Stretchable Shape-sensing Ribbons
Stephanie J. Woodman, Anjali Agrawala, and Rebecca Kramer-Bottiglio
Mechanical Engineering and Materials ScienceYale University
New Haven, CT, USA
stephanie.woodman@yale.edu

Abstract—Future robots will boast mutable morphology, properties, and behavioral control policies to adapt to changing tasks
and environments. Soft robots offer an appealing platform foradaptive shape change, as the constituent soft components may
stretch and reform into new target shapes. Typical soft robot
proprioception and control are achieved by embedding stretch
sensors into a robot’s body at locations of anticipated strain
during task performance. By mapping the neutral length of
those sensors to the neutral (unactuated) shape of the robot,
shape changes are detected when the sensors deviate from thosepositions. However, this approach relies on a fixed neutral shapeand corresponding mechanics model, which is not the casefor shape-changing robots. To introduce a mechanics-model-free
approach to shape estimation for shape-changing robots, wereport a sensory ribbon that fuses stretch and orientation data toreconstruct the 3D shape of the ribbon in free space and apply
it to the surface of arbitrary host objects.
Index Terms—shape sensing, soft robotics, shape-change

2023 IEEE SENSORS | 979-8-3503-0387-2/23/$31.00 ©2023 IEEE | DOI: 10.1109/SENSORS56945.2023.10325035

I. I NTRODUCTION
It is generally accepted that there are optimal forms forany desired function [1], which has led to the pursuit ofshape-changing robots that can adapt their morphology andbehavioral control policy towards changing tasks and environments [2]. Such adaptive shape-change is uniquely possible
with soft robot platforms, due to the inherent stretchability
and morphability of soft materials and components [3]–[7].
Shape-changing robots require closed-loop shape control.
However, current soft robot proprioception, state estimation,and control approaches are not amenable to changes in neutral
body shape. The typical approach is to 1) embed stretchable
sensors—either resistive or capacitive [8]–[10]—into the bodyor surface of a soft robot, 2) note the sensor readings when
the robot is unactuated and in its neutral shape, and 3)
infer actuation and motion from sensor readings that deviate
from those corresponding to the neutral shape. Coupled withmechanics and kinematics models of the robot’s shape, thissimple approach is effective when the neutral shape of therobot is unchanging. However, for robots with mutable shapes,
a new model-free approach is needed.
A model-free approach is possible: a surface shape can bereconstructed with measurements of orientation at multiple
points along the surface and the distance between each of
the points [11], [12]. This approach has previously beenThis material is based upon work supported by the National Science
Foundation under IIS-1954591. S.J.W. was supported by a NASA NSTGRO
Fellowship (80NSSC22K1188). A.A. was supported by an NSF Graduate
Research Fellowship, DGE-2139841.

used to construct inextensible shape-sensing arrays [13]–[15]. However, for inextensible arrays, information is lostwhen the subject stretches or deforms (i.e., if the underlying
body stretches—thereby changing the distance between thesensors—the approach fails). Mathematically, the NyquistShannon sampling theorem states that for any single curve,
at least two tangents pointing along the curve are required
to determine the curvature κ, but this yields no information
about scale [16]. We, therefore, surmise that introducing
stretchable strain sensors between orientation sensors should
yield extensible shape-sensing arrays that can measure boththe surface shape and scale of an underlying body.
In previous work, we attempted to realize robust shapeestimation via a platform fusing orientation sensors andstretchable circuits. Our work used embedded liquid-metal
capacitive strain sensors that dynamically measure the distancebetween orientation sensors [17]. However, interfacing thesilicon integrated circuits with soft substrates and conductors
proved challenging—a problem that has been independently
addressed in the literature [18]—and we were previously
unable to measure curvatures and stretch simultaneously.
Herein, we present a sensing platform that positions stretchable, textile-based capacitive strain sensors that can be easily
fabricated from readily accessible materials [19] between offthe-shelf 9-axis orientation sensor breakout boards (BNO055,Adafruit, Inc.) (Fig. 1a-c). Using this platform, for the firsttime, we illustrate the benefits of stretch in surface-based
shape sensing and demonstrate the platform’s potential utility
in closed-loop shape control for emerging shape-changing
systems. We validate the platform’s accuracy on shapes withincreasing sinusoidal frequency, as well as increasing featureamplitudes and correspondingly increased perimeter lengths.
Our results show that the incorporation of the stretch sensors
between the orientation sensors allows the system to fullyreconstruct the target shapes and length scales.
II. FABRICATION AND E XPERIMENTAL M ETHODS
Our sensing system is a ribbon consisting of six stretchsensors and six orientation sensors (Fig. 1c-d). The ribbon ofstretchable sensors was fabricated first. As illustrated in Fig. 1e(and further detailed in [19]), each sensor is multi-layered: anouter electrode made of stretchable, conductive fabric wraps
around two layers of a stretchable, non-conductive fabricdielectric and an inner electrode. All layers are adhered witha stretchable textile adhesive. This layering architecture forms

