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

Capacitive sensor measurement rate improves by pre-stretching*2021 IEEE 4th International Conference on Soft Robotics (RoboSoft) | 978-1-7281-7713-7/20/$31.00 ©2021 IEEE | DOI: 10.1109/RoboSoft51838.2021.9479328

Elze Porte†1 , Thomas Sipple†1 , Lina Sanchez Botero1 , Dylan Shah1 and Rebecca Kramer-Bottiglio1

at an excitation frequency of 200 Hz, and at approximately
100 Hz at an excitation frequency of 10 kHz.
The capacitance measurement is often based on the
lumped-parameter model, which assumes the entire sensor
can be represented by a single lumped capacitance andlumped resistance [8], [10], [11]. At high measurement
frequencies, the lumped model is no longer an accurate
representation of the system [8], [12] because the depth ofpenetration of the applied voltage reduces with increasing
frequency [13]. The lower penetration means that the measured capacitance only represents part of the sensor, resulting
in a lower measured capacitance that underestimates theexperienced strain [8], [9], [12].
Lowering the electrode resistance is expected to increase
the frequency at which capacitance, and thus strain, is
accurately measured [8]. Repeated stretching of the sensors
may decrease the resistance, as is observed in several highly
stretchable capacitive [8], [14] and resistive sensors [15],[16], [17], [18], where conductivity is achieved by adding
carbon or graphite to a non-conductive matrix. Explanations
given for the resistance decrease are hysteresis effects [17],[14], sample slipping from the testing clamps [18], and thecreation of new conductive paths with stretch [8].
The aim of this paper is to develop a method that increases
the measurement rate of capacitive stretch sensors with
conductive composite electrodes. We use cyclic stretching of
the sensors to reduce the resistance in the sensor electrodes,
which allows for higher measurement rates. We investigatechanges in the electrode layers from the stretching processby scanning electron microscope (SEM) imaging, and study
the effects of the used strain rate and strain value on thecyclic pre-stretching process. This work contributes to theaccurate control of fast actuating soft robotic systems.

Abstract— Large-deformation capacitive stretch sensors have
proven to be a reliable sensing method for soft robots andwearables. However, the measurement rate at which capacitanceis accurately measured is often limited by the relatively highresistance of the conductive composite electrodes. At high measurement frequencies, the measured capacitance underestimates
the real capacitance, resulting in inaccurate strain estimation.
High measurement rates allow for fast sensor feedback, whichis essential for closed loop control of fast moving systems. In thiswork, we show that the measurement rate of elastic capacitive
sensors with conductive composite electrodes can be increased
by cyclic pre-stretching of the sensors before each use.

I. INTRODUCTION
Many soft robots have slow (i.e., sub-Hz) nominal actuation speeds [1], [2]. Recent progress on faster actuation has
led to several robots that operate at high actuation frequencies above 10 Hz, including a soft wall-climbing robot [3],and a modular crawling robot using dielectric elastomer
actuators [4]. Highly stretchable and fast sensors are required
to accurately control these rapidly-actuating robots. Althoughhighly stretchable capacitive sensors are a reliable choice tomeasure strains in soft robotic systems, with demonstrated
closed-loop control [5] and consistent performance overmany strain cycles [6], [7], the measurement frequency ofthese sensors is often limited due to their relatively large
size and high electrode resistance [8], [9].
Strain can be measured from a plate capacitor, because its
capacitance increases linearly with strain [6], [7], [8]. The capacitance can be determined from impedance measurements,
as described in detail by Tayrich and Anderson [8]. In short,the impedance consists of the resistance R and reactance Xof the system, and is measured based on the phase shift
between an applied voltage signal and the resulting current
signal. The measured reactance can be directly translated into
capacitance C by:
C=

1
2πf · | X |II. MATERIALS AND METHODS
A. Sensor fabrication(1)

