IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 4, NO. 3, JULY 2019

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Robotic Skins That Learn to Control
Passive Structures
Jennifer C. Case , Michelle C. Yuen , Jane Jacobs, and Rebecca Kramer-Bottiglio

Abstract—Robotic skins incorporate sensors and actuators into
stretchable and flexible planar substrates. Wrapping a robotic skinaround a passive, deformable structure imparts controllable motion onto that structure, rendering it an active robotic system.
Robotic skins can be applied to the surface of a structure, thenremoved and re-applied to the surface of another structure. This
reconfigurability enables use of the same robotic skin to achieve
multiple motions, which depend on the interaction between the skinand its host structure. Considering the broad range of use cases for
robotic skins in resource-limited environments, it may not be possible to pre-characterize this skin–structure interaction for all potential systems. Therefore, it is advantageous to have systems that canlearn their models in situ, which saves considerable time in realizing
a functional system. Previously, we have shown that robotic skins
can be used to estimate state and stiffness of the underlying passive
structure they are attached to. In this letter, we demonstrate how
this ability to measure state and stiffness can be used to learn model
parameters in situ for feedforward control, and show how feedback
control can be implemented simultaneously with the same system.
We further show how this learning is expandable to multi-segment
systems and will compensate for gravitational effects by adjustingmodel parameters.
Index Terms—Modeling, control, and learning for soft robots,
sensor-based control, robotic skins.

I. INTRODUCTION
HEN working in remote locations with limited accessto resources, it is advantageous for a robotic system tobe versatile so that it can accomplish a variety of tasks. For

W

Manuscript received October 15, 2018; accepted March 10, 2019. Date of
publication March 27, 2019; date of current version April 3, 2019. This letter
was recommended for publication by Associate Editor C.-H. Yeow and Editor
K.-J. Cho upon evaluation of the reviewers’ comments. This work was supportedby the Air Force Office of Scientific Research under the Young Investigator program (FA-9550-16-1-0267) and by the National Aeronautics and Space Administration (NASA) under the Early Career Faculty program (80NSSC17K0553).
The work of J. C. Case was supported by a NASA Space Technology Research
Fellowship (NNX15AQ75H). The work of M. C. Yuen was supported by aNASA Small Business Technology Transfer Grant (80NSCC17C0030). The
work of J. Jacobs was supported by a NASA Connecticut Space Consortium
Grant (NNX15AI12H). (Corresponding author: Jennifer C. Case.)
J. C. Case and M. C. Yuen are with the School of Mechanical Engineering,Purdue University, West Lafayette, IN 47907 USA, and also with the School ofEngineering & Applied Science, Yale University, New Haven, CT 06473 USA(e-mail:,jennifer.case@yale.edu; michelle.yuen@yale.edu).
J. Jacobs and R. Kramer-Bottiglio are with the School of Engineering &Applied Science, Yale University, New Haven, CT 06473 USA (e-mail:, jane.
jacobs@yale.edu; rebecca.kramer@yale.edu).
This letter has supplementary downloadable material available at
http://ieeexplore.ieee.org, provided by the authors. This video shows the robotic
skins, the learning process, and control of the system using a variety of control
strategies. This size of the video is 16.6 MB.
Digital Object Identifier 10.1109/LRA.2019.2906552

Fig. 1. (a) A two-segment continuum robot made from two robotic skins
wrapped around soft cylindrical segments. The sensors and actuators in the
robotic skins are used to derive properties of the underlying segment and to control the system. (b) A visual description of a bending segment. (c) A cross-sectionof a segment with sensor labels.

this, we look to soft robotic systems which are lightweight andmechanically robust in unknown environments [1]–[3]. Whilesome soft robotic systems have shown multifunctionality [4]–[6]and reconfigurability [7], [8], most are still generally designed
around completing a single task, such as locomotion [1], [9],[10], grasping [11]–[13], or manipulation [14], [15]. In contrast,
robotic skins, which incorporate both sensing and actuation in a
flexible planar substrate, are versatile: the same robotic system
can be used across a wide variety of applications, including locomotion, grasping, manipulation, and wearables [16]. Robotic
skins operate by attaching to deformable host structures and imparting motion onto those structures. They are removable andtransferable, meaning they can be attached to one host structure
to attain one behavior, then removed and attached to a different host structure to attain a different behavior. This ability to