Authorized licensed use limited to: Yale University. Downloaded on January 23,2024 at 19:04:18 UTC from IEEE Xplore. Restrictions apply.

Fig. 1. Overview and fabrication. a, Un-stretched and b, stretched sensor ribbon and measured shape. c, Sensor ribbon laid flat. d, Strain sensor stretched.
e, Exploded view of strain sensor; SLL denotes strain-limiting layer. f, Velcro attachment of orientation sensor to sensing ribbon.

a parallel plate capacitor such that when the sensor undergoes
strain, the capacitance increases. The five-layer design shields
the sensor from sensitivity to twisting or external pressures.
To derive the relation between capacitance change and displacement (sensor length), five sensor samples were strainedon a mechanical testing device (Instron 3345) while measuring
capacitance, and a quadratic equation was fit to the averaged
data (Fig. 2). In the full ribbon system, one dielectric fabriclayer is common across each of the six sensors. Strain-limiting
layers of inextensible woven fabric were placed at the ends ofeach sensor to support the orientation sensor breakout boards,
which were secured by Velcro (Fig. 1f). The ends of the ribbon
also had Velcro to close the ribbon during testing.
To collect data and estimate shape, each strain sensor wasinterfaced with a capacitive sensor processing board (MPR121,Adafruit, Inc.; rise time = 1 µs, charge current = 39 µA),and each orientation sensor was interfaced with a multiplexer(TCA9548A, Adafruit, Inc.). The processing board and themultiplexer were connected to a microprocessor breakout
board (Arduino Nano, Arduino). The shape estimations wereobtained using spherical interpolation (commonly referred toas “Slerp,” [20]) between the six orientations, with the strain
sensor providing the distance between each orientation.
To evaluate the utility and accuracy of the shape-sensing
ribbon, we generated twelve shapes with various radial frequencies and amplitudes/perimeters, mimicking the effects ofexpansion of soft actuators on a robot body. We generated
these shapes using Equation (1), where r(Θ) gives the polar
coordinates of the output shape, rmean is the mean radius ofa circle, A is the amplitude of surface features, ω is the radialfrequency of surface features, ϕ is the phase (always zero forour shapes), and Θ is the angle from the polar axis.
r(Θ) = rmean (1 + Asin(ωΘ + ϕ))(1)

In Fig. 3, from left to right, radial frequency increases from0 to 2, 3, and 4; From top to bottom, the amplitude of theradial features and shape perimeter length are increased to set
the ribbon’s strain to 0%, 20%, and 40%, respectively. In moredetail, the dimensions of the two-dimensional shapes are asfollows. Fig. 3a-d: perimeter of 480 mm (the unstrained lengthof the ribbon, thus the ribbon is at 0% strain applied aroundthe perimeter) and amplitude of 0.2; Fig. 3e-h: perimeter of
580 mm (20% strain) and amplitude of 0.3; Fig. 3i-l: perimeterof 680 mm (40% strain) and amplitude of 0.4. The shapes werelaser cut out of acrylic (ULS VLS 2.30DT).
The sensing ribbon was wrapped around each shape fivetimes. The shape measurement was calculated during postprocessing, along with finding the mean absolute error (MAE)
between the experimentally measured shape and the groundtruth shape, provided by the CAD model. The smallest Euclidean distance was found between each data point in themeasured shape and points along the ground truth shape.
These distances were averaged to find the MAE of each trial.
The MAE values were then averaged across the five samples,yielding the reported cumulative MAE value in Fig. 3.