Sensors were fabricated similar to the method reported by
White et al. [6]. In summary, the capacitive sensors consistof two silicone-based electrodes with expanded intercalated
graphite (EIG) as conductive filler, separated by a silicone
dielectric layer. EIG was prepared by heating expandable
graphite flakes (Sigma Aldrich) to 800 °C and subsequent
sonication in cyclohexane for 1 h at 70% (Q500 1/2” tip,
Qsonica). The EIG-cyclohexane mixture was sieved througha 212 µm mesh and boiled down to achieve approximately
3 wt% EIG. The mixture was manually stirred into DragonSkin10 (Smooth-on, Inc.) at a ratio that achieves 10 wt%
EIG after evaporation of the solvent during curing. The EIGsilicone composite was rod-coated on a PET substrate andwhere f is the frequency of the applied voltage signal, also
referred to as the excitation frequency. A higher excitation
frequency results in a higher measurement rate of the capacitance, and therefore of the strain. For example, our LCR
meter outputs capacitance data at a maximum rate of 0.5 Hz*This work was supported by a NASA Small Business Technology
Transfer grant (80NSSC17C0030).
† Authors contributed equally to this work
1 Schoolof Engineering and Applied Sciences, Yale University,
New
Haven,
CT,USA
email:{elze.porte,

thomas.sipple, lina.sanchez-botero,dylan.shah, rebecca.kramer}@yale.edu
978-1-7281-7713-7/21/$31.00 ©2021 IEEE

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Capacitance (pF)

80

Fig. 1. The elastic capacitive sensors, comprising expanded intercalated
graphite-based conductive composite electrodes.

75 2% decrease line
max. frequency
1st cycle

70

65

60
0

left to cure completely. DragonSkin 10 was rod coated on
top of the EIG-silicone layer, and folded onto itself justbefore full curing to create the 3-layered structure with twoelectrodes separated by the dielectric. The sensor thickness
is approximately 1 mm. Sensors were laser-cut (Universal
Laser Systems VLS 2.30, 30 W) to have a rectangular initialactive area of 9.8 x 1 cm. Figure 1 shows a picture of thesensors.

max. frequency max. frequency max. frequency
500th cycle
10th cycle
50th cycle

1st cycle
10th cycle
50th cycle
500th cycle

1000

2000
3000
Frequency (Hz)

4000

5000

Fig. 2. Representative example of the measured capacitance at 75% strain
for the first, 10th , 50th , and 500th strain cycle. The black line indicates theapproximate 2% capacitance drop from the measured capacitance at 200 Hz.
For clarity, a single 2% decrease line is shown, although in the rest of ourreported results the 2% decrease was established from the capacitance at
200 Hz for each measured cycle.
15
Max frequency (kHz)B. Cyclic stretching setup
Pre-stretching experiments were carried out using a custom cyclic tester. A detailed description of the tester iscaptured in Appendix A. In short, the rotational motion ofa motor is transmitted to a linear slider to which the sensor
is connected, resulting in a fast strain system that is capableof performing hundreds of strain cycles within a couple ofminutes. The stretch length of the sensors is controlled by
the transmission settings in the hardware. A small pre-strain
of approximately 8 mm was applied to all sensors to remove
slack in the sensors at 0% strain during testing.
During the standard pre-stretching procedure, sensors werecycled at least 500 times to a maximum deformation of
80 mm at a rate of 60 rpm, resulting in a maximum strain of
approximately 75% at a strain rate of 150%/s. The cyclic
testing was interrupted at regular intervals to record data
while the sensor was stationary at 0 and 75% strain. The
effect of strain rate was investigated by performing additional
tests at 30 and 90 rpm, and the effect of maximum strain
was investigated by increasing the maximum deformation to
150 mm (140% strain) at 32 rpm to ensure a similar strain
rate (150%/s) as in the standard tests.
An LCR meter (Keysight E4980A/AL) was used to measure capacitance and resistance of the sensors, using its
frequency sweep function. A frequency sweep goes througha series of increasing excitation frequencies, and records thecapacitance and resistance for each frequency. Measurements
were performed while the sensor was stationary at 0% and
75% strain, regardless of the maximum strain applied in the
pre-stretching procedure.

averagebatch 1 individual
batch 2 individual

batch 110

batch 2

5

0
0

100

200
300
400
Cycle number (-)

500

600

Fig. 3. Average maximum frequency at 75% strain up to 500 cycles witherror bars indicating the standard deviation (n = 6-9 after removal of outliers,
with data points considered outliers when the sensor was accidentallyshorted during the measurement). Individual measurements were included
to show divide between sensor batches (n = 2-4 per batch). Dashed grayline was added to guide the reader.