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IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 4, NO. 3, JULY 2019transfer from system-to-system makes robotic skins useful fortasks in unstructured environments that may require the system
to adapt to changing task requirements.
In this letter, we present robotic skins that learn about theirunderlying host structures to facilitate feedforward control of thesystem. We demonstrate this approach on cylindrical continuum
segments since they are widely applicable in soft robotics andcan be easily stacked to create multi-segment arms, as shownin Figure 1(a). In this work, we define “learning” as the ability
to use sensory information to obtain certain values of the hoststructure, specifically length, radius, and bending stiffness ofthe segments, and apply those values to populate control models. Previously, we demonstrated how robotic skins can be used
to estimate both state and stiffness of cylindrical continuum segments [17]. Here, we show how this ability to estimate state andstiffness of structures can be extended to learn model parameters of continuum segments made from different materials in
situ, which enables feedforward control. We show the necessityof having the skins learn by considering both a generalized feedforward model, which is provided with a bending stiffness, andcompare it to our learned bending stiffness estimation. Additionally, we use the sensors in the robotic skin to apply feedback
control both on its own and in combination with our learned
feedforward model control. Finally, we demonstrate how thisability to learn about the underlying structures is expandable tomulti-segment systems and is able to adjust parameters (i.e., thebending stiffness) to account for gravity, which is not includedin the model of the cylindrical segment.
While there are many control strategies in soft robotics[18]–[21], we believe this is the first demonstration of robotic
skins learning about structures for control purposes. By learning
about the system, it is possible to change the system on-the-fly
without the need to intervene and perform time-intensive system
re-calibrations manually.
II. MODELThe model used in this work was developed from existingmodels in continuum robotics [22]–[24], which describe the deformation of cylindrical segments given loads that run parallel
to or spiral around the segment [25]. While dynamic models ofthese continuum robots exist [26]–[28], this work focuses on a
static model to demonstrate that simple models can be used withrobotic skins to control soft continua.
A full model description is presented in [17], and is summarized briefly here. The state of a cylindrical segment can be
described by segment length (lseg ) and curvature in the x- andy-axes (respectively, κx and κy ). A visual representation of curvature is shown in Figure 1(b). Sensors that are aligned parallelto the neutral axis of the segment can be used to identify thestate of the segment:
κx =lseg − ls,4
ls,2 − lseg=
lseg rlseg r(1a)κy =lseg − ls,3
ls,1 − lseg=
lseg rlseg r(1b)where ls,i for i = 1, 2, 3, 4 is the length of the ith sensor, as
shown in Figure 1(c), and r is the radius of the segment. The

bending stiffness of the combined segment and skin (Kb ) can be
estimated by applying a single actuator force (F ) and relating
this to the system curvature:
Kb =where κ =



rF
κ

(2)

κ2x + κ2y .
III. FABRICATIONThe robotic skins, shown in Figure 2(a), were designed to fit
around cylindrical segments (r = 17.5 mm and lseg = 100 mm).
Though the segment dimensions are carried over from our priorwork [17], we improved upon the robotic skin design to have it
learn all necessary segment properties (r, lseg , and Kb ) on its
own. Thus, the approach we present here can be readily applied
to passive cylindrical segments of arbitrary sizes and materials (within reason). This concept can be expanded to arbitrary
shapes in future work. In the following, we discuss the fabrication of the actuators, sensors, robotic skins, segments, and theexperimental setup.
A. Actuators
The model assumes actuators that either contract or elongate and, thus, we chose to use McKibben pneumatic actuators
which contract as they are pressurized. Each actuator was madewith a latex balloon bladder surrounded by mesh braid (1/4”
dia., McMaster-Carr). The balloon was tied on one end with thebraid ziptied onto the balloon just inside of the knot, as shown in
Figure 2(b). On the other end, we inserted Tygon tubing (6.4 mm
outer diameter, 1.6 mm inner diameter) into the balloon and secured two zipties over the braiding around the tubing to prevent
leaking. The McKibben actuator was designed to be 120 mmlong to allow a sufficient range of motion, but still contract
enough (to ≈85 mm) to deform the segment when pressurized.
B. Sensors
We used capacitive strain sensors to measure the lengths andradii of segments. The sensors were fabricated as a parallel-plate
capacitor using an exfoliated graphite and silicone composite
for the conductive layers and pure silicone elastomer for the dielectric layers. These sensors have five layers to help isolate thesensors from external disturbances. Descriptions of how to makethe exfoliated graphite composite and the five layer sensor material are available in [29] and [16], [17], respectively. The sensors
were designed with an active (gauge) length of 80 mm (overall length 132.1 mm). The vertical sensors were pre-strained by
20 mm when installed on the segment; the horizontal sensors
were designed with a 16.5 mm pre-strain. The sensors were redesigned from [16], [17] to be more compact and now have thesensor board sitting on top of the sensor material rather than attached externally to the sensor footprint. Figure 2(c) shows how
the final sensor components were assembled. The polystyrene(0.65 mm thick) and PET (0.1 mm thick) ends were cut with alaser (Universal Laser Systems VLS 2.30). The ends were sewn
through the available holes to hold the sensor together. Finally,
the end with the exposed copper was wrapped in electrical tape

