2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
Madrid, Spain, October 1-5, 2018

Design for Control of a Soft Bidirectional Bending Actuator
R. Adam Bilodeau*1,2 , Michelle C. Yuen*1,2 , Jennifer C. Case1,2 , Trevor L. Buckner1 ,Rebecca Kramer-Bottiglio1,2Abstract— In this paper, we present sensor-controlled antagonistic pneumatic actuators (SCAPAs) that integrate provensoft robotic actuators and sensors into a simplified, controllable design. The antagonistic actuators together compose
a bidirectional bending actuator with embedded capacitive
strain sensors. By designing the SCAPAs from the groundup for closed-loop control, we are able to minimize both thenumber of constituent components and the types of materials
used, and further streamline the manufacturing processes.
These improvements are embodied in the multipurpose useof a single conductive fabric sheet for both actuation andsensing, integrated into an otherwise all-silicone device. Such
reduced material complexity allows us to use simple finite
element analysis (FEA) models to predict the performance of agiven design. We compare various designs to maximize sensor
effectiveness using FEA and experimentally verify the suitabilityof select designs for state reconstruction. After converging on
our final design, we demonstrate that this design evaluation
process enables the use of simple control strategies to achieve
closed-loop control.

Keywords: soft material robotics, hydraulic/pneumatic actuators, sensor-based control
I. I NTRODUCTION
Elastomer-based pneumatic actuators have been demonstrated as highly adaptable functional systems [1]. Initial
work presenting inflatable “pneu-nets” in an elastomericbody demonstrated that the silicone structures could grip
objects or slowly walk when given simple, open-loop commands [2], [3]. Since then, they have seen significant forward
progress in their fabrication, adaptablility, and control [4].
However, this forward progress has come coupled withboth a rise in the manufacturing complexity of casting thepneumatic chambers [5], [6], and in the design complexity
as additional sensory systems are embedded [4], [7]–[9]. It
has also increased the need for on-demand high-pressuresand vacuums [10]–[12] and their corresponding, often bulky,
equipment. This trend of increased complexity will likely
only rise as researchers strive to derive additional functionality, logic, or adaptability out of otherwise inert soft materials.
One of the challenges of soft robotic systems is in creating reliable controls [13]. Since inflatable soft technologies
experience large deformations during operation, and are
constructed with viscoelastic materials, closed-loop control
is not a trivial task [14]. Though pneumatic actuators were
*RAB and MCY are co-first authors.
1 School of Engineering and Applied Science, Yale University, New
Haven, CT, USA
2 School of Mechanical Engineering, Purdue University, West Lafayette,
IN, USA rbilodea@purdue.edu, yuenm@purdue.edu,

rebecca.kramer@yale.edu
978-1-5386-8094-0/18/$31.00 ©2018 IEEE

Fig. 1. Sensor-controlled antagonistic pneumatic actuator (SCAPA). (a)Overhead view of a SCAPA sweeping across its full range of achievablecurvatures, κ. (b) Due to its fully soft construction, the SCAPA can berolled up, compressed, and still return to full functionality. (c) Optical
microscope image of the interface between the actuator, embedded sensor,
and conductive fabric. (d) A cross-section schematic of a SCAPA, including
an indicator for the location of the optical image in (c).

demonstrated early on, development of soft sensors capableof matching the physical response of these systems lagged
behind. As such, much of the state-of-the-art in soft robotic
controls has focused on predictive models and feed-forward
controls [15]–[19] or on actuator (pressure) feedback rather
than true state reconstruction and closed-loop control via
sensors [20], [21]. Recently, there has been an increase in
the use of finite element analysis (FEA) to better understandand predict the response of a soft system [5], [22]–[24], but
due to material non-linearity and large system deformation,these FEA models are complex and difficult to implement.
Forays into sensor-enabled closed-loop control have usedcommercially available flexible sensors to demonstrate state
reconstruction and control [25]–[27]. These sensors also
provide a strain-limiting layer while providing the statereconstruction feedback.
Recent advances in silicone-based all-soft sensors are
beginning to allow for more advanced demonstrations ofclosed-loop control in soft actuators. Early soft sensors usedconductive liquid metals embedded in elastomer as highdeformation resistive sensors [28], [29]. These have beenused both as embedded sensors for state reconstruction and5936