III. RESULTS AND DISCUSSION
A. Characterizing maximum measurement frequency
Repeated stretching of the sensors to 75% strain was
performed to increase the maximum excitation frequency atwhich capacitance was accurately measured. In this paper, we
defined the maximum excitation frequency as the frequency
at which the measured capacitance at 75% strain fell morethan 2% from the capacitance measurement at the lowest
tested frequency (200 Hz). For our sensors, this capacitance
reduction corresponds to a strain measurement error of lessthan 5%, which was set as an arbitrary acceptable error.
Measured at 200 Hz, the average capacitance change between
0% and 75% strain was 35 pF, and the deviation between
capacitance measurements taken at 7 intervals over 500 prestretching cycles was less than 1 pF for all tested sensors.
The capacitance of the sensors has previously been shownto increase linearly with strain [5], [6].
Fig. 2 shows the measured capacitance at 75% strain
up to an excitation frequency of 5000 Hz for a representative sensor sample, including the line that indicates the

C. Morphology of sensors
The surface morphology of the EIG electrodes was characterized using an SEM (Hitachi SU-70) under an accelerated
voltage of 2 kV. All samples were sputter coated with iridium
before observation. Samples for SEM characterization werelaser-cut from the active area of the sensors.
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600

100

500

80

Resistance (k )Resistance (k )2% reduction. The decreasing capacitance with increasing
excitation frequency means that the measured capacitancedoes not represent the actual capacitance at high frequencies
for all cycle numbers. The maximum frequency at which
the capacitance is accurately measured, where the measured
capacitance crosses the 2% decrease line, shifts to higher
frequencies with increasing strain cycles.
The maximum frequency increases consistently with thenumber of cycles across all tested samples (Fig. 3). The
average improvement after 500 cycles was approximately
800%, with the largest increase observed within the first
200 cycles (approx. 600%). The improvement between 400500 cycles was only 3%, so minimal further improvements
are expected at higher cycles. Additional measurements after
1000 cycles for five samples only showed an average 6%
increase between 500-1000 cycles, confirming the minimal
improvement at higher cycles. We do not expect the prestretching procedure to have a meaningful effect on thesensor’s lifetime, since we have previously tested our sensors
up to 100.000 cycles without failure [6].
The relatively large deviation of the average maximum
frequency is thought to relate to batch variations. Although
the batch sizes are too small to assign statistical significanceto the data, the individual sample measurements shownin Fig. 3 indicate that samples can be grouped together
in their manufacturing batch with maximum frequencies
above (batch 1) and below average (batch 2). Although
the manufacturing process was identical between batches,
random differences may exist in the thickness of the coatedlayers, EIG particle size, and EIG concentration in theelectrodes. These parameters can affect the conductivity ofthe electrodes [6], and thus affect the signal penetration
depth [8], [13]. The general trend regarding the increased
maximum frequency with increasing number of strain cycles
can be expected regardless of specific sample characteristics,
since similar trends were observed for all samples (Fig. 3).
Dynamic stretching of the sensors was essential to achieve
the large increase in maximum frequency. Prolonged static
stretching of the sensors did not result in the same improvement. Sensors that were cycled repeatedly (400 cycles at
60 rpm) increased their maximum frequency by an averageof 680%, while sensors that were stretched to 75% and held
for the same time period (6.7 minutes) showed a maximum
increase of only 30%. This suggests that stress-relaxationof the silicone matrix has a minimal effect on maximum
frequency, and dynamic stretching is required to use prestretching as a method to improve sensor performance.
The maximum frequency increase after pre-stretching thesensors is not a permanent change in the sensor’s properties.
In a separate test, an average reduction from approximately
5 kHz to 2 kHz maximum frequency was observed for threesamples that were left to rest (0% strain) for at least 48 h
after cyclic testing. Although the 2 kHz value was higher
than the original maximum frequency of the new sensors(approximately 1 kHz), subsequent pre-stretching was required to recover the sensor’s maximum frequency to its level
observed directly after the initial pre-stretching procedure.