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Fig. 2. (a) The robotic skin is composed of two layers of spandex instrumented with sensors and actuators. Diagrams show the layout of the skin. (b) Diagram anddimensions of the actuators. (c) Components and construction of the sensors. (d-e) A Dragon Skin 10 Slow elastomer segment with polystyrene skin attachments
both (d) without and (e) with the robotic skin.

to prevent spurious signals arising from contact with objects.
To reduce noise in the sensor response, we applied an exponential filter to the sensor output, sf,t = αsr,t + (1 − α)sf,t−1 ,where sf,t is the filtered response at time t, sr,t is the raw
sensor response at time t, and α is the decay rate, which we
set α = 0.8.
C. Robotic Skins
The robotic skins, shown in Figure 2(a), were organized suchthat they were able to learn the segment dimension. Each robotic
skin consisted of two layers of spandex, six capacitive strain
sensors and four actuators. Two horizontal sensors in the bottom
layer measured the circumference of the underlying cylinder toallow the skin to determine the radius of the system while theother four vertical sensors in the top layer measured the segment
length and are aligned as shown in Figure 1(b). The sensors weresewn directly onto the spandex fabric. An actuator was ziptied
in place over each of the four vertical sensors using a 3D printed
actuator attachment (Printrbot Metal Plus).
In order to facilitate testing, snap buttons were incorporated
into the skins to allow for quick connection (≈1.5 min) anddisconnection (≈0.7 min) from segments (Figure 2(d-e), Supplemental Video). The skins themselves were 140.0 mm ×160.1 mm and had muslin reinforcements where the sensor andactuators were attached and where snap buttons were mounted.

The button snaps were mounted through both layers of spandex
to hold the two layers together and were located underneathall sensor-actuator attachment points and in all four corners of
the skin.
D. Continuum Segments
For the continuum segments, we used two elastomers withdifferent stiffness properties and fabricated them such that they
could easily connect and disconnect to each other as well as therobotic skins (Figure 2(d)). The segments were molded from
Dragon Skin 10 Slow (Smooth On, Inc.) and Smooth-Sil 935(Smooth-On, Inc.), which have elastic moduli of 265 kPa and536 kPa, respectively [17]. Male and female end caps were mechanically locked onto either end of the segment by casting thesegments with the caps in place so that the elastomer infiltrated
the porous body of the caps. The end caps and the molds for thesegments were 3D printed with a Form 2 SLA printer (FormLabs). To attach the robotic skin to the elastomer, we madepolystyrene (1.6 mm thick) fabric attachments (Figure 2(d)).
These attachments were cut out using a laser cutter (Universal
Laser Systems VLS 2.30) and have snap buttons placed on thetabs, which were bent in place by heating the polystyrene andbending the tab over. When assembled with the robotic skin
(Figure 2(e)), the tension in the skin holds the fabric attachments securely on the ends of elastomer segment. The ability to2488

