An Any-Resolution Distributed Pressure Localization Scheme Using a
Capacitive Soft Sensor Skin
Harshal A. Sonar 1 , Michelle C. Yuen1,2,3 , Rebecca Kramer-Bottiglio2 and Jamie Paik∗1
Abstract— We present a method to determine the locationof an applied pressure on a large area, monolithic siliconebased capacitive sensor. In contrast to pressure sensor arrays
composed of n × n discrete sensors, we utilize a single sensor
body with a single instrumentation interface to detect n pixels.
We interrogate the capacitive sensor at different frequencies,
thus modulating the effective length of the sensor. These
interrogation frequencies are governed by the sensor’s total
capacitance, resistance, and desired spatial resolution of thesensor. We developed an analytical model to calculate thefrequency response at different length segments of the sensor
and used the results to determine the interrogation frequencies
for experimental studies. We performed experimental tests
on a 1 × n sensor strip and an n × n sensor sheet andshowed that we could attain greater than 90% accuracy inpredicting the location of the applied pressure using a model
generated by a multi-class kernel support vector machine. Thisapproach towards distributed localization of point pressures
greatly reduces the hardware complexity in comparison todiscrete sensor arrays and increases the physical robustnessof the system.

Fig. 1. The soft monolithic silicone-based capacitive sensor skin deforming
into a mug. The sensor skin measures 120x120x4 mm3 with 70 pF of overall
capacitance.

I. INTRODUCTION
Robotic systems that interact with their surroundings needto detect and localize the contact with an object. Pressure
sensor arrays are a well-developed technology with multiple commercially available devices (TakkTiles, Sensitronics,
Tekscan, Sensing Tex, BodiTrak, SureTouch). However, themajority of these commercial devices incorporate materials
that are stiffer or more strain-limited than those commonly
demanded by softer interfaces, hindering their integration.
Researchers have developed various approaches to“soften” pressure sensing for soft robotics, human-computerinteractive system, and wearable applications. Two common
approaches for measuring pressure are by measuring theresistance of a deformable, soft or fluid conductor or bymeasuring the capacitance of a deformable capacitor. Some
resistive sensing approaches include the use of conductive
polymer composites [1]–[3] or embedding liquid-metal microchannels in silicone elastomer [4]–[7]. Capacitive sensing
approaches use a variety of materials for both the conductive
electrodes and the dielectric layer. Electrode materials can bebroadly classified into metal thin film [8]–[11], liquid metal[12], [13], conductive silicone composite [14]–[17], conductive fabrics [18]–[20], hydrogels [21], carbon nanotubes [22],and carbon grease [23], [24]. The dielectric layers have been
1 Reconfigurable Robotics Lab, Institute of Mechanical Engineering,École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland. 2 Schoolof Engineering and Applied Science, Yale University, New Haven, CT, USA.
3 School of Mechanical Engineering, Purdue University, West Lafayette, IN,
USA. email: jamie.paik@epfl.chcomposed of silicone foam [8], [9], [18], native silicone [11]–[15], [17], [21], [22], polyurethane [10], and acrylic foam
tape [23], [24].
Though the transduction means to convert pressure to asignal may differ, the majority of these devices utilize asingle sensor to make a single measurement of pressure.
In order to distribute sensing capability over larger areas,
researchers have patterned multiple pixels individually [5],[8], [19], [25] over the sensing region at the desired spatial
resolution. However, as the number of sensors increases, sodoes the number of interfaces to the electronics. For thepractice, the sheer number of wires can become unwieldy,prone to breakage, increasing the stiffness of the systemand therefore, higher resolution uniform surface systems
are difficult to design and implement. One way to mitigate
this issue in scalability is to use the electrodes on the
top and bottom of the substrate in orthogonal rows andcolumns to create pixels at the intersections [1], [9]–[12],[14], [17], [20], [22]. This approach reduces the numberof interfaces for an n-by-n grid from O(n2 ) to O(n), a
further improvement is to leverage the frequency-dependent
characteristics of large-area capacitors to reduce the numberof interfaces to two for an n × n pixel array. Interrogating acapacitor at multiple frequencies effectively creates multiple
sensing regions within the area of a single capacitive sensor
body [23], [24], [26]. Another interesting way to reduce thenumber of electrodes for touch-sensing applications is to use