400
300

60

0
0

75% strain
0% strain*

40
20 increase due to cracks
formed in first stretch

200
100

decrease due toparticle alignment

0
0

100

200
300
400
Cycle number (-)

500

600
60

*

100

200
300
400
Cycle number (-)

500

600

Fig. 4. Average resistance measured at 1 kHz at 0 and 75% strain fromthe first to the 500th cycle, the error bars indicate the standard deviation(n = 7, (*n = 4, error bars indicate minimum and maximum values)), andthe dashed line was added to guide the reader. Inset shows more detail up
to 100 kΩ.

Max frequency (kHz)Max frequency (kHz)15
batch 1batch 2

10

5

0
0

50
100
Resistance (k )150
15Resistance (k )Fig. 5.
Relationship between the electrode resistance and maximum
excitation frequency. Data points indicate individual measurements, grouped
into the two manufacturing batches. Dashed line was added to guide thereader. Inset shows more detail between 0-150 kΩ.

To maximize measurement frequencies, pre-stretching thesensors before each use is therefore recommended.
B. Relating maximum measurement frequency to resistance
The resistance of the sensor electrodes was measured
simultaneously with the capacitance to investigate the relationship between electrode resistance and maximum excitation frequency. The resistance of the electrodes was
expected to be the determining factor for the penetration
depth of the voltage signal, and therefore to be directly
related to the maximum frequency. Fig. 4 shows the average
resistance response that was measured simultaneously withthe capacitance data to determine the maximum frequency inFig. 3. The resistance was measured at 0% strain in addition
to the standard measurements at 75% strain to provide abaseline for the system.
All samples followed the general trend shown in Fig. 4:
brand new EIG electrodes exhibit an initial low resistancestate (cycle number 0, <40 kΩ), followed by a sudden
increase in resistance after the first cycle at both 0 and 75%
strain (cycle number 1), and finally a monotonic decrease inresistance with increasing strain cycles (cycle number >1).
For all cycle numbers, the electrode resistance at 75% strain
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[20]. The sensors that have been pre-stretched show cracks
in the surface perpendicular to the strain direction (Fig. 6b).
These cracks form with the first strain of the sensor andare thought to lead to an initial breakdown of the surface
conductive network, which can explain the sudden increase
in resistance during the first strain cycle. The cracks only
appear in the electrodes and do not affect the dielectric layer
and the sensor’s actual capacitance.
The crack openings in the pre-stretched sensor reveal
an inner dense layer of stretched EIG networks, oriented
along the direction of strain deformation (Fig. 6b). We
hypothesize that the cyclic deformation promotes reorderingand alignment of the EIG sheets within the cracks. For
uniaxial strain, the sensor becomes compressed transversally,and both forces work in tandem to align and connect the
conductive pathways within the cracks, leading to a reduction
in electrode resistance which in turn increases the frequency
range of the capacitive sensors.
The decrease in resistance under dynamic strain cycles
has been reported previously for different carbon based
conductive filler/elastomer matrix composites [21], [22],[23], [24], [25]. This behavior has been associated withthe formation of additional conductive pathways by theorientation and stacking of conductive aggregates/particles in
the composite [22], [23], [24], as well as the breaking [20]and thinning [26] of the polymer matrix induced by shear
deformation. All mechanisms improve the contact between
the particle filler, resulting in a decrease in the resistance inthe conductive composite materials.
The removal of the external force/deformation partiallyrelaxes the system, which increases the resistance of the conductive composite [21]. The relaxation mechanism can explain the observed decrease in the maximum frequency withtime when sensors are rested at 0% strain. Re-orientationof the EIG with stretching will happen in subsequent strain
cycles, which is in agreement with our observation thatelectrode resistance increases during rest (0% strain) but canbe “recovered” with pre-stretch cycles prior to each use.

Fig. 6. SEM images of a) new sensor and b) pre-stretched sensor (1000cycles) under approximately 50% strain.

