wrapping a robotic fabric around a soft cylinder,
and propose a model that is compatible with a variety of host
body materials. The model is able take sensor data from therobotic fabric and then estimate both state and stiffness of
the underlying structural material. We show the functionalityof our model on three different materials: polyethelene foam,
Dragonskin 10 Slow elastomer, and Smooth-Sil 935 elastomer.
Simplified models that are able to provide both state andstiffness estimations are an important tool that can lead toadvancements in control of soft robots.

I. INTRODUCTION
Soft robots have many applications, but are generally
designed with a specific task in mind, such as locomotion[1]–[3], grasping [4]–[6], or manipulation [7], [8]. In orderfor soft robots to operate in unstructured environments, they
will need to adapt to different environments, tasks, andinteractions, and some examples of multifunctional [9]–[11]and reconfigurable [12], [13] soft robots have been shown.
Here, we propose robotic fabrics. Robotic fabrics integrate
both sensing and actuation elements with a fabric substrate,and can be wrapped around soft, passive bodies (e.g., foams,
elastomers, tensegrity structures, etc.) to impart motion onto
those bodies. By reorienting a robotic fabric on the surface
of a deformable body, or placing it on a different body withdifferent properties and/or morphology, different motions andtasks may be achieved [14], [15].
Creating robots out of 2D fabrics has been previously
demonstrated. Fabrics have been used to lighten a system
while providing a yielding structure [16]. Our previous
work includes demonstration of a fabric sensory sleeve thatprovides state estimation of an underlying 3D structure [17],as well as robotic fabrics that include variable stiffness
actuating fibers [15] or integrated sensors and actuators [14].
In the latter work, the sensing elements in the robotic fabricwere not sufficient to quantitatively estimate system state.
In this paper, we introduce a robotic fabric prototype
containing conductive composite-based capacitive sensors
and pneumatic McKibben actuators. We wrap this robotic
fabric around passive cylindrical bodies to create active

Fig. 1. (a) Sensors and actuators are placed on fabric in an alternating
pattern to create a robotic fabric. Button snaps are placed on the sides andan adhesive gel is applied to the underside of the knit fabric. (b) The robotic
fabric is wrapped around a passive body. The actuators are numbered inwhite while the sensors are numbered in color. (c) An example of a robotic
fabric wrapped around and deforming a polyethene foam cylinder.

continuum joints (i.e., actuators contract along the length ofthe cylinder). Further, we derive a corresponding analyticalmodel that uses the sensors embedded within the fabric toestimate both state and stiffness of the underlying cylinder.
Robotic fabrics may be applied arbitrarily to passive hostbodies, and the material properties of these bodies may not
be known beforehand. Therefore, it is valuable to be able
to retrieve that data from the robotic fabric itself. Here, ouranalytical model is applied to a relatively simple configuration to estimate the stiffness properties of the underlying host
body by leveraging known actuator forces and system state.
In the future, this work can be extended to more complex
configurations and systems and could be used to generate
system models that benefit feed-forward soft-bodied control
approaches.
II. MODEL

1 School of Mechanical Engineering, Purdue University, West Lafayette,

Our system consists of a robotic fabric with parallel actuators and sensors wrapped around a cylindrical deformablebody (Fig. 1a-b). When an actuator contracts, it causes theIN, USA2 School of Engineering & Applied Science, Yale University, New Haven,
CT, USA

978-1-5386-4516-1/18/$31.00 ©2018 IEEE522

where the appropriate equations are selected for determining
κx and κy , depending of the axis of curvature. Note that if
there are three accurate sensors, a combination of equations
can be selected from Eqns. 1 and 2 as needed.
B. Stiffness Estimation(a)

The state estimation model may be extended to also
estimate the bending modulus or elastic modulus of the underlying material. Note that in order to estimate the stiffness,
we must first estimate the state. For the stiffness estimation,
we require at least one actuator that is placed parallel to thecentral axis of the body. Contracting this actuator will cause
an equilibrium between the actuator force and the passive
cylinder to be reached, which is dependent on the bending
stiffness of the cylinder. We relate the bending stiffness (Kb )to the actuator force (F ) as:
rb F
.
(3)
Kb =
κ
Noting that Kb = EI, we can also determine the elastic
modulus (E) of the material. We assume linear material
properties, which has been previously validated using similarmaterials [20], and that the second moment of inertia (I) is
known to calculate E as:
rb F
E=
.
(4)
Iκ