Fig. 2. Electrical equivalent circuit diagram and results of the analytical model of the 1D sensor strip. (a) Schematic of a single element in the 1D sensor
strip. A photo of the sensor cross-section of the sensor strip. (b) Model of a 1 x 3 pixel array. The interface is located on the left end; the distance or pixel
index increases from this point along the sensor. The top schematic shows a top view of the physical device; the bottom schematic shows the corresponding
electrical equivalent circuit. (c) Plots of the signal amplitude calculated at each node over a frequency sweep. The black horizontal line marks the -3dB
threshold. The interrogation frequencies are the frequencies at which the signal amplitude curves intersect the -3dB line.

electric field tomography on a large conductive film [27].
In this work, we present a pressure sensing methodology
for localization of point pressures on a monolithic, soft
capacitive sensor (Figure 1) by interrogating the sensor at
multiple frequencies to modulate the effective length of thecapacitive sensor “seen” by the measurement system. Using
the resistance and capacitance values of a physical sensor
prototype, we developed an analytical model for the 1D
representation of the capacitive sensor. Using this model, we
calculated the frequency response of the sensor at different
effective sensor lengths to find their corresponding cutoff
frequencies. We then used the calculated cutoff frequencies
as the interrogation frequencies in experimental tests. Experiments were performed by pressing at various locations on
a 1D sensor strip and a 2D sensor sheet wherein the series
resistance (Rs ) and parallel capacitance (Cp ) of the sensor
were measured using an LCR meter at the interrogation
frequencies. Because the sensors are monolithic, with nopre-determined measurement locations, we discretized thesensors into different sized pixels to attain different levels of
spatial resolution. We then input the Rs and Cp values into a
multi-class kernel support vector machine (KSVM) to createa classification model for localizing the point pressures.
Through evaluation of the SVM using a confusion matrix,
we found that we achieved between 90-100% accuracy inpredicting the location of the applied pressure.
The major contributions of this work are: 1) fabricationof a monolithic soft capacitive foam skin for measuring
distributed pressure locations, 2) a method to localize appliedpressure by leveraging the effect of interrogating the capacitor at different frequencies, 3) demonstration of a reductionin the number of interfaces to one for a 1 × n and two for

an n × n sensor skin while maintaining high localization
accuracy.
II. P HYSICAL EMBODIMENTThe sensors were fabricated as a large, parallel plate
capacitor using a silicone and expanded graphite composite
for the conductive electrodes, and silicone foam for the
dielectric layer. The two components were made separately,
and then glued together using a thin layer of silicone. As
pressure is applied to this deformable capacitor, the thicknessof the dielectric layer decreases, resulting in an increase incapacitance.
The conductive composite material was fabricated in a thinfilm using a rod-coating method as described in [28]. In thiswork, we modified the graphite loading to increase the sheet
resistance from 1 kΩ. to 50 kΩ., reducing the sensitivityof the sensor to electromagnetic noise and decreasing thecutoff frequency. By using a conductive composite material,
it is possible to modify the sheet resistance of the capacitor’s
electrodes to better accommodate the interrogation frequency
capabilities of the LCR measurement system, or vice versa.
The silicone foam was fabricated by mixing silicone
elastomer (DragonSkin 10 Slow, Smooth-On) with various
sizes of sugar spheres (Suglets, Colorcon) to create a very
soft, open-cell foam. We mixed 40 g silicone with 120 gof sugar spheres with diameters between 500-1700 µm, andthen pressed the mixture into a 4 mm deep frame to forma large, thick sheet. After the silicone cured, the sheet was
submerged in 80 ◦ C water for 6 hours to cause the sugar
to dissolve out of the foam, changing the water every hour.
After allowing the water to evaporate from the pores, thefoam sheet was adhered on both sides to the conductive

composite film using a thin silicone glue layer. The final areaof the capacitive sensor was cut manually using a precisionknife.
In addition to the customizability of the electrode sheet
resistance, the unit capacitance of the sensor sheet can be
modified by changing the thickness of the silicone dielectricfoam. Furthermore, the stiffness of the foam can be tuned
by changing the ratio of sugar spheres to silicone, or bychoosing silicones of different stiffnesses.