is higher than at 0% strain. The resistance measured at 75%
strain drops rapidly within the first 50 cycles, which is theinverse trend as observed between maximum frequency andcycle number (Fig. 3).
Fig. 5 confirms the relationship between resistance andmaximum frequency. The graph shows that the highest maximum frequency was achieved when very low resistance wasmeasured and that a low maximum frequency corresponded
to a high resistance. This relationship also confirms thedifference between the two manufacturing batches, withbatch 2 showing generally low resistance and high maximum
frequencies compared to batch 1.
The resistance of the electrodes may be affected bychanges in temperature, as observed in resistive sensors [7],[18]. We monitored the temperature of three samples withan infrared thermometer (Lasergrip 800, Etekcity) before,
after and half-way through a continuous run of 500 cycles at
90 rpm. The temperature fluctuated within 0.5 ◦ C between
measurements, indicating that the sustained strain rate did
not lead to an increase in temperature that can explain thechanges in the electrode resistance.
To further understand the resistance changes from the dynamic pre-stretching procedure, SEM images of the sensor’s
electrodes were taken before stretching (Fig. 6a), and while
under approximately 50% strain after pre-stretching 1000
cycles to 75% strain (Fig. 6b). Images of the EIG sheets thatare used as conductive fillers in the electrodes are shown in
Fig. 10 in Appendix B.
The brand new EIG electrode has an interconnected wrinkled surface structure, made up of numerous EIG sheets andsilicone resin (Fig. 6a). The isotropic wrinkling structuresuggests strong interaction between the EIG sheets in thecomposite, which leads to a low initial resistance value [19],C. Effect of pre-stretching parameters
Different pre-stretching strain rates and values were tested
to investigate their effect on the maximum excitation frequency. No effect of the chosen strain rate was observed,
with the tested strain rates ranging from 75 to 225 %/s
all showing a very similar increase in the maximum frequency with the number of cycles (Fig. 7). The maximum
strain in the pre-stretching process also did not lead toany observable differences. Fig. 8 compares the maximum
frequency of sensors that were stretched to 140% strain in
the pre-stretching procedure to sensors that were tested in thestandard procedure (75% strain, repeated from Fig. 3). All
measurements were taken at 75% strain to provide a directcomparison. The graph shows that the maximum frequencyof the 140% strain tests fall within the deviation from thesensors pre-stretched to 75% strain. These findings indicatethat the number of cycles is the dominant factor to increase
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Max frequency (kHz)7

can distinguish between true capacitance changes and unintended changes due to high excitation frequencies. Our prestretching method provides a practical solution to increase asensor’s maximum excitation frequency and avoid this sourceof measurement uncertainty.
The pre-stretching method to increase the measurement
frequency of the sensors can enable more accurate control
of faster moving robots. According to the Nyquist sampling
theorem, a signal—such as the motion of a soft robot—
can be perfectly reconstructed if the signal is measured
at least twice as fast as its highest frequency component.
However, noise makes this more complicated in practice,and commonly-accepted best practices suggest that sensing
frequencies should be at least 10 times the signal frequency
to make sampling rate a negligible source of error, andtherefore maximize the controllability of a robot [28]. Although our reported maximum excitation frequencies arein the kHz range, the sensing circuits impose additional
reductions in attainable sample rate. For example, our LCR
meter could only measure capacitance data at 0.5 Hz withan excitation frequency of 200 Hz, and is limited to ameasurement rate of approximately 100 Hz for excitation
frequencies above 10 kHz. This means that to measure arobot that exhibits motions with contributing factors above
10 Hz, other measurement techniques are required.
All measurements in the current work were taken with an
LCR meter that uses impedance measurements to calculate
the capacitance and resistance of the sensors, but the prestretching method is also expected to increase the measurement rate using other capacitance-measuring schemes. Other
measurement methods include: charging the sensor electrodefor a fixed amount of time and measuring the time to decay toa known voltage [6], [29], and charging a sensor for a known
amount of time at a constant current and measuring thecorresponding maximum attained voltage [30]. The charging
times of the sensor will decrease with decreasing resistance,
resulting in faster measurement rates for both methods.
Resistive sensors may provide a higher sensing rate compared to capacitive sensors because they do not require charging of the dielectric. Resistive sensors, however, can haveother drawbacks. First, the resistance of particle filled sensors
can change with the number of strain cycles [15], [16], [17],[18], as we also observe in the resistance measurements ofthe electrodes in the current work. Second, most resistive
sensors have a nonlinear resistance response to strain [7],[18], [31], [32], [33], which complicates calibration of thesensors. It is well documented that capacitive sensors have alinear capacitance response to strain [6], [7], [8], [18]. Third,
resistive sensors generally show stronger viscoelastic effects
than capacitive sensors, such as hysteresis [7], [18], [31] andovershoot behaviour [18], [33]. The use of capacitive sensors
has many benefits, and the pre-stretching method reduces the
drawbacks on sensing frequency.
In our recent work, we compared capacitive sensors
that used a graphite conductive silicone composite to a
multiphase composite (MPC) of eutectic gallium-indium(eGaIn), silicone, and graphite [34]. The low resistance