Fig. 2. Sensor characterization.
Capacitance vs. displacement fromfive sensor samples, and the quadraticfit (R2 = 0.999) used to approximate
stretch in the sensing ribbon. Cloud
represents one standard deviation.

III. R ESULTS
The sensing ribbon is able to capture sinusoidal curvatureswith radial frequencies 0, 2, and 3 with relatively low MAEs,
even as the amplitude and perimeter increase. We note a sharp
increase in the MAE for a radial frequency of 4, which isexpected, as there are no longer enough orientation sensors tocapture the additional curvatures.
Average MAE increases across each radial frequency as
strain increases. This loss of accuracy at higher strains could
be due to increased sensor-to-sensor variation at displacements
greater than 10 mm, as seen in Fig. 2. Despite the increasein MAE, the system is still able to reasonably capture theAuthorized licensed use limited to: Yale University. Downloaded on January 23,2024 at 19:04:18 UTC from IEEE Xplore. Restrictions apply.

Fig. 3. Average MAE with increasing strain/amplitude, and radial frequency. Representative samples of the shape measurements (blue curves) comparedto the ground truth shapes (dotted lines), for each shape tested. Locations of the orientation sensors (OS) are denoted on the estimated shape, and their true
location is also shown in the schematic of the ground-truth shape above each test. MAE values were averaged over five trials, and the axes and scale in (a)apply to all subplots.

curvature and size of shapes with ≤3 radial sinusoids and withamplitudes and/or perimeters that correspond to ≤40% ribbon
strain. With an inextensible system, only the shapes in Fig. 3ac (0% strain) would have been accurately captured. Using
stretchable sensors, the shapes in Fig. 3e-g,i-k are measurable.
IV. D ISCUSSION
The results herein indicate that, as long as the number oforientation sensors is at least double that of the target object’sradial frequency, the stretchable sensing ribbon can capturechanges in both shape and scale of shape-changing hosts.
Because the sensor ribbon is designed to be general-purpose,
we did not tailor sensor placement to best capture eachtested shape. Consequently, we noticed difficulties capturing
both shallow curvatures, as in Figs. 3c, f, & j, and very
sharp curvatures, as in Fig. 3k. We suspect that capturing
shallow curvatures with the sensor ribbon was difficult because
compliance in the Velcro attachment of the orientation sensors
led to the orientation sensors not lying perfectly tangent to theshape. Capturing sharp curvatures was difficult because theorientation sensors were not placed intentionally close to sharp

curves, and the measurement method smoothly interpolates
between the orientation measurements. With a higher sensor
density, sharper curvatures could be captured, but at the costof an increasingly complex system.
The inextensible attachment mechanism that linked the endsof the sensing ribbon led to the slightly asymmetric placementof orientation sensors, which may have affected the accuracyof reconstructing concave curvatures, as in Fig. 3c, between
orientation sensor 0 and orientation sensor 5. Without theasymmetry, this concave curvature would have been capturable, as validated by the concave curvatures in Fig. 3g & k,where the asymmetry is minimized with higher strains.
This work serves as a step towards shape estimation for
topologically complex systems and will enable closed-loop
shape control of next-generation shape-changing robots. In
future work, we will improve upon the sensor ribbon design byaugmenting the hardware and shape reconstruction algorithms
to work for three-dimensional (3D) shape estimation. Future
experiments will include expanded sensor arrays and tests on
dynamically shape-shifting 3D platforms.

Authorized licensed use limited to: Yale University. Downloaded on January 23,2024 at 19:04:18 UTC from IEEE Xplore. Restrictions apply.