IEEE ROBOTICS AND AUTOMATION LETTERS, VOL. 4, NO. 3, JULY 2019

rearrange the segments and the skins using the snap buttons madeit easy to assemble and disassemble the system for testing.
E. Experimental Setup
The robotic skin-elastomer system was attached to a basewhich held it vertically for experiments (Figure 1(a)). The 3D
printed base had a female interlocking mechanism (FormLabs,
Form 2) to lock the segment in place. Mortar board was placed
over the 3D printed part and clamped in place to stabilize thesystem. The overall experimental setup was designed to allow
the system to be quickly changed for various segments.
A central microcontroller (Arduino Uno) was used to communicate with the skins during operation. This microcontroller
used I2C communication to read from and write to the sensor
boards and pressure regulators that drive the actuators to a desired pressure [30]. The Arduino Uno relayed all the results to
a computer through serial communication to record the system
response.
IV. CHARACTERIZATION
A. Sensors
The sensors were characterized in a materials testing machine(Instron 3345) after they were integrated into the skin to determine a linear fit for each sensor. The skin was stretched such thatthe gauge length of the sensor stretched from 95 mm to 120 mm
in steps of 2.5 mm; three sensor readings for each sensor werecollected at each step. This process was repeated 10 times for a
total of 30 data points at each step. The results for each sensor
were averaged together and a linear fit, ICi = a0,i ls,i + a1,i ,was found for each sensor’s response. ICi refers to the number of instruction cycles corresponding to the discharge time of
the ith capacitive sensor within a measurement query and thus,
serves as a proxy for the sensor’s capacitance. aj,i for j = 0, 1
are the parameters of the equation for the ith sensor. A representative plot of the response and fit of a single sensor is provided
in Figure 3(a). Since each sensor is unique, this characterization
was performed on each sensor to attain an accurate relationshipbetween length and sensor reading.
B. Actuators
The actuators were characterized prior to integration to relate
the actuator’s force response to its length and internal pressure.
Each actuator was secured into the materials testing machine at
an initial length of 110 mm, inflated to a constant air pressure,and then contracted to 70 mm at a rate of 40 mm/min. This
test was performed at several pressures (10, 15, 20, and 25 psi)
which were held constant using pressure regulators [30]. We
then related the force to both length and pressure to obtain atheoretical surface fit:2
Fi = b0,i + b1,i pi + b2,i la,i + b3,i pi la,i + b4,i la,i(3)where Fi is the ith actuator force, pi is the internal pressure of the
ith actuator, la,i is the ith actuator length (we assume la,i ≡ ls,iin our model), and bj,i for j = 0, 1, 2, 3, 4 are parameters forthe ith actuator. A representative plot showing the responses
and fits of a single actuator is provided in Figure 3(b). Since

Fig. 3. Representative plots of (a) sensor and (b) actuator characterization.
(a) Sensor characterization relates the sensor length to the sensor response given
in instruction cycles . (b) 2D representation of the actuator characterization. The
shaded regions represent the 95% confidence interval of the experimental data
and the black lines represent the theoretical fits.

each actuator is unique, this characterization was performed oneach actuator to attain an accurate relationship between length,pressure, and force.
V. RESULTS
A. State Estimation
State estimation was enabled by the model presented in
Section II and the actuator characterization. The model was implemented in a MATLAB simulation that predicted the system
state (i.e., κx and κy ) given the segment radius, bending stiffness, and actuator pressures. The segment radius was measured
from our horizontal sensors using the following equation:r = (ls,h + c + Δskin )/2π

(4)where ls,h is the average length of the two horizontal sensors, c
is the inextensible length of the polystyrene tabs (27.5 mm), andΔskin is the length the spandex fabric stretched, independent of
the sensors. Because the sensors did not wrap all the way aroundthe circumference of the segment, portions of the skin stretchedwithout being measured by the sensors. For this work, we manually measured that unobserved stretch when needed. Complementing the simulation, the bending stiffness can be found via
Equation 2 given the actuator characterization results (Equation (3)), segment radius, and curvature (i.e., system state). To
demonstrate the robustness of our approach, we tested (1) different segment diameters while holding input pressures constantand (2) different pressure inputs while holding the segment diameter constant.
To demonstrate the skin’s adaptability to segments with varying diameters, we compared the skin’s theoretical and actual curvature on multiple Dragon Skin 10 Slow segments (35, 40, and
45 mm diameters). We set a single actuator to 22 psi, recorded
the horizontal sensor lengths, and captured photos of segment.
For the 35, 40, and 45 mm diameter segments, we found that