6
5
4
3
2

75%/s
150%/s100225%/s

100

200
300
400
Cycle number (-)

500

600

Fig. 7. Average maximum frequency for three different strain rates. Error
bars indicate maximum and minimum values (n = 3) and the dashed grayline was added to guide the reader.

Max frequency (kHz)

15

10

5
pre-stretched to 140%
average stretched to 75%

0
0

100

200
300
400
Cycle number (-)

500

600

Fig. 8. Maximum frequency up to 500 strain cycles for sensors stretched
to 140% strain compared to the average maximum frequency for sensors
stretched to 75% strain (repeated from Fig. 1, error bars indicate the standard
deviation (n = 6-9)). Maximum frequency was measured at 75% strain for
all sensors.

the maximum frequency during the sensor pre-stretchingprocess.
Since we did not observe an effect of the maximum
strain value on the maximum frequency, we hypothesizethat the sensors may not have to be stretched to their
expected maximum strain, and that large improvements may
be observed from stretching to lower strain values. Althoughfurther work is required to establish a lower limit for thestrain value, we hypothesize that alignment of the EIG
network may happen when the surface cracks start to clearly
appear since the SEM images indicated that EIG sheets alignin the direction of strain within the cracks to form a low
resistance network. Observing our sensors, we expect this tohappen at about 20% strain. We still recommend initially prestretching sensors to at least their expected maximum strain
to remove any plastic effects that occur from the Mullins
effect [27] and initial crack formation.
D. Implications for soft robotic systems
To the best of our knowledge, this is the first study thatuses sensor pre-stretching to improve measurement rates.
Although a more complicated transmission line model can
predict measured lumped capacitance as a function of measuring frequency [8], we are unaware of any methods that
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of the MPC sensors allowed their capacitance to be measured by a circuit with a time constant on the order ofmicroseconds [35], whereas our custom circuit to measure
the EIG based sensors operates with a time constant on theorder of milliseconds [6], [29]. However, the MPC sensors’
performance comes with drawbacks: increased expense, anarrower operating temperature range (eGaIn solidifies below
15°C), and an increased likelihood of short-circuiting wheneGaIn leaks out of the sensors due to cuts or manufacturing
imperfections. The current pre-stretching method provides asolution to cheap, reliable, and fast sensing.

strain. One end of the sensor was kept stationary, while theother end was mounted on the slider. Each cycle of the motor
results in one strain cycle of a sensor. The motor is controlled
by an Arduino Uno and Cytron motor shield, and poweredby a 12 volt power supply. The motor speed is controlled bya closed loop system utilizing a shaft encoder to ensure thatthe chosen rpm is maintained throughout the trial.
B. EIG morphology

IV. CONCLUSIONS
The maximum measurement frequency was investigatedduring cyclic stretching of capacitive stretch sensors. Twomain conclusions were drawn. First, the maximum frequency
was increased by reducing the electrode resistance, which
was achieved by repeatedly stretching the sensors before use.
Second, the most important pre-stretching parameter was thenumber of strain cycles. No effect of strain rate and strain
value was observed. Collectively, these results point to thepotential of pre-stretching conductive composite dielectric
elastomer sensors prior to use to achieve optimal sensor
readings at high sensing frequencies.

Fig. 10.

ACKNOWLEDGMENT
E.P., T.S., and R.K.B. thank our collaborators at Otherlab:
Karen Robinson, Tim Duggan, Conor O’Brien, and Jim
McBride for valuable discussions regarding the applicationsof this work.

APPENDIX
A. Custom cyclic tester details
The setup consists of a motor, connection disk, connection
arm, and linear guidance slider (Fig. 9). The motor directly
drives to connection disk, and motion is transferred to thelinear guidance slider by the connection arm between theslider and disk. The further the connecting arm is placed
towards the outside of the disk, the larger the maximum

Fig. 9.

SEM image of EIG sheets.

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