The interrogation frequencies fi were obtained for our
1D sensor prototype (Figure 2(a)), with dimensions 100mm
× 20mm, series resistance of 50kΩ/mm and capacitanceof 108f F/mm. The plots of αi (f ) for the 1x3, 1x4 and1x5 pixel sensor networks are shown in Figure 2(c). The√interrogation frequencies corresponding to where αi = 1/ 2
were used in the following experimental section.
IV. E XPERIMENTAL R ESULTS
A. Experimental Methods

III. A NALYTICAL M ODELThe sensor is modeled as a network of coupled resistancesand capacitances spread across the sensor plane [29]. For
our application, our goal was to locate the pressure pointthat is effectively changing the overall sensor capacitance.
The model was developed by dividing the sensor into infinitesimally small 1-dimensional resistive and capacitive
components (Figure 2(a)) spread over the length of sensor(Figure 2(b)). The voltage and the current equations for modeling the sensor can then be derived from the Telegrapher’sequations on an electrical transmission line [29] as follows:∂V (x, t)= −(R + jωL)I(x, t) = −RI(x, t)(1)∂x∂I(x, t)= −(G + jωC)V (x, t) = −jωCV (x, t)(2)∂xwhere, x is the distance from the voltage application point
and R, L, C, and G are the characteristic values for line
components per unit length. In the case of our sensor, wehave a negligible inductance(L ≈ 0) and trans-conductance(G ≈ 0) (Figure 2(a)). Combining Eq. 1 and Eq. 2, we obtainthe full form of the equations as:∂ 2 V (x, t)∂ 2 I(x, t)
2
=
γ
V
(x,
t);
= γ 2 I(x, t) (3)
∂x2
∂x2
√
where, the propagation constant, γ = α + jβ = jωRC.
The sensor with length l can be divided into n virtual sensor pixels, each represented as an RC couple (Figure 2(b)). In
order to distinguish the pressing of each individual pixel weneed at least n−1 interrogation frequencies. We chose the interrogation frequencies ({f1 , ..fi , ..fn }) to be the frequencies
at which the traveling voltage wave at distances xi = il/n
for i ∈ 1 : n (i.e., the distance between the interface and the“end” of each pixel) is attenuated to half power.
The attenuation factor, α, for the traveling voltage wave
is:
√
(4)
α(f ) = e(−Re(γ)x) = e(− πRCf x)
Hence, the attenuation functions for each pixel end point
i in an 1 × n pixel sensor are:

We performed a series of experiments to evaluate theproposed method for localizing point pressures. Six total
configurations were tested: 1 × n sensor strip and n × n
sensor skin, and by discretization the full length l into
3, 4, and 5 (virtual) pixels. In each test, we applied a 2
mm displacement to each pixel to double the capacitanceof each pressed region. We then performed a frequency
measurements at all fi for 1 × n (∀ n ∈ 3 : 5) pixel
sensor array while recording the Rs and Cp values using an
LCR meter (Hioki IM3253). Six repetitions of the frequency
sweep for each pixel were obtained to form a feature-richdataset. We then input these datasets (fi , Rs (fi ), Cp (fi )∀fi )into a multi-class kernel support vector machine (KSVM) togenerate a model to classify which pixel (1 × n sensor strip)
or pixel column (n × n sensor skin reduced to 1 × n sensor
strip) was pressed.
B. K-SVM Classification
Support vectors machines are widely used in learningbased classification to divide the dataset into separate classes.
While standard SVMs are designed for linear classification
between binary classes using a hyper-plane passing throughmaximal margin of separation between the two classes [30],we require n-class classification for a 1xn pixelated matrix.
Furthermore, the non-linearity of Rs and Cp as a functionof frequency (Figure 2(c)) demands a non-linear classifiermodel. Thus, we employed a multi-class K-SVM classification method for the pixel localization [31] using the errorcorrecting output codes (ecoc) model in the Matlab Statistics
and Machine Learning Toolbox (Mathworks). For each class(pressed pixel, i), the training data consisted of the Rs andCp values measured in the interrogation frequency sweep.
The SVM’s classification performance was assessed using
a k-fold cross-validation model applied on the training datathat randomly partitions the data into k sets where k − 1
sets was used to train the model and the remaining set wasused for cross-validation of the model. The accuracy of themodel was reported as a confusion matrix, where the model’s
predicted pixel (Output Class) was compared against the true
pixel (Target Class).