as external sensors for closed-loop control [6], [8], [30],[31]. More recently, soft conductive silicone composites havebeen demonstrated as reliable, repeatable, high-deflection
capacitive sensors that can be placed externally on soft joints
for 2D and 3D state reconstruction [32]–[36] or as integrated
resistive sensors providing both proprioception and tactile
feedback in closed-loop controlled pneumatic grippers [37].
As an alternative, stretchable optics have been demonstrated
as embedded sensors in pneumatic actuators, providing state
reconstruction, curvature control, and tactile feedback [7],[38]. With all this available research into soft sensors andcontrollable soft systems, we see an opportunity to synthesize
simpler robotic constructs without losing functionality orutility.
In this paper, we present sensor-controlled antagonistic
pneumatic actuators (SCAPAs, Figure 1) which integrate
proven soft robotic actuation and sensing technologies in a
simplified design targeting controllability of the system state(i.e. design for control). Specifically, we embed siliconebased capacitive strain sensors [39] into pneu-net bending
actuators [1], which we then assemble as antagonistic pairs
to achieve bi-directional, controllable actuation. Compared
to previous work, we make two key improvements to thesystem: 1) utilizing inextensible conductive fabric as boththe strain-limiting layer for the actuators and the groundplane for the capacitive sensors, and 2) utilizing the same
silicone material in both the actuators and sensors. These
improvements result in fewer constituent components, fewer
interfaces between dissimilar materials, and fewer manufacturing steps. This reduction in physical complexity allows us
to use a simple FEA model to predict the quality of a given
design, which we experimentally verify. We compare various
candidate designs using the FEA model and subsequent
experimental tests to determine which design can provide
strong state reconstruction. Finally, we select a SCAPA design and use it to demonstrate closed-loop curvature control
using various basic feedback control strategies.
II. P HYSICAL E MBODIMENTA SCAPA consists of an antagonistic pair of thin bending pneumatic actuators, each with an embedded capacitive
sensor for differential measurement of curvature (Figure 1).
At the core of each SCAPA is conductive fabric, which
serves dual purposes as both the strain-limiting layer for theactuators and as the grounding electrode for the sensors. The
system’s reduced profile allows us to roll a SCAPA into a
compact cylinder without damaging any of the constituent
components (Figure 1(b)). Previous work used conductive
fabric as both the strain-limiting layer of a one-sided pneumatic actuator and an electrode for capacitive contact detection [40]. Here, we expand on their work by using the fabricin a state feedback sensor for closed-loop control, rather thanobject detection.
The sensors are constructed as a parallel-plate capacitor using an expanded graphite silicone composite for theactive conductive layer and unmodified silicone elastomer
for the dielectric layer. As the sensor geometry changes

Fig. 2. (a-c) Manufacturing the SCAPA. (a) The capacitive sensors werefirst fabricated in large films and then laser cut into the desired patterns.
(b) The casting process created the pneu-net actuators while simultaneously
embedding a sensor in the actuator body. (c) Conductive fabric was glued
between two actuators to create the antagonistic bending system and theelectronics controlling actuation and measure the sensors were attached to
the SCAPA. (d) Photos showing two of the designs explored. The actuator
body, sensors, and conductive fabric are clearly visible in the cross-sectional
images. (e) For all experiments performed, each SCAPA was fixed verticallysuch that the tip would sweep horizontally. A camera was situated above
the SCAPA to record truth data on its curvature.

