Sensor Tendons for Soft Robot Shape Estimation
William R. Johnson III, Anjali Agrawala,
Xiaonan Huang, Joran Booth, and Rebecca Kramer-Bottiglio
Dept. of Mechanical Engineering and Materials Science
Yale University, New Haven, CT, USA
will.johnson@yale.edu

Abstract—Tensegrity robots are deformable robots that require
highly-stretchable and reliable sensors for proprioception andclosed-loop control. We introduce capacitive sensor tendons madeof liquid metal electrodes and dielectric silicone that are capableof high strains on the order of hundreds of percent that double as
the tensile elements of tensegrity robots. The electromechanicalresponse of the sensor tendons is characterized in ultimate strain,
cyclic, and relaxation experiments to demonstrate the sensors’
reliability in robotics applications.
Index Terms—tensegrity, shape estimation, capacitive sensing

2022 IEEE Sensors | 978-1-6654-8464-0/22/$31.00 ©2022 IEEE | DOI: 10.1109/SENSORS52175.2022.9967136

I. I NTRODUCTION
Soft robotics aims to create robots that can survive harsh
impacts, adapt to changing environments, and interact safelywith humans [1]. Soft sensors are needed to endow soft robots
with the proprioception and feedback control necessary torival their traditional, rigid counterparts [2]. Soft sensors havebeen developed to sense strain [3], touch [4], texture [5],pressure [6], force [7], temperature [8], and twisting andbending [9]. However, more work is needed to demonstrate
the efficacy and reliability of these sensors in robotics.
Tensegrity robots are a class of soft robots made fromrigid struts and compliant tendons. High strength-to-weightratios and the ability to survive harsh impacts make tensegrity
robots desirable for autonomous exploration of unpredictableenvironments including planetary surfaces [10]. However,feedback control and state estimation of tensegrity robots
are currently limited by insufficient onboard sensing. [11].
Designing effective and reliable sensors for tensegrity robots
is challenging due to their many degrees of freedom andthe large deformations they experience. In previous work,
researchers have used silicone strain sensors with graphite
inclusions [12] and resistive sensors made from conductive
thread [13]. However, these sensors were only demonstrated atstrains less than 100%, limiting the magnitude of deformations
the robot could experience.
Here, we introduce highly stretchable sensor tendons designed for tensegrity robots. The sensor tendons are capacitive
strain sensors made from liquid metal paste encapsulated ina silicone elastomer. A common design for tensegrity robots
involves a combination of actuated cables and passive cables
that act like springs [14]. Accordingly, we designed two typesof sensor tendons. Active tendons run in parallel to actuatedcables. Active tendons need to be reliable sensors for feedback
control, but they do not need to exert high forces because
the actuators in parallel can do so. Passive tendons double as

Fig. 1. (i-v) Bulk fabrication process for active tendons using oxidized eutectic
gallium-indium (oGaIn). The main differences between fabricating active andpassive tendons are the silicone material used and the dimensions of thetendons. (vi) Photograph of the active (left) and passive (right) tendons.

the tensegrity robot’s passive springs. Passive tendons have noactuators in parallel, so the forces they exert are essential forthe tensegrity robot to recover its original shape after actuation.
For the sensor tendons to be reliable in soft robot applications, they must maintain their electrical and mechanicalproperties at high strains, through many cycles, and after
being held in tension for long time periods. In this work,
we demonstrate sensor tendons that meet these standards. InSection II, we describe the design and fabrication process ofboth active and passive sensor tendons. In Section III, wecharacterize the sensor tendons’ electromechanical response
at high strains, in cyclic tests, and in relaxation experiments.
II. D ESIGN AND FABRICATION
Sensor tendons are highly stretchable capacitive strain sensors made from silicone elastomers (Eco-Flex 30 or DragonSkin 20; Smooth-On), a liquid metal paste made fromeutectic gallium-indium (eGaIn), strain-limiting fabric, andflexible wire leads. Capacitive strain sensors were chosen for
their high accuracy, linearity, cyclic stability, and negligible
hysteresis [3]. The liquid metal paste is oxidized eGaIn, orAuthorized licensed use limited to: Yale University. Downloaded on June 27,2023 at 19:52:33 UTC from IEEE Xplore. Restrictions apply.