(b)

Fig. 2. (a) Sensor placement. Sensors are placed at even intervals to alignwith the x- and y-axes. Sensor 1 is on the opposite side of sensor 3 behindthe cylinder. (b) Schematic of a constant curvature beam.

cylinder to curve (Fig. 1c). To model this system, we first
assume constant curvature, which allows us to adapt models
developed for continuum robots [18], [19]. We further assume that no compression occurs along the central axis of thecylindrical body and that the system is not subject to externalloads. Note that this model is dependent on sensor placement
rather than type, and should therefore be extendable to othercomponent choices regardless of the specific components
implemented in this paper. Similarly, this model can be used
for a variety of actuators as long as the exhibit contracting
behavior required for the model.

III. MATERIALSThe robotic fabric prototype implemented here employsa Spandex fabric substrate, capacitive sensors based on a
conductive elastomer composite, and pneumatic McKibben
actuators. Note that while we have miniaturized some pneumatic components [21], the purpose of this work is not topresent an untethered system. Additionally, the model should
be applicable to other types of actuation that operates onchanges in length, such as cables and shape memory alloy
coils, which may be easier to untether than pneumatics.

A. State Estimation
To estimate system state, we assume that the sensors in the
robotic fabric follow the curvature of the bending cylinder(i.e., perfect contact between the exterior fabric and internalbody). Our robotic fabric prototype includes four evenly
spaced sensors, which, when placed around the cylinder,
can be used to define a coordinate frame such that the xand y-axes align with the sensors (Fig. 2a). We define asegment with constant curvature in two ways: (1) using thelength of the segment (s), curvature (κ), and angular offset
of curvature (φ); and (2) using the length of the segment (s),curvature along the x-axis (κx ), and curvature along the yaxis (κqy ). We can convert between these two definitions usingκ = κ2x + κ2y and φ = tan−1 (κy /κx ). These variables areschematically shown in Fig. 2b.
With reliable data from all four sensors, we derive thesystem curvatures as:
s4 − s2
s1 − s3κx =, κy =
,
(1)
2srb
2srb

A. Sensor Fabrication
The capacitive sensors were made from a conductive elastomer composite with expanded intercalated graphite (EIG),
as described in [22]. Each sensor consisted of five alternating
layers of conductive elastomer composite and inert elastomer,
where the two outer layers of conductive elastomer composite were grounded to shield the sensor from environmental
noise. The conductive elastomer composite was composed ofDragonskin 10 Slow (Smooth-On, Inc.) mixed with 10wt%
EIG, and the inert elastomer was Dragonskin 10 Slow.
The sensors were fabricated via rod coating using a 1/2”10 Acme threaded rod (97014A634, McMaster-Carr). First,
a layer of conductive elastomer composite was coated onto apolyethylene terephthalate (PET) film (8567K12, McMasterCarr) and cured. A subsequent layer of inert elastomer wascoated on top, followed by another layer of conductive
elastomer composite on just half the surface. A final inert
layer was coated and allowed to partially cure until it was“tacky.” The multilayer sheet was then folded over for tacky
bonding, and a foam roller was used to remove air bubbles.

where si refers to the length of the ith sensor and rb is theradius of the cylindrical segment. Eqn. 1 assumes that all
sensors are giving accurate information. However, unless thecylinder is being simultaneously strained and bent, it is likelythat only two or three sensors are giving reliable data while
the other sensors are buckled or slack. Using only two or
three sensors, we we derive the system curvatures as:
s − s2s1 − ss − s3s4 − s=, κy =
=
, (2)
κx =
srb
srb
srb
srb
523

(a)

(a)

(b)

(b)
Fig. 4. (a) Schematic of actuator with dimensions given and parts labeled.
Note the drawing is not to scale. (b) Force-strain plots for the four actuators
used on the robotic fabric. Each plot corresponds to one actuator. The
average response for the experimental data is shown as a dashed line of red
for 69 kPa, green for 103 kPa, and blue for 138 kPa. The colored clouds
around the means represent 95% confidence intervals for twelve cycles. The
black lines represent a 2-degree polynomial fit of the average responses.