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TABLE IISETTLING TIME OF VARIOUS CONTROL STRATEGIES

the horizontal sensors (r = 18.6 ± 0.6 mm.). Equation (1) requires the segment length to determine the curvatures of thesystem. Slight variations in the initial segment length can havea large impact on the resulting κi calculations, which can resultin errors for our state estimation. Thus, we used unique initial
sensor lengths (ls,1 = 100.4 ± 0.3 mm, ls,2 = 103.3± 0.8 mm,
ls,3 = 101.7 ± 0.3 mm, ls,4 = 98.4 ± 0.4 mm, with an overall
average of lseg = 100.9 ± 3.1 mm) for these curvature calculations depending on which sensors are used for the κi calculations. Similar to our previous work [17], the state estimation
predicted by the sensors required a corrective offset (1.5 m−1
for this work) to match the state of the system.
The estimated states, given as κx and κy , are shown in
Figure 4(b) for each state alongside the model-predicted state.
The error in curvature did not exceed 0.7 m−1 , which we believe is an acceptable level of error for a 2D robotic skin being
wrapped around 3D structures. This error can be reduced in the
future by improving upon the state estimation model, sensor
accuracy, and adaptability of the skin design.
Fig. 4. (a) Comparison of measured and theoretical segment curvatures acrossdifferent radii. Additionally, the plot shows the accuracy of the sensor-measured
segment diameter. (b) State estimation results for each of the states presented inTable I. The error bars represent the 95% confidence interval.
TABLE ISTATE ESTIMATION CONDITIONS

Δskin = 0, 8, 16 mm, respectively, which indicates that thestretching skin could be treated as a spring. We used ImageJ tomeasure the curvature from the images. Figure 4(a) shows how
the measured diameters and curvatures compare to the modelpredicted curvatures at various diameters. From the measured
curvature, we calculated the bending stiffness of the different
segments as 56, 82, and 135 kN mm2 for the 35, 40, and 45 mm
diameter segments. A linear regression was fit to these values togenerate stiffnesses at different segment diameters for the theoretical model. We found that there is good agreement between
the measured and theoretical values of curvature.
To verify that the skin’s vertical sensors can also be used
for state estimation, we compared the state generated by thesensors to the theoretical model. This verification was performed on a Dragon Skin 10 Slow segment across seven actuation states (Table I) each tested 10 times. We measured thesegment length with the vertical sensors and the radius with

B. Control
With reasonable state estimation, we implemented several
control approaches for the one-segment system to evaluate theefficacy of each. The first approach was feedforward control
which uses a model to predict what the inputs (pressures) of
the system should be. For this, we considered two feedforward
models: a generalized model, which had the bending stiffness
supplied, and a learned model, which used a learning sequence
in combination with state estimation to determine the bending
stiffness of the segment. Additionally, we explored feedback
control both on its own and in combination with learned feedforward models. Note that all of these single segment tests were
performed with a single robotic skin to demonstrate that a single
skin is not characterized for a particular material. The controllers
operated at 10 Hz. The performance of each controller is represented by the average error per second (error/s) in Figure 5
and the settling times shown in Table II. By analyzing all ofthese control methods, we can select which control strategy isappropriate for future applications.
1) Feedforward Control: Because the robotic skins are able
to detect material properties from the underlying structures andthe constituent components have been thoroughly characterized,
we were able to develop an approximate model of the system for
feedforward control which predicts what actuator pressures arenecessary for a desired state. For a given desired configuration(κx,d and κy,d ), the actuator pressures should be set as follows
from Equation (3):pi =2Fi − b0,i − b2,i la,i − b4,i la,ib1,i + b3,i la,i

(5)

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Fig. 5. Control response using (a) generalized model feedforward control, (b) learned model feedforward control, (c) feedback control, and (d) learned modelwith feedback control. The average error in control response is shown in (e). The colors in (e) correspond to the controllers in (a)-(d). Control response of twosegments is shown in (f). The black line represents κx,des and κy,des while the colored line represents the average system response across three trials. The shaded
region represents the 95% confidence interval.