√

αi (f ) = e(−Re(γ)xi ) = e(− πRCf xi ) ∀i ∈ 1 : n (5)√At half power attenuation, αi = 1/ 2, and thus theinterrogation frequencies can be calculated as:fi =(ln αi (f ))2
0.0382=f or i ∈ 1 : n
2
πRCxi
RCx2i

(6)

C. 1 × n Sensor Strip
We first performed the experiments on a sensor strip thatwas discretized to form 1x3, 1x4, and 1x5 pixel arrays(Figure 3, top row). The data collected during these experiments are shown in Figure 3, middle row. As reported
in the analytical model, at lower frequencies, the measured

Fig. 3. Single dimensional 1 × n sensor strip experiments. (Top row) Photos of the same 1 × n sensor with differently sized pressure applicators to create
1x3, 1x4, and 1x5 pixel arrays, from left to right. (Middle row) Plots of capacitance over a frequency sweep while different pixels are pressed. (Bottomrow) Confusion matrices used to evaluate the efficacy of the support vector machine in classifying each pixel press. An extra class (0) representing “Nopixel pressed” in 1x3 confusion matrix shows that the model can detect when a pixel is actually pressed.

capacitance was found to be the same, regardless of which
pixel is pressed. As the frequency increases however, we
begin to see differentiation in the capacitance depending on
which pixel was pressed. When the first pixel is pressed,a larger capacitance (relative to an un-pressed sensor) is“seen” across all interrogation frequencies. However, whena more distant pixel i is pressed, at frequencies above thecutoff frequency fi , the effective length of the capacitor has
shortened behind the pixel such that the pressed pixel is not“seen”.
The multi-class KSVM showed nearly perfect performancein classifying which pixels were pressed. The confusion matrices (Figure 3 (bottom row)) show an overall classification
percentage of 100 % for the 1x3 and 1x4 tests, and 96.7 % for
the 1x5 test. In the 1x5 test, the error was in misclassifying
the 4th and 5th pixels. This result can be directly observedin the capacitance vs. frequency plot for the 1x5 case whichshows prominent overlapping between the curves of the twomost distal pixels.
D. n × n Sensor Skin
We expanded upon the 1 × n experiments to n × n
sensor sheets discretized into 3x3, 4x4, and 5x5 pixel arrays(Figure 4). Our goal in this study was to correctly identify thecolumn j in which a pixel (i, j) was pressed, when probingfrom the y-axis. From extension of the 1D analytical model
to 2D, the cutoff frequencies were calculated to be identicalto the 1D case. However, we found experimentally that thecutoff frequencies (i.e. where there were maximal differencesin measured Cp and Rs depending on which column’s pixel
was pressed) were in fact five times higher, ranging from
1kHz to 200kHz. We therefore interrogated the sensor at
at 20 frequencies logarithmically spaced between 1kHz and
200kHz to create an even more feature-rich dataset withwhich to build the classification model.
The results for training and prediction for 1xnth column
classification are presented in Figure 4(c). It is important tonote that the 2D classification results have n times lower sensitivity as 1D example. Use of 20 interrogation frequencies
and feature extraction from both resistance and capacitancechange of the sensor sheet improved the classification from
≈ 60% using 10 frequencies to >90% for the 3x3 and 4x4
matrices. As the pixel size reduces, the change in capacitance from pressing a pixel relative to the overall sensor
capacitance decreases. The reduction in sensitivity results