Fig. 3. (a) Sensor dimensions. (b) Instruction cycle-strain plots for the four
sensors used on the robotic fabric. Each plot corresponds to one sensor. The
average response is shown as a blue line. The colored clouds around themeans represent the 95% confidence intervals for ten cycles. The black line
represents a linear approximation of these data.

Once cured, the sensors were cut out using a 30 W CO2 laser
patterning system (VLS 2.30, Universal Laser Systems). The
sensors were then removed from the PET film and cleaned ofdebris with soap and water. A staple was used to electricallyconnect the two grounded layers of the sensor. The sensors
were connected to a signal conditioning board using stripsof copper-coated Kapton (Pyralux, Adafruit). Dimensions of
the sensors were chosen isolate the deformation to an active
region that is 90 mm x 10 mm, as shown in Fig. 3a.

uniaxial strain for wrapping around objects, but will notstrain where the sensors and actuators are anchored.
The sensors and actuators were sewn in an alternating
sensor-actuator pattern onto the knit part of the substratesuch that they spanned the Spandex fabric. The sensors werepre-strained to 100 mm (from original length of 90 mm),while the actuators were pre-compressed to 100 mm (fromoriginal length 120 mm). This pre-compression was done toallow actuators to both stretch and compress while the systembends, since the model assumes both stretch and compression
on the outer walls of the cylinder.
Button snaps were applied at the edges of the robotic
fabric to allow attachment around a body. Finally, a coatingof adhesive gel (Silbione RT gel 4717, Blue Star Silicones)
was added to the knit fabric portions to help prevent slipping
between the fabric and host body during actuation. The
sensors and actuators were controlled with an Arduino Uno.
The Arduino Uno acts as a slave for a Python script run on
Lenovo Thinkpad laptop.

B. Actuator Fabrication
To fabricate the McKibben actuators, a figure-8 knot was
tied in one end of a latex balloon. The balloon was placed
inside a 1/4” mesh (9284K2, McMaster-Carr) and a zip tie
was placed just inside the knot to hold the mesh onto theballoon. Tygon tubing (6.4 mm outer diameter, 1.6 mm innerdiameter) was inserted in the open end and two zip ties wereapplied to hold the mesh and balloon tight to the tubing.
The McKibben actuators were controlled through a pressure
regulator board. The resulting actuators are 120 mm in length
fully stretched (Fig. 4a) and contract to approximately 85 mm
when fully actuated.

IV. RESULTS & DISCUSSION

C. System Integration

A. Sensor Characterization

The sensors and actuators were integrated with afabric substrate. The fabric substrate consisted of a
100 mm x 120 mm spandex fabric section sewn to
20 mm x 120 mm knit fabric on either end. Spandex waschosen for the deformable section of fabric due to its highstretchability. Knit fabric was chosen for the ends because it
stretches slightly in only one direction, which allows some

Sensors were characterized within the full robotic fabricsystem. The robotic fabric prototype was sewn to two brassrods on the top and bottom and loaded in a materials testingmachine (3345, Instron). The robotic fabric was strain cycled
11 times starting at a length of 90 mm, which was the initiallength of the sensors, and pulled to 120 mm, which was
the limiting strain due to the actuators. The first strain cycle
524

TABLE I
PARAMETER VALUES FOR THE LINEAR FIT EQUATIONS THAT REPRESENTTHE AVERAGE SENSOR RESPONSE . N OTE THAT SENSOR NUMBERING

THAT REPRESENT THE AVERAGE ACTUATOR RESPONSE . N OTE THATCORRESPONDS WITH F IG . 1 B .

ACTUATOR NUMBERING CORRESPONDS WITH F IG . 1 B .

a0
a1

Sensor 1
101
20400

Sensor 2
100
20900

Sensor 3
65
21300

TABLE IIPARAMETER VALUES FOR THE 2- DEGREE POLYNOMIAL EQUATIONS

Sensor 4
97
21600

kPa
69
103
138

was not included in the data analysis to remove the Mullin’s
effect [23]. The results from the ten sequent strain cycles
were averaged together for each sensor and are shown in
Fig. 3b. Note that the data from the sensors is reported here
in instruction cycles, which is the number of instruction
cycles the sensor’s microprocessor goes through while thesensor charges and discharges (related to time to charge
and discharge and, thus, the capacitance of the sensor). We
implemented a linear fit (IC = a0 ε + a1 ) for each sensor
relating the sensor response to strain, where IC represents
instruction cycles from the sensor, ε represents strain, and ai
represent the parameters for the equation, which are given
in Table I.