where the actuator lengths can be defined asla,1 = lseg (1 + κy,d r)(6a)la,2 = lseg (1 + κx,d r)(6b)la,3 = lseg (1 − κy,d r)(6c)la,4 = lseg (1 − κx,d r)(6d)and the forces of the actuators are defined as
κy,d Kbr
κx,d Kb
If κx,d > 0 : Fa,2 = 0, Fa,4 =r
If κy,d > 0 : Fa,1 = 0, Fa,3 =

κy,d Kb, Fa,3 = 0r
κx,d Kb, Fa,4 = 0
If κx,d < 0 : Fa,2 = −r
If κy,d < 0 : Fa,1 = −

(7a)
(7b)

(7c)
(7d)

To demonstrate the need for these robotic skins to learn about
their underlying material, we tested feedforward control witha generalized model where the bending stiffness was set at
Kb = 60 kN mm2 and compared it to a learned model strategy
where the stiffness is estimated by the skin ahead of time. Bothfeedforward models use the learned lseg and r values, which
are found immediately when the system is powered, since thoseare necessary for state estimation. For the learned feedforward
model, the stiffness estimation was performed prior to running

CASE et al.: ROBOTIC SKINS THAT LEARN TO CONTROL PASSIVE STRUCTURES

the controller (shown in Supplemental Video). Each actuator
was sequentially pressurized to 15.0, 18.5, and 22.0 psi. Using
the sensors to measure the curvature, a stiffness value was calculated at each condition for a total of 12 stiffness measurements.
These measurements were then averaged together to obtain thelearned bending stiffness of the system. By allowing the system
to learn about the system’s behavior in situ, the control signal isbetter tuned to the system, which results in a reduced error.
Figure 5(a) shows the results of the generalized model feedforward control for both a Dragon Skin 10 Slow and SmoothSil 935 elastomer segment. Here, we can see the feedforward
control for the Dragon Skin 10 Slow segment performed wellsince the generic bending stiffness value was around the bending stiffness for this specific skin-elastomer system. When thefeedforward controller with the same generic bending stiffness
was applied to a different material (Smooth-Sil 935), the response of the system suffered, as evidenced by the increased
error. In contrast, Figure 5(b) shows the system response when
the robotic skin learned about its own bending stiffness. The
bending stiffnesses were found to be Kb = 65 ± 4 kN mm2 andKb = 105 ± 7 kN mm2 for Dragon Skin 10 Slow and SmoothSil 935, respectively. The average error of each response is plotted in Figure 5(e) and this shows the slight improvement in error
between the generalized model feedforward (shown in green)
and learned model feedforward (shown in red) controllers for
the Smooth-Sil 935 segment. For the Dragon Skin 10 Slow segment, the learned feedforward model did not perform as wellas the generalized feedforward model due to slight error in thelearned stiffness estimation. Overall, we observed that the performance of the learned feedforward model is comparable tothat of the generalized feedforward model.
2) Feedback Control: Although the feedforward model
showed reasonable accuracy in approximating the system, inaccuracies in the model itself and the input values to the model (i.e.,bending stiffness) resulted in non-negligible error between thecommanded and achieved segment curvatures. Since the robotic
skin already has sensors, we implemented feedback control toreduce curvature error by adjusting the actuator pressure. We
used a proportional-derivative (PD) feedback controller that applied a change to the pressure based on the error. The controller
algorithm is given as
If κy,d > 0 : p1 = 0, p3 + = kp (κy,d − κy )κy,d − κy
+ kd
(8a)
Δt
If κx,d > 0 : p2 = 0, p4 + = kp (κx,d − κx )
κx,d − κx
+ kd
(8b)
Δt
If κy,d < 0 : p1 − = kp (κy,d − κy )κy,d − κy+ kd, p3 = 0 (8c)Δt
If κx,d < 0 : p2 − = kp (κx,d − κx )
κx,d − κx+ kd, p4 = 0 (8d)Δtwhere kp and kd are the proportional and derivative gains andΔt is the change in time.