due to applied strain or pressure, the capacitance changes
measurably. White, et al. previously conducted a study of thematerials and manufacturing of these strain sensors, as wellas their response to many cycles of strain [39]. We made thesensors out of the same elastomer as was used in the actuator
body, resulting in a nearly invisible, fully bonded interface
between the sensor and actuator (Figure 1(c)). This material
continuity reduces risk of delamination failure that can occur
at interfaces between dissimilar materials. We also leverage
the single material construction to simplify analysis of strain
fields in the device’s silicone walls.
To bend a SCAPA, one of the actuators is inflated while
the other is vented to atmosphere. This bend causes thecapacitance of the embedded sensors to change. The actuatorinflation is controlled by “pneumatic servos” which serve
effectively as 3-port, digital pressure regulators [41]. To readthe capacitance change, we use custom signal conditioning
boards that charge the sensor for a fixed length of timeand record the time it takes to discharge to ground voltage(based on [39] with modified software). The entire system iscontrolled using an Arduino Mega communicating with thepneumatic servos and the sensor signal conditioning boards
via I2C protocol.
A. Fabrication
The SCAPAs were manufactured in three phases: 1) sensor
fabrication, 2) actuator casting, and 3) assembly (Figure 2(ac)). As stated previously, the conductive fabric acted as ashared ground layer for both capacitive sensors. To makethe rest of the sensor, we cast the remaining two layers in

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a sheet by rod-coating first the silicone-graphite composite(DragonSkin 10 Slow, Smooth-On; Expandable graphite,
Sigma-Aldrich) for the active electrode layer [39], followedby the pure silicone for the dielectric layer (DragonSkin 10Slow) (Figure 2(a)). Upon curing, we used a laser to cut
out two U shapes that fit along the outside edges of theactuators. We cleaned the cut shapes with ethanol and laidthem in the bottom of the actuator molds. The molds were
fabricated from laser-cut acrylic sheets (Figure 2(b)). We
poured silicone into the molds (DragonSkin10 Slow; SilcPigsilicone dye, Smooth-On), degassed the cast material in a
vacuum chamber, and clamped a lid on top to ensure uniform
thickness across all actuators. After the actuators cured, we
glued one to each side of inextensible conductive fabric(Technicot, LessEMF) using additional uncured silicone,
completing both the actuators and the sensors. The tubing
for the actuators was inserted and epoxied to the actuator
body (Sil-Poxy, Smooth-On), and connected to the pneumatic
servos (Figure 2(c)). The capacitance signal conditioning
boards were sewn directly to the grounding fabric to improvethe electrical contact between the two. Flexible copper-cladpolyimide strip electrodes extending from the signal conditioning boards were sandwiched against the active silicone
sensor layer by two polystyrene plates that were also sewn
to the fabric. These strip electrodes allowed for a larger
contact area between the interfacing surfaces, giving thesignal conditioning board a strong electrical connection to
the active layer.
III. D ESIGNIn order to properly characterize and study a symmetricactuator sensor pair, we defined a simple, perspective-based
nomenclature to differentiate the sensors and the curvatureof the SCAPA. From the top-down perspective shown in
Figure 1(a), when the right-side actuator is inflated, the
SCAPA body will bend to the left, which we define asa negative curvature. Conversely, when the left actuator is
inflated, the SCAPA body bends to the right, which we define
as a positive curvature. The sensors located in the left andright actuators are referred to as the left and right sensors,
respectively.
In theory, when the curvature is positive, the capacitanceof the left sensor should increase due to stretching andPoisson thinning of the dielectric layer. Similarly, the rightsensor should increase in capacitance as the sensor length iscompressed. By convolving the two sensor signals it should
be possible to determine the curvature of the SCAPA forstate feedback to the controller [31].
In practice, with a highly deformable sensor embeddedin the actuator, we must consider how the sensor response
is coupled to all deformations in the soft body, from those
we want to measure (curvature proprioception) and those we
do not want to measure (inflation expansion). To address
this coupled response, we performed a design study of thecross-sectional geometry to develop designs in which thesensors would be minimally affected by actuator pressure.
This design study consisted of two parts: 1) FEA modelingFig. 3. Design study to determine the effects of sensor width and placementon the quality of the sensor output. (a) Schematic of the loading conditions
for the FEA (left) and cross-section geometry (right), with only the boxed
section being modeled. (b) Sketches of the initial modeled geometry andthe FEA results. Design 1 shows the base case for the system. Design 2
reduces the width of the sensor and Design 3 moves sensor to the topof the actuator. (c) Experimental verification plots showing the sensor
responses to curvature. The circles indicate experimental data and the line isa quadratic fit with the shaded region being a 95% confidence bound about
the regression.