oGaIn, and it is made by stirring eGaIn in ambient air togenerate large quantities of amorphous gallium oxide [15],[16]. OGaIn was chosen as the conductive layer for its low
electrical resistivity (2.95 × 10−7 Ω m−1 ) and enhanced
adhesion to silicone [15]. The sensors are fabricated layer
by layer in batches on a backing layer of 0.04” polyethylene
terephthalate (PET) and then cut out using a laser cutter. The
fabrication process is shown in Figure 1.
Active tendons, which do not need to exert high forces,
are made with the relatively soft silicone Eco-Flex 30 while
passive tendons, responsible for elastic restoring forces, aremade with relatively stiff DragonSkin 20. The fabrication
process for both types of sensor tendons is similar. First, a1 mm layer of silicone is draw coated on a 0.04” sheet ofPET. Two strain-limiting fabric strips are impregnated withthe silicone and placed on top of the pre-cured layer to form
the ends of each sensor. After four hours of curing at room
temperature, a paper mask is applied so that a layer of oGaIn
can be painted on top with a popsicle stick to form theelectrodes. Wire leads are added to 3 mm × 5 mm pads at theend of each electrode with a drop of oGaIn. A 1 mm layer ofsilicone with a thin strip of fabric to cover the leads is applied
on top. After four hours of curing at room temperature, weapply an extra 1 mm layer of Eco-Flex 30 for the active sensors
to prevent bridging between the liquid metal electrodes (thisstep is not necessary for the passive tendons). After curing,
the second layer of oGaIn is applied via a paper mask, andwire leads are added in a similar manner. The last layer isencapsulated in 1 mm of silicone, and a final layer of strainlimiting fabric is applied. After another four hours of curing
at room temperature, the batch of sensors is placed in a laser
cutter, and the sensors are cut into their final shape. Excessmaterial is removed with a knife. One batch of active tendonsproduces 17 sensors that are 65 mm in length while one batchof passive tendons produces 14 sensors that are 130 mm inlength (lengths are measured from the center of the of theattachment holes on each sensor), although the process could
be further scaled. Finally, some silicone adhesive (Sil-Poxy;Smooth-On) is added to either side of the passive sensor
tendons to reinforce the stress concentration at the edge of thefabric ends (this step is not necessary for the active tendons).
III. E XPERIMENTAL M ETHODS
Sensor tendons on tensegrity robots must exhibit electricaland mechanical robustness at high strains, over many cycles,
and after long time periods held in tension. Sensor tendons
with these properties will enable tensegrity robots to achieve
large deformations and reliable closed-loop control. In thissection, these properties are demonstrated for active andpassive sensor tendons via pulling to failure, cyclic testing,and relaxation experiments.
A. Pull to Failure
Three active tendons and three passive tendons were pulledto failure on a materials testing system (Instron 3345) at arate of 16 mm/s, and the results are shown in Figure 2. The

Fig. 2. Three active and passive sensor tendons were pulled to failure. Activetendons broke at 600% strain while passive tendons broke above 300% strain.