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Fig. 6. Simulation showing how the feedback controller responds to changes inbending stiffness. The black line is the reference while the blue, red, and yellow
lines show systems with bending stiffnesses of 60 KN mm2 , 80 kN mm2 , and100 kN mm2 , respectively.

Here, we compared using only feedback control, shown in
Figure 5(c), and using feedback control alongside the learned
feedforward controller, shown in Figure 5(d). Since the system
was entirely modeled, including the actuators, we built a simulation that predicted the system performance given a set ofpressure inputs. This simulation was used to tune the feedback
controller gains (kp = 0.75 and kd = 0.005), which were kept
constant across all the tests regardless of materials, shown in
Figure 6. For the learned model, the bending stiffnesses were
found to be Kb = 69 ± 2 kN mm2 and Kb = 100 ± 5 kN mm2
for the Dragon Skin 10 Slow and Smooth-Sil 935 segments, respectively. The slight variations in the bending stiffness between
these and the previous values are due to the fact that the system
performs the learning sequence each time the controller is run
rather than using a single system learning result across all tests.
The average error responses are presented in Figure 5(e) for the
feedback (blue) and feedforward and feedback (magenta) controllers. Using only feedback control, we can see that the system
is controlled well and actually better controlled than the feedforward alone, as seen by the error measurements presented in
Figure 5. Using a combination of learned model feedforward
and feedback, we see an additional improvement in control ofthe system. The settling time of the system is improved dueto the feedforward component of the controller, as shown in
Table II, while the modeling error is reduced due to the feedback component of the controller.
While there is an advantage in using the combination of feedforward and feedback, this may not be necessary for every application and feedback alone may be sufficient. In scenarios
where the system has a slower time response, it would be advantageous to use the combined feedback and feedforward controller, rather than pure feedback, since the feedforward model
can be changed to account for the time component of the system.
C. Multi-Segment Control
To demonstrate that this combination of feedback and learned
model feedforward control method is expandable to multisegment continuum robots, we created a two segment systemwith a Dragon Skin 10 Slow segment stacked on top of a
Smooth-Sil 935 segment. Each segment was controlled by independent feedforward controllers, and thus, each performed
its own characterization to learn about its model consecutively(first the bottom segment, then the top) before beginning thecontrol sequence. The bending stiffnesses were found to be2492

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Kb = 55 ± 3 kN mm2 and Kb = 140 ± 10 kN mm2 for Dragon
Skin 10 Slow and Smooth-Sil 935, respectively. The bottom segment was able to compensate for the additional weight of the top
segment by increasing the bending stiffness estimation for the
Smooth-Sil 935 segment. Based on the performance observedin the single-segments tests, we modified the control signal forthe two-segment system to keep the desired curvature within theobserved limits. The results of this two segment test are shownin Figure 5(f) and in the Supplemental Video. From these plots,
we observe that by using this simple learning approach, controller performance is maintained as the system is expanded tomultiple segments.
VI. CONCLUSION
In this letter, we demonstrated how robotic skins can be used
to learn system parameters to create feedforward models, andto implement feedforward and feedback control of elastomericcontinuum robots. We showed how different forms of feedforward and feedback control affect system performance. Givenhighly accurate models, feedforward control can be used alone
to control systems. However, in the case of robots created onthe-fly, for example by wrapping robotic skins around arbitrary
soft passive bodies, these models may not be available. As such,the efficacy of such on-the-fly robots relies upon the ability
to self-characterize or learn system parameters in situ for adequate feedforward control. To refine learned feedforward control, robotic skins can simultaneously incorporate feedback to
improve overall system performance. The robotic skin-enabledapproach presented here allows for greater versatility and deployability of controllable soft robotic systems. Control of thesesystems can be further improved by applying adaptive control
to the feedforward model, and tuning gains of the feedback controller. Additional work on the control of multi-segment continuum arms includes developing higher-level controllers that wrap
around individual segment controllers to control aspects of thesystem such as end-point position. We also plan to develop a generalized model of the robotic skins to explain how they interact
with underlying structures and to explore alternative actuatorsthat can apply more force and increase the maximum curvatureachieved by the system. In conclusion, robotic skins can learnsystem parameters in situ and use the generated feedforward
model in tandem with feedback control to effectively transformarbitrary soft passive structures into robots on-the-fly.
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