to predict deformation fields in the actuator cross-section due
to inflation expansion, and 2) empirical verification of thedesign’s effect on sensor response.
A. FEA modeling of cross-section
A series of FEA simulations were run in SolidWorks toassess the deformation in the sensor region due to inflation(Figure 3). The analyses were set up using a 2D cross-sectionof the SCAPA, with reduced geometry to encourage fastersolution times. Expecting large deformations in the wall, thesimulations were run using a nonlinear solver. Our model
includes three assumptions:

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1) A fixed fabric layer that is completely inextensible, perfectly flexible, and perfectly bonded to the silicone. We
are confident with this assumption due to the orders-ofmagnitude difference in tensile elasticity between thesilicone and fibers in the fabric, and because we choseare placed along the outer wall of the device, we considered
only this section as our area of interest, and simplify ourmodel accordingly. This simplification is further supported
by inspecting additional modeling work that has recently
been performed [5], [23]. Instead of applying pressure toa geometric reconstruction of the whole cross section, weapplied an upward force equivalent to the pressure lifting
the pneumatic pocket, acting along a moment arm. Thisaccounted for both a lifting motion and bending moment
experienced at the juncture between the pneumatic pocket
and the actuator wall (Figure 3(a)). We then applied theremaining internal pressure directly to the wall’s edge. Dueto symmetry, it was only necessary to analyze one side of
the structure.
In this analysis, we were primarily interested in sensor
strain in the y-direction (normal to the fabric), as definedby the axes in Figure 3(a). Since one half of the parallelplate capacitor is a wide fabric sheet, sensor displacement inthe x-direction should not affect the sensor output. However,y-strain will have a significant impact on the sensor, as
it reflects changes in the distance between the electrodes,
while discounting bulk motion of the entire system in they-direction. Any y-strain in and under the sensor induces
a sensory response that is not reflective of the SCAPA’s
bending motion. By marking out the area of the sensor in
our FEA model, and plotting the strain in the y-direction, weclearly see the effects of actuator inflation on compression
and tension in the sensor (Figure 3(b)).
B. Sensor Characterization & Model Verification
Fig. 4. Design exploration of various geometries that should limit the effectof actuator inflation on sensor response. (a) Schematic of the the loading
conditions for the FEA (left) and the cross-section geometry (right), with
only the boxed section being modeled. (b) Sketches of the initial modeled
geometry and the FEA results. Design 4 and 5 introduce a notch along
the outer edge of the actuator with the sensor embedded near the fabriclayer and on top of the notch respectively. Design 6 increases the distance
between the sensor and the pneu-nets by increasing the width of the actuatorwall. (c) Experimental verification plots showing the sensor responses tocurvature. Design 6 began to twist while actuating resulting in unpredictablesensor responses. The circles indicate experimental data and the line is aquadratic fit with the shaded region being a 95% confidence bound about
the regression.

a fabric with an open weave that allowed the pre-cured
silicone to fully permeate between all the fibers.
2) Uniform material throughout the elastomer, since boththe sensor and the actuator are silicone, the active composite layer is very thin, and there is little conductive
filler in the composite itself.
3) Linear elastic behavior of the silicone, where E =0.12 MPa, obtained via a linear extension test on
dogbone shaped silicone samples using an Instron 3345
materials testing system, with samples tested to 50%
strain at 100% strain per minute.
Previous work showing detailed 3D analysis of an inflating
elastic chamber indicate that the thick outer walls experiencestresses that are 2-3 orders of magnitude less than the thin,
expanding ‘roof’ of the chamber [22]. Since our soft sensors