kPa
69
103
138
kPa
69
103
138
kPa
69
103
138

Actuator 1
b0
b1
192.6
-116.5214.8-141.1229.3-180.3
Actuator 2
b0
b1
179.5
-114.2181.2-140.4193.8-171.9Actuator 3
b0
b1
207.0
-123.5206.5-138.8232.9-185.1
Actuator 4
b0
b1
179.4
-104.7200.1-135.1216.1-170.1

b2
17.9
23.3
34.3
b2
18.2
26.9
35.1
b2
19.0
23.7
35.4
b2
15.4
22.8
33.2

is determined by the “active” length of the fabric (i.e., the
100 mm length of spandex).
The cylinder-robotic fabric system was placed vertically,
as seen in Fig. 1, and two markers were placed along
the central axis where the curvature occurred. Actuator 1,
shown in Fig. 1b, was activated to a specific pressure after
which a single sensor response was collected from all the
sensors. Note that this data was collected with an Arduino
Uno from each sensor’s signal conditioning board. A photo
was taken in each deformed configuration, which was used
to generate truth state data. Deformation was repeated fivetimes for a number of pressures (approximately 69, 103,
138, 172 kPa, or 10, 15, 20, 25 psi) for each cylinder, thus
collecting five sensor responses and pictures at each position.
The actual (truth) curvature of the system was determinedfrom the photos using ImageJ, and the estimated curvature
was calculated using the sensor data and our corresponding
model. Specifically, we used data from sensors 1 and 4 to
calculate the curvatures. Note that the sensor data was onlyused if it fell within the linear region of the sensor response(strain greater than 10%). Figure 5 shows the results of thesetests.
Using the model to estimate state allows us to analyze
a complex 3D deformation without the need for multiple
sensor calibrations at various system positions. Rather, we
can take advantage of pre-existing models and reform themaround sensor data. However, as with any model, there arelimitations, which can be seen in Fig. 5. The estimatedcurvature for the Dragonskin 10 Slow and Smooth-Sil 935
elastomer cylinders tracks fairly well, but there is a clear
offset between the actual curvature and estimated curvature.
In contrast, the estimated curvature for the foam cylinder
gets decreasingly accurate with higher pressures, which isdue to the material properties of the foam. While the sidesof the elastomer cylinders are able to stretch and compress

B. Actuator Characterization
To measure the performance of the actuators, each one
was placed in a materials testing machine (3345, Instron) andinitially held at 120 mm for a given pressure. We sought tocharacterize true performance of the individual actuator, andnot performance of the integrated robotic fabric, and therefore characterized the actuators before they were integrated
into the robotic fabric. The actuators were strain cycled
between 120 mm to 80 mm at 40 mm/min for 12 cycles. This
test was repeated at different pressures: 69, 103, and 138 kPa.
The first two cycles were discarded from the analysis sincethese involved breaking-in of the actuators. The results ofthis test can be seen in Fig. 4b. Although theory exists that
describes the behavior of McKibben actuators, it does notaccount for friction or expansion of the balloon and differsfrom the actual performance significantly [24]. Therefore, weelected to use a 2-degree polynomial (F = b0 ε2 +b1 ε+b2 ) torepresent the responses of our actuators, which matches the
responses well. The parameters for this equation are given
in Table II.
C. State Estimation
In order to test the state estimation model, we wrapped
the fabric around three different cylindrical body materials:
polyethelene foam, Dragonskin 10 Slow elastomer (E =265 kPa), and Smooth-Sil 935 elastomer (Smooth On, Inc;E = 536 kPa). Note that despite the fact that elastomers
such as Dragonskin 10 Slow and Smooth-Sil 935 have anonlinear stress-strain response, they have a linear responseat low (<40%) strains [20]. The polyethelene foam washollow with an outer diameter of 35.0 mm and an innerdiameter of 18 mm. The two elastomers were solid with anouter diameter of 33.8 mm. The outer diameters correspondto rb in our model, while s is 100 mm. The length of s525

Fig. 5. Pressure-curvature data for the foam and elastomer cylinders. The
curvature from the photos is shown as red filled squares, black filled circles,
and blue filled triangles. The model estimation is shown as red hollow
squares, black hollow circles, and blue hollow triangles. The error bars
represent 95% confidence intervals.