Fig. 4. (a) Photo of the 2D sensor sheet with a pressure applicator for the 5x5 pixel discretization. The foil protruding under the wood frame along theleft and bottom edges was used to interface the LCR meter to the sensor electrodes. The index nomenclature is overlaid on top. (b) Frequency responsesof Rs and Cp measured in the 3x3 matrix experiments. (c) Confusion matrices for the 3x3, 4x4, and 5x5 sensor configurations, respectively, after training
using a multi-class support vector machine. An extra class (0) representing “No pixel pressed” was added solely to the 3x3 classification.

in a lower classification accuracy wherein the misclassified
pixels are predicted to be in one of the adjacent columns(Figure 4(c) 5x5). We observe that the classification accuracy
decreases at pixels furthest away from the interface, where
the sensitivity of the measurement method is lowest. The
performance degradation becomes even more evident as we
increase the resolution beyond the 5x5 matrix, at which
point the limits of the current measurement system arereached. By superimposing measurements and classifications
from interrogating at both the x- and y-axes, an improved
classification of pixel location can be obtained.
V. C ONCLUSION AND F UTURE W ORK
We have presented a method to localize applied pressure
on a soft 2D monolithic capacitive sensor. In comparison
to a sensing region composed of n × n discrete sensors,
the proposed approach greatly simplifies fabrication anddrastically reduces the number of interfaces from n2 to justtwo, facilitating integration of surface pressure measurement
in soft robots. We demonstrated that pressures could be
localized by interrogating the sensor at multiple frequencies
to record the Cp and Rs values, and inputting those measurements into a trained kernel support vector machine toreport the location of pressure in both 1 × n and n × n pixel

arrays. We used a KSVM to perform non-linear, multi-classclassification that yielded excellent results in both the 1 × n
and n × n pixel arrays.
From this preliminary study, there are many directions inwhich to take this work: improving localization accuracy inthe 2D case, investigating the spatial resolution and load
sensitivity of the system, further testing using differently
shaped objects and non-flat surfaces, and measurement ofmultiple contact points by interrogating from more than
two interface locations. To improve the localization accuracy
within a 2D array, we found preliminary results that showedthat the KSVM could also be used to predict the pressure
location in rows (i) orthogonal to the interface (y-axis), in
addition to columns (j). While the accuracy of this model
expectedly is lower, the results nonetheless demonstrated
that there is further information encoded in the Rs andCp values gathered from a single interface beyond just the
localization within columns parallel to the interface. Thus,
we hypothesize that we can utilize the two sets of Rs andCp values gathered by interrogating from the two axes totrain four KSVMs and then convolve the KSVM models toimprove localization accuracy. Furthermore, we would liketo investigate the sensitivity of the system in terms of thespatial resolution. As we found in our 2D experiments, thesensitivity of the pressure sensor reduces as we travel awayfrom the interface. A sensitivity and information theoretic
analysis [14] would provide information on the pixel size
limits, based upon the magnitude of the smallest measurable
capacitance change, as a function of distance from theinterface.
In terms of implementation on a soft robotic system, there
remain several open questions in using this system. These
opportunities include measurement of continuous values ofpressure, localization of multiple contact points, identification of pressure application with non-square shapes, implementation of the sensor on curved surfaces, and investigating
the effect of stretch on the system. The methods that wehave presented in utilizing a soft, capacitive sensor skin to
localize pressure application leverages the unique propertiesof a large-area, deformable capacitor while providing thebenefits of monolithic fabrication, more efficient interfacing, and a more physically robust device. This approachenables applications beyond soft roboticists to more easily
determine interactions between soft robot systems and theirsurroundings, by distributing contact pressure sensing across
any surface.
ACKNOWLEDGMENTS
This work is funded by the Swiss National Science Foundation
through the National Centre of Competence in Research (NCCR)
in Robotics. MCY is supported by the National Science Foundation
Graduate Research Fellowship (Grant DGE-1333468).

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