active tendons all broke around 600% strain while the passive
tendons all broke above 300% strain. The ability to achieve
high strains without breaking makes these sensors desirable fortensegrity robots, which experience large deformations duringlocomotion. The capacitance of each sensor exhibited a linear
relationship with strain [17]. Active tendons exerted lowerforces than passive tendons because they are thinner and madefrom a softer material.
B. Cyclic Testing
To remove the Mullins effect [18] before cyclic testing,active and passive sensor tendons were pre-stretched once tothe highest strains they would experience during the test, 300%
and 140% strain, respectively. During testing, the active andpassive tendons were repeatedly extended by 120 mm and150 mm, respectively, corresponding to the strains they weredesigned to experience on a tensegrity robot. Three sensors ofeach type were tested at a rate of 16 mm/s, and the results fromone sample of each type are shown in Figure 3. One active
tendon broke after 200 cycles, likely due to manufacturing
defects, but the rest survived the full 400 cycles of testing.
Both active (gauge factor 0.88) and passive (gauge factor 0.86)
tendons have stable, repeatable, and linear capacitance values,
making them highly reliable sensors for feedback control.
The peak force of the active tendons decreases by just 7.5%
over 400 cycles. The passive tendons elongate throughout thecyclic testing, leading to a quick reduction in peak force (6.4%
over the first 10 cycles) before they begin to stabilize (12.4%
decrease over 200 cycles). Unlike the active tendons madefrom Eco-Flex 30, the passive tendons made from DragonSkin
20 exhibit noticeable mechanical hysteresis.

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Fig. 3. The cyclic testing results of one active tendon over 400 cycles and one passive tendon over 200 cycles are shown above as a function of engineeringstrain and below as a function of cycle count. Capacitance is linear and highly repeatable for both sensors. Passive tendons exhibit a 12.4% decrease in force
over 200 cycles and notable mechanical hysteresis. The peak force of the active tendons decreases by just 7.5% over 400 cycles.

corresponding to the lengths they were designed to have in theresting configuration of a tensegrity robot. The capacitanceand force of each sensor was measured once per day for
one week, and the results are shown in Figure 4. Of theseven active tendons tested, three broke due to the clamping
mechanism; only the sensors that lasted all seven days areshown. None of the three passive tendons tested failed during
the week of testing. The capacitance of both types of sensors
remained stable after one week as did the force of the activetendons. The slight variations in capacitance measurements
may have been the result of re-clamping the sensors at slightly
different lengths in between force measurements. On average,
the passive tendons show a 1.25 N (8%) decrease in force
over the first day before beginning to decrease more gradually(16.6% over seven days).
IV. C ONCLUSION

Fig. 4. Active and passive sensor tendons were held in tension at 240% strain
and 110% strain, respectively, for seven days. Error bars for the active andpassive tendons represent the range of four and three samples, respectively.

C. Relaxation Experiments
Before the relaxation experiments, active tendons were precycled five times to a length of 165 mm (240% strain) andpassive tendons five times to a length of 250 mm (110%strain). Then, the sensor tendons were clamped to a 0.25”
acrylic frame at the respective 165 mm and 250 mm lengths,

We present the design and facile fabrication of highly
stretchable sensor tendons and characterize their effectivenessas sensors for soft robot proprioception. The sensors survive
high strains, so they are advantageous for soft robots thatexperience large deformations. Their electrical response isstable and repeatable after many actuation cycles and long time
periods in tension, making them highly reliable sensors for
robot state estimation and feedback control. The mechanicalstiffness of the passive tendons decreases with cyclic loadingor after a few days under constant tension. When used as therestoring springs on tensegrity robots, they will have to bereplaced every few days or designed to be stiffer than needed
such that they will remain strong enough after their initial
relaxation. Future work will demonstrate these sensor tendons
estimating the shape of a tensegrity robot in real time.