To verify the FEA modeling, we initially modeled threedesigns with different sensor sizes (8mm or 4mm wide) andlocations (embedded or on top of actuator) and then built
these designs to experimentally evaluate their viability forcurvature state reconstruction (Designs 1, 2 and 3, shownin Figure 3(b-c)). Using the experimental setup shown in
Figure 2(e), we mounted the SCAPAs onto a stand such thatboth actuators were perpendicular to the benchtop. We sewed
a thin strip of Teflon to the tip of the actuator to minimize
friction during motion. A webcam was mounted overhead
to record the curvature truth data of each SCAPA during
actuation. In each experiment, we actuated both actuators
individually through a range of inflation pressures between
6-11 psi (at 1 psi increments and five repetitions at eachpressure), in a randomized order. This range of pressurescorrespond to the range of curvatures shown in Figure 1.
Once inflated to the desired pressure, we allowed the actuator
to settle into a steady state for 5 s. We then sampled andrecorded the sensors 100 times over a period of 10 s andaveraged the data to obtain a representative sensor reading.
Finally, we took a photo of the actuator from which wemeasured the curvature of the actuator (truth data) using athree-point fitting algorithm that assumes constant curvaturein the system.
We plotted the sensor values against the curvature toevaluate the design’s performance (Figure 3(c)). We firstnormalized the sensor data to the data range between 05939

curvature (x0 ) and the minimum measured sensor value(xmin ): xnorm = (x − x0 )/(x0 − xmin ). In an ideal
bending beam, negative curvatures would correspond to theright sensor’s capacitance increasing and the left sensor’s
capacitance decreasing, with the converse expected whenbending to the right. Instead, we observed that both sensors
have a parabolic response. In Designs 1 and 2, this response
is centered near a curvature of 0 m−1 , while the response
in Design 3 shows a significant offset. Because of this, thepositive and negative curvatures for Designs 1 and 2 cannot
be well-distinguished, even when convolving the two sensor
signals. We hypothesize that this is due to the sensor response
being coupled with inflation pressures. As suggested by the
FEA models for these two designs, there is a field of y-strain(marked in blue) cutting through the location of the sensors.
Design 3’s asymmetric response corroborates the conclusions
from the FEA, which suggests that only a portion of thearea under the sensor is undergoing strain, and so the sensor
is only marginally affected by actuator inflation. This initialdesign study showed us that our FEA model is able to predict
the impact of sensor placement in a cross-section, even with
our embedded modeling assumptions.

Fig. 5. Sensor calibration results for Design 4 (see Figure 4) comparing
the actual curvature to state reconstructed curvature. The shaded region
represents the 95% confidence interval. The inset shows an inflated SCAPA
with a fitted circle used to measure the actual curvature. r is the radius of
the circle and κ is the curvature.

IV. C LOSED L OOP C ONTROL
A. SCAPA Design Selection

C. Design Exploration
Having experimentally verified our FEA model, we used
it to qualitatively examine multiple cross-section designs
without the need for building physical prototypes. After
testing many designs that varied in geometric parameters,
we removed those that performed poorly in the FEA models
and converged on three designs (Designs 4, 5, and 6, shownin Figure 4(b)). These designs minimized the impact of theactuation pressure on the sensor, and we fabricated each
design to confirm the results of the FEA. Designs 4 and 5
introduce a stress-relieving notch in the actuator wall above
the sensor; Design 6 widens the wall of the actuator andmoves the sensors further away from the pneu-nets.
Our results show that the notched designs isolated thesensors from a significant portion of the actuator inflation
deformation. The sensors’ responses in Designs 4 and 5 show
unique pairings of left and right sensor values across theentire range of curvatures tested. Compared to Design 3,
the confidence bounds on Design 4 and 5 are greatly reduced, indicating a stronger and more repeatable response tocurvature change. Additionally, we observed that the sensor
values rise above 0, indicating that the sensors’ capacitances
increase as expected, albeit slightly, when it is on the outsideof the curve.
The results of the experimental characterization of Design 6 indicate a breakdown in our simplified FEA model.
The increased wall width changed the deformation dynamics
of the actuator. Rather than simply bending, the SCAPA
twisted and/or curled into a bowl-like shape, which resulted
in highly unusual, asymmetric sensory response (Figure 4).
This sort of dynamic 3D response was not accounted for in
our simplified 2D FEA, indicating a model limitation.