Fig. 7.
Pressure-curvature data for the elastomer cylinders with theestimation data adjusted for the error. The adjusted model estimation isshown as black circles and blue triangles filled in with green for thefoam and elastomer, respectively. The error bars represent 95% confidence
intervals. This figure shows that in practice the error in the model can becompensated to get more accurate results.
TABLE IIIE STIMATED ELASTIC MODULUS AT VARIOUS PRESSURES . T HE PERCENTERROR IS DETERMINED FROM THE MEAN VALUE .

Pressure (kPa)
69
103
138
Avg

Dragonskin 10 Slow
Eest (kPa)% Error228 ± 1414%
195 ± 1726%
296 ± 712%240±919%

Smooth-Sil 935
Eest (kPa) % Error
655 ± 24022%459 ± 9114%640 ± 5119%585±2429%results.
D. Stiffness Estimation
In order to estimate stiffness, we need to know the force
from the actuator, which can be found using the force-strain
equations from Table II. First, the length of the actuator(sactuator ) is found from our model as:

Fig. 6. Error in estimated and actual curvature. Fits for the data are shown
as dashed lines.

sactuator = s(1 − κrb ).

as the cylinder bends, the foam cylinder can compress, butdoes not stretch as well as the elastomer. This means that thefoam cylinder does not follow the assumptions of the model
and, at most, the model is only useful at low pressures.
The errors between the mean estimated curvatures andmean actual curvatures can be seen in Fig. 6. Errors in
the Dragonskin 10 Slow and Smooth-Sil 935 elastomer
responses are nearly constant. Hence, we may add a final
adjustment to our data to compensate for model error andimprove the estimation by adding either our steady state error
into model such that:qκestimated =κ2x + κ2y + e,

(6)This length is then converted to strain and fed into the forcestrain equation for Actuator 1 to get the approximate force.
With known forces, we used the adjusted curvature datafrom Fig. 7 along with Eqn. 4 to estimate the elastic modulus
for both elastomers at pressures of 69, 103, and 138 kPa, andthe results are shown in Table III. Notably, the estimatedstiffness is most accurate (less than 10% error) when the
results from all the tests are averaged together.
V. CONCLUSION
In this paper, we have derived models to estimate the stateand stiffness of a soft cylindrical body that is deformed
from its surface by robotic fabric. The models leverage
feedback from sensors embedded within the robotic fabricto estimate curvature state of the cylinder, and further use
this state information alongside known actuator forces to(5)where e is the constant error in the curvature for theelastomer cylinders. As an example, Fig. 7 shows the data
adjusted for the observed error, which demonstrates that themodel error can be corrected in practice to get more accurate
526derive the elastic modulus of the cylinder material. We
have evaluated the accuracy of the proposed models on
representative cylinder body materials and found that themodels are highly applicable across a range of curvatures
for elastic materials, but only applicable at low curvatures
for certain foam materials.
Simplified models that work with sensor data are necessary
to track complex 3D movements of soft robotic systems.
The state estimation model derived herein may be useful inthe development of soft systems that utilize surface strains
for information, such as sensory skins, robotic skins, androbotic fabrics. Integrated conformable systems that canmanipulate arbitrary deformable bodies from their surface(e.g., robotic fabrics) will further need to infer body material
properties, such as stiffness, from the robotic fabric itself toinform system models and predict performance. In future
work, we will expand our study to more materials andmultiple samples of the same material to determine how
robust the model is to changes, which will determine its
usefulness in unstructured environments. Additionally, we
can take advantage of a robotic fabric’s ability to estimate
the stiffness of its host body material within a feed-forward
controller, which requires a known stiffness, alongside asensory feedback controller, to help control the state of thesystem.

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ACKNOWLEDGMENT
This work was supported by the Air Force Office of
Scientific Research under award number FA9550-16-1-0267.
JCC and DSS are supported by NASA’s Space Technology Research Fellowships (Grants NNX15AQ75H and
80NSSC17K0164, respectively). MCY is supported by a
National Science Foundation Graduate Research Fellowship(Grant DGE-1333468).
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