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R EFERENCES[1] D. Rus and M. T. Tolley, “Design, fabrication and control of soft robots,”
Nature, vol. 521, no. 7553, pp. 467–475, 2015.
[2] H. Wang, M. Totaro, and L. Beccai, “Toward perceptive soft robots:Progress and challenges,” Advanced Science, vol. 5, no. 9, p. 1800541,
2018.
[3] J. Shintake, E. Piskarev, S. H. Jeong, and D. Floreano, “Ultrastretchable strain sensors using carbon black-filled elastomer composites andcomparison of capacitive versus resistive sensors,” Advanced Materials
Technologies, vol. 3, no. 3, p. 1700284, 2018.
[4] C. Larson, B. Peele, S. Li, S. Robinson, M. Totaro, L. Beccai, B. Mazzolai, and R. Shepherd, “Highly stretchable electroluminescent skin for
optical signaling and tactile sensing,” Science, vol. 351, no. 6277, pp.
1071–1074, 2016.
[5] D. Hughes and N. Correll, “A soft, amorphous skin that can sense andlocalize textures,” in 2014 IEEE International Conference on Robotics
and Automation (ICRA). IEEE, 2014, pp. 1844–1851.
[6] Y.-L. Park, B.-r. Chen, and R. J. Wood, “Soft artificial skin with multimodal sensing capability using embedded liquid conductors,” in 2011
IEEE SENSORS. IEEE, 2011, pp. 81–84.
[7] D. M. Vogt, Y.-L. Park, and R. J. Wood, “Design and characterizationof a soft multi-axis force sensor using embedded microfluidic channels,”IEEE Sensors Journal, vol. 13, no. 10, pp. 4056–4064, 2013.
[8] S. Konishi and A. Hirata, “Flexible temperature sensor integrated with
soft pneumatic microactuators for functional microfingers,” Scientific
Reports, vol. 9, no. 1, pp. 1–9, 2019.
[9] I. Van Meerbeek, C. De Sa, and R. Shepherd, “Soft optoelectronicsensory foams with proprioception,” Science Robotics, vol. 3, no. 24,p. eaau2489, 2018.
[10] M. Vespignani, J. M. Friesen, V. SunSpiral, and J. Bruce, “Design ofSUPERball v2, a Compliant Tensegrity Robot for Absorbing Large
Impacts,” in 2018 IEEE/RSJ International Conference on Intelligent
Robots and Systems (IROS), Oct. 2018, pp. 2865–2871.
[11] D. S. Shah, J. W. Booth, M. Vespignani, K. Bekris, R. Kramer-Bottiglio
et al., “Tensegrity robotics,” Soft Robotics, vol. 9, no. 4, pp. 639–656,2022.
[12] J. W. Booth, O. Cyr-Choiniere, J. C. Case, D. Shah, M. C. Yuen,
and R. Kramer-Bottiglio, “Surface actuation and sensing of a tensegrity
structure using robotic skins,” Soft Robotics, vol. 8, no. 5, pp. 531–541,2021.
[13] W.-Y. Li, A. Takata, H. Nabae, G. Endo, and K. Suzumori, “Shaperecognition of a tensegrity with soft sensor threads and artificial muscles
using a recurrent neural network,” IEEE Robotics and Automation
Letters, vol. 6, no. 4, pp. 6228–6234, 2021.
[14] A. P. Sabelhaus, J. Bruce, K. Caluwaerts, P. Manovi, R. F. Firoozi,
S. Dobi, A. M. Agogino, and V. SunSpiral, “System design andlocomotion of superball, an untethered tensegrity robot,” in 2015 IEEE
international conference on robotics and automation (ICRA). IEEE,
2015, pp. 2867–2873.
[15] X. Wang, L. Fan, J. Zhang, X. Sun, H. Chang, B. Yuan, R. Guo,
M. Duan, and J. Liu, “Printed conformable liquid metal e-skin-enabled
spatiotemporally controlled bioelectromagnetics for wireless multisite
tumor therapy,” Advanced Functional Materials, vol. 29, no. 51, p.
1907063, 2019.
[16] W. Kong, N. U. H. Shah, T. V. Neumann, M. H. Vong, P. Kotagama,
M. D. Dickey, R. Y. Wang, and K. Rykaczewski, “Oxide-mediatedmechanisms of gallium foam generation and stabilization during shear
mixing in air,” Soft Matter, vol. 16, no. 25, pp. 5801–5805, 2020.
[17] W. R. Johnson, J. Booth, and R. Kramer-Bottiglio, “Integrated sensing
in robotic skin modules,” in 2021 IEEE Sensors. IEEE, pp. 1–4.
[18] L. Mullins, “Softening of rubber by deformation,” Rubber chemistry andtechnology, vol. 42, no. 1, pp. 339–362, 1969.

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