We chose to use Design 4 to demonstrate closed loop
control. This particular design (demonstrated in Figure 2(d))
met all of the goals we sought to achieve for improved state
estimation: simplified manufacturing with embedded sensing
cast into the actuator in a single-step, a sensory responseto actuator strain in which both actuators produced distinct
responses to the actuator’s shape change, and low variationin the sensory response with respect to curvature. Afterchoosing this design, we then remounted the system in our
testing setup, we and collected a new set of calibration datausing a higher refinement in pressure steps (incrementing by
0.5 psi) to get a better resolution in curvatures.
B. Empirical Model
Once the sensor data was correlated with the measured
curvature of the system, a generalized least squares regression was used to determine the coefficients for the following
equation:κ = a0 + a1 S1 + a2 S2
where κ is the curvature of the SCAPA, Si are the raw sensor
output values from the sensor boards, and the constants ai
are the coefficients of the fit. Using the regression model,
we reconstructed the curvature for each set of sensor values gathered during calibration, and plotted it against themeasured curvature values (see Figure 5). The fit has a 95%
confidence interval of 5.549 m−1 or 10.58% of the full scale.
C. Controllers
We tested the system response of our SCAPA using
three different controllers (Table I). These controllers arecomposed of two different control loops (a logic loop and a
proportional-logic loop, diagrammed in Figure 6) with two
different internal logic controllers (whose state machines are

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TABLE I
NAMING CONVENTION FOR THE THREE CONTROLLERS IMPLEMENTINGTHE CONTROL LOOPS IN F IGURE 6 AND STATE MACHINES IN F IGURE 7.

Controller NameControl Loop

State Machine

Simultaneous

Logic

Dynamic

Fixed Rate
Quasi-Static (FRQS)

Logic

Quasi-Static

Varying Rate
Quasi-Static (VRQS)

Logic +
Proportional

Quasi-Static

Fig. 6.

Control loops used to follow the input signal.

sketched in Figure 7). We used a target curvature (κinput ) as
the input signal for all three controllers. This signal could beeither positive or negative, and all three logical controllers
had a built-in filter to switch between which of the two
actuators was active, based on the sign of the desired curve.
The physical design of the SCAPA instilled some common
requirements for each controller. First, since the inactive
actuator was compressed during actuation, it was always
held in the ‘deflate’ state to ensure that its internal pressure
was equal to atmosphere. Second, the capacitive sensors are
sensitive to the activation of the solenoids in the pneumatic
servos [41]. To compensate, we added intermediary ‘settling
time’ states with a fixed delay (tsettle = 100 ms) inwhich sensor-reading was locked out (all smaller circles in
Figure 7). Finally, the hold response of all three controllers
would trigger if the sensory response was within a bandaround the signal curvature, derived from the model error(see Figure 5).
As outlined in Table I, we named each controller basedon the operation goal. The simultaneous controller, the mostbasic controller we could implement, is a logic controller that
increases, holds, or releases pressure in the pneumatic actuator, while sampling the sensors simultaneously. The quasistatic logic state machine removes the dynamic response of
the physical system from the sensor data by locking out thesensor reading when the actuator is inflating or deflating. The
inflation or deflation time was either fixed (fixed rate quasistatic controller, FRQS) or could vary proportionally to thecurvature error (varying rate quasi-static controller, VRQS).
The FRQS controller used only fixed values for all of thetimings, coded directly into the logic controller. It operated
on a 250 ms cycle frequency, actuating for 50 ms, settlingfor 150 ms, and then reading the sensors 10 times during thelast 100 ms (and averaging the data). In contrast, the VRQS
controller used proportional control to determine the timingthat the actuator should be allowed to inflate/deflate (between
0-450 ms). Since the proportional timings allowed for muchlarger inflate/deflate times during large jumps in the input
signal, we were able to allow the system to settle for longer(350 ms) without slowing down the overall performance,
and thus improve the sensor data retrieved and therefore theaccuracy of the controller.
D. System Response

Fig. 7.