R EFERENCES[1] R. Pfeifer and J. Bongard, How the body shapes the way we think: a
new view of intelligence. MIT press, 2006.
[2] D. Shah, B. Yang, S. Kriegman, M. Levin, J. Bongard, and R. KramerBottiglio, “Shape Changing Robots: Bioinspiration, Simulation, andPhysical Realization,” Advanced Materials, vol. 33, p. 2002882, may2021.
[3] E. Steltz, A. Mozeika, N. Rodenberg, E. Brown, and H. M. Jaeger,“JSEL: Jamming skin enabled locomotion,” 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2009,
pp. 5672–5677, dec 2009.
[4] D. S. Shah, J. P. Powers, L. G. Tilton, S. Kriegman, J. Bongard, andR. Kramer-Bottiglio, “A soft robot that adapts to environments throughshape change,” Nature Machine Intelligence 2020 3:1, vol. 3, pp. 51–59,nov 2020.
[5] R. Baines, S. Freeman, F. Fish, and R. Kramer-Bottiglio, “Variablestiffness morphing limb for amphibious legged robots inspired by chelonian environmental adaptations,” Bioinspiration Biomimetics, vol. 15,
p. 025002, feb 2020.
[6] H. T. Lin, G. G. Leisk, and B. Trimmer, “GoQBot: a caterpillarinspired soft-bodied rolling robot,” Bioinspiration Biomimetics, vol. 6,
p. 026007, apr 2011.
[7] R. Baines, S. K. Patiballa, J. Booth, L. Ramirez, T. Sipple, A. Garcia,F. Fish, and R. Kramer-Bottiglio, “Multi-environment robotic transitions
through adaptive morphogenesis,” Nature, vol. 610, no. 7931, pp. 283–289, 2022.
[8] S. Seyedin, P. Zhang, M. Naebe, S. Qin, J. Chen, X. Wang, and J. M.
Razal, “Textile strain sensors: a review of the fabrication technologies,performance evaluation and applications,” Materials Horizons, vol. 6,
no. 2, pp. 219–249, 2019.
[9] B. Shih, D. Shah, J. Li, T. G. Thuruthel, Y. L. Park, F. Iida, Z. Bao,
R. Kramer-Bottiglio, and M. T. Tolley, “Electronic skins and machinelearning for intelligent soft robots,” Science Robotics, vol. 5, p. 9239,
apr 2020.
[10] H. Souri, H. Banerjee, A. Jusufi, N. Radacsi, A. A. Stokes, I. Park,
M. Sitti, and M. Amjadi, “Wearable and stretchable strain sensors:materials, sensing mechanisms, and applications,” Advanced Intelligent
Systems, vol. 2, no. 8, p. 2000039, 2020.
[11] N. Sprynski, N. Szafran, B. Lacolle, and L. Biard, “Surface reconstruction via geodesic interpolation,” Computer-Aided Design, vol. 40,pp. 480–492, apr 2008.
[12] T. Stanko, S. Hahmann, G. P. Bonneau, and N. Saguin-Sprynski,“Shape from sensors: Curve networks on surfaces from 3D orientations,”
Computers Graphics, vol. 66, pp. 74–84, aug 2017.
[13] A. Hermanis, R. Cacurs, and M. Greitans, “Acceleration and MagneticSensor Network for Shape Sensing,” IEEE Sensors Journal, vol. 16,
pp. 1271–1280, mar 2016.
[14] T. Hoshi and H. Shinoda, “3D shape measuring sheet utilizing gravitational and geomagnetic fields,” Proceedings of the SICE AnnualConference, pp. 915–920, 2008.
[15] P. Mittendorfer, E. Dean, and G. Cheng, “3D spatial self-organization ofa modular artificial skin,” IEEE International Conference on Intelligent
Robots and Systems, pp. 3969–3974, oct 2014.
[16] C. E. Shannon, “Communication in the Presence of Noise,” Proceedingsof the IRE, vol. 37, no. 1, pp. 10–21, 1949.
[17] D. S. Shah, S. J. Woodman, L. Sanchez-Botero, S. Liu, and R. KramerBottiglio, “Stretchable Shape-sensing Sheets,” Under review at Advanced Intelligent Systems, 2023.
[18] D. F. Fernandes, C. Majidi, and M. Tavakoli, “Digitally printed stretchable electronics: a review,” Journal of Materials Chemistry C, vol. 7,pp. 14035–14068, nov 2019.
[19] L. Sanchez-Botero, A. Agrawala, and R. Kramer-Bottiglio, “Stretchable,breathable, and washable fabric sensor for human motion monitoring.,”
Advanced Materials Technologies (Accepted).
[20] K. Shoemake, “Animating rotation with quaternion curves,” in Proceedings of the 12th annual conference on Computer graphics and interactivetechnologies, pp. 245–254, ACM Digital Library, 1985.

Authorized licensed use limited to: Yale University. Downloaded on January 23,2024 at 19:04:18 UTC from IEEE Xplore. Restrictions apply.