State machines used in the logic controllers.

The responses of the three controllers are shown in Figure 8. The input signal is shown as a solid black line, with themean system response shown as a solid blue line and 95%
confidence error bound shaded. For each controller, we also
calculated the mean error in curvature of the experimental
response from the signal (the average absolute difference
between the signal curvature and the SCAPA’s curvature atany given moment in time) in order to quantitatively judge
the three different controllers.
As is evident in Figure 8, the simultaneous controller
performed poorly, with the system having an average curvature error of 17.6 m−1 . The immediate, continuous feedback
caused the controller to whip the actuator back and forth5941

Fig. 8. Closed-loop curvature control using the Simultaneous, Fixed Rate Quasi-Static, and Varying Rate Quasi-Static controllers, with two different
proportional gains in the VRQS controller. Each plot shows the reference signal (black) and the reconstructed curvature (blue - both mean and 95%
confidence bounds), and indicates the mean deviation (error) of the system response from the desired curvature for the whole test.

so wildly that we discontinued the test before completion
to prevent damage to the actuator. We hypothesize thatthe (potentially internal oscillatory) dynamic response of
the physically inflating system was coupled into the sensor
response in a way that was unpredicted in our quasi-static
empirical model, causing the measured curvature to vary.
Switching to the FRQS controller, the SCAPA’s performance improved, with an average curvature error of only
4.4 m−1 . This immediate improvement further reinforced
our conclusion about the simultaneous controller: that theinternal dynamics of the physical silicone, combined with thesensitivity of our sensors, resulted in sensor responses thatgave inaccurate feedback to the logic control loop. In orderto improve the error further, we allowed the fill time to varywith a proportional controller. We tested two different gains(0.09 and 0.11) and the average error reduced to 2.9 m−1 and2.8 m−1 , respectively. This exercise demonstrates that softbodied control is achievable using a just simple proportional
control loop.

only minimal error. With both functional antagonistic actuators and feedback sensors, the SCAPA we presented is afully autonomous, soft pneumatic robot.
Future efforts will explore the dynamic behavior of the
SCAPAs and expand from a single SCAPA to multiple
units connected in series to form a fully controllable softcontinuum manipulator. Future work will also focus on exploration of the FEA, quantitatively comparing run-time andmodel complexity with the physical response. By changing
the assumptions, material properties, modeled regions andincluding out-of-plane stresses, which can result in additional unexpected warping and buckling, we will be able
to optimize the model for both speed and result quality.
Additionally, a quantitative comparison of presented control
strategies and additional controllers (for example, PID),
each with optimized timings and gains, should be studied
through automated empirical testing. Finally, coupled sensor
responses could be used to determine when an external force
is acting on the SCAPA.

V. C ONCLUSION AND F UTURE W ORK

VI. ACKNOWLEDGMENTS

In this paper, we presented sensor-controlled antagonistic pneumatic actuators (SCAPAs), designed for simplified
fabrication and control. Towards streamlined and efficientfabrication, we utilized conductive fabric to serve as boththe inextensible layer for the actuators enabling bending, andas the ground layer of the embedded capacitive sensors. In
order to achieve curvature control, we designed the SCAPAs
so that the embedded sensors would respond to curvature,
rather than actuator inflation. We used FEA modeling andexperimental characterization of the sensor response to curvature to evaluate various SCAPA geometries and determine
an appropriate design. After selecting an appropriate design,
we demonstrated that the chosen SCAPA design could becontrolled with a simple quasi-static control strategy with

The authors would like to thank Dylan S. Shah for assisting withthe operation of the pneumatic servos, and Dr. Joran W. Boothfor his assistance in assembling the controllers. This work was
supported by the US Air Force Office of Scientific Research underaward number FA9550-16-1-0267, by which RAB was funded.
MCY is supported by the National Science Foundation Graduate
Research Fellowship (Grant DGE-1333468). JCC is supported by
the National Aeronautics and Space Administration Space Technology Research Fellowship program (Grant NNX15AQ75H).

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