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Thermotropic Vine-inspired Robots
Shivani Deglurkar1∗, Charles Xiao1∗, Luke Gockowski1, Megan T. Valentine1, and Elliot W. Hawkes1
Abstract—Soft and bio-inspired robotics promise to imbue
robots with capabilities found in the natural world. However,
many of these biological capabilities are yet to be realized. For
example, current vine- and root-inspired everting robots rely on
centralized control outside of the robotic tendril to process sensor
information and command actuation. In contrast, roots in nature
control growth direction in a distributed manner, with all control,
sensing, and actuation local. Such distributed control is useful
for robustness and parallelization particularly while the plants
search for resources (light, water, favorable soil, etc.). Here we
present an approach for exploiting these biological behaviors via a
thermotropic vine-inspired robot; the device uses local, material-
level sensing, actuation, and control embedded in its skin to
grow toward a source of heat. We present basic modeling of
the concept, design details, and experimental results showing its
behavior in varied heat fields. Our simple device advances vine-
inspired everting robots by offering a new, distributed method
of shape control, and could lead to eventual applications such as
highly parallelized robots for fire-fighting or search-and-rescue
operations.
I. INTRODUCTION
Over the past decades, bio-inspired robotics and then soft
robotics have gained interest [1], owing partly to their ability
to easily adapt to changing environments without complex
mechanisms. Vine-inspired everting robots, or “vine robots,”
are a class of soft robot made of an inverted, flexible, thin-
walled pneumatic tube that everts when pressurized, length-
ening from its tip [2], [3], [4], [5], [6], [7]. Because this
lengthening involves no relative movement of the body with
respect to the environment, the robot can reliably extend
through constrained environments, even when the properties
of the path and obstacles are unknown.
Current control schemes for vine robots are centralized,
relying on sensor data processed by either human operators
or an autonomous computer controller to steer towards a tar-
get. For human-controlled teleoperation, the operator receives
information from the sensors, decides on the control scheme,
and sends the appropriate signal(s) to the robot (e.g., [8]). For
autonomous control, computer vision can be implemented to
parse a scene and direct the robot to a pre-determined target
(e.g., [7]). Another method of centralized control scheme uses
tropisms, or directed motility along a gradient [9]. Tropisms
have been demonstrated in a plant-inspired robot with em-
bedded sensing capabilities and a sensorized root-inspired
centralized control algorithm [10].
This work was supported in part by NSF Grants CMMI-1944816 and
EFMA-1935327. The work of C. Xiao was supported by the NSF Graduate
Research Fellowship Program.
1Department of Mechanical Engineering, University of California, Santa
Barbara, CA 93106.
∗Equal contribution. Emails: shivani deglurkar@ucsb.edu,
charles xiao@ucsb.edu
Fig. 1. A: Schematic of thermotropic vine-inspired robot concept. B:
Realization of the concept: a pneumatic everting robot grows forward and
toward the right where the heat source is located. Image taken with an IR
camera.
While such centralized control is useful when a single robot
is employed, it has limitations when many robots are needed,
for example, to run a large-scale parallelized search of a space.
A human operator simply cannot control dozens of robots
simultaneously, and a centralized autonomous system grows
unfeasibly complex (wiring, valving and pumps for actuators,
etc.) and increasingly expensive as the central base of the robot
controls a larger and larger number of “tendrils.”
Distributed control [11] is a different paradigm that has
the potential to address these challenges, and a version of it
is found in biological vines and roots [12]. In these natural
systems, growth is directed by environmental cues sensed by
each individual vine or root without any central processing.
For root systems, hundreds or even thousands of individual
roots can simultaneously steer. Further, if some of the vines
or roots are damaged or removed, the others remain fully
functional. In robotics, swarms and collectives demonstrate
effective use of distributed control (e.g., [13], [14], [15]).
In practical terms, implementation of such a distributed
control scheme in a robot containing many vine-like ten-
drils, requires that the sensing-control-actuation system found
in each tendril is simple and inexpensive. Current steering
mechanisms for vine robots, including motorized pull tendons
(e.g., [16]), pneumatically-controlled latches (e.g., [7]), and
artificial muscles (e.g., [8], [17], [18]), all require electronic
arXiv:2301.07362v1 [cs.RO] 18 Jan 2023
sensing, control, and power, limiting their use in highly paral-
lelized distributed control systems. A promising alternative is
a “material-level” scheme that leverages the intrinsic materials
properties of the soft robot body. The capabilities of a number
of functional materials to sense, compute, or actuate in re-
sponse to external stimuli (such as heat, light, electromagnetic
fields, or chemical conditions) have been demonstrated [19],
[20]. Among these, thermal stimuli are particularly promising
due to the availability of phase change materials that can
undergo significant changes in properties or volume as a
function of temperature [21], [22].
In this work, we present a decentralized control method
for vine-like robots that uses material-level sensing-control-
actuation loops embedded directly in the skin to achieve
thermotropism–i.e., directed motion toward a heat source
(Figure 1). The local sensing and actuation is achieved using
the liquid-gas phase change of a low-boiling-point fluid that
is distributed along the sides of an everting robot body using
series pneumatic artificial muscles (sPAMs) [23]. The sPAMs
located on the robot side closest to the heat source will actuate
first, shortening that side of the robot, and steering it toward
the heat source. In this way, we develop the first everting robot
with distributed, material-level control.
What follows is a description of the design and fabrication
of the device, a model describing the coupled mechanical
and heat transfer effects present in heat-activated artificial
muscles, experimental characterization of sPAM actuation and
the demonstration of a heat-activated vine robot extending
towards a heat source. We conclude with a discussion of the
robot performance and next steps.
II. DEVICE DESIGN
A. Heat-activated sPAM Design
The basic concept for the actuator is based on the pleated
pneumatic artificial muscle [24], [25], which when arranged
in series, form a sPAM [23]. Increasing internal pressure
results in volumetric expansion, radial swelling, and length
contraction. Such actuators have been traditionally actuated by
pumping compressed fluid into the device using a continuous
fluid passageway, such that a single source of pressurized air
causes all pouches to inflate. This limits the possibility of
local curvature control. In contrast, we isolate the inflation of
each segment in the series by sealing it individually, thereby
enabling localized actuator response. Further, instead of using
a pneumatic pump, we fill the actuator with a low-boiling-point
fluid that vaporizes when heated, causing a local increase in
pressure and enabling local curvature control. We select Novec
7000 as a working fluid due to its low boiling point (i.e., 34 °C
at atmospheric pressure), non-toxicity, and compatibility with
a broad selection of polymer films. We use a quartz heater
(Infratech W-7512 SS) with an approximate emission peak
of 3.2 µm, although the presented design process could be
adapted for other heat sources, such as fire.
Choosing an appropriate IR absorber and designing its
placement is critical to creating a fast thermotropic actuator re-
sponse. We considered two paradigms: either using an opaque,
Fig. 2. Transmittance measurements of different materials polymeric materi-
als (solid lines, left axis). The normalized intensity of the blackbody radiation
representing the heater (dotted line, right axis) and an object held at the boiling
point of Novec 7000 (dashed line, right axis).
absorbing material for the sPAM skin, which requires heat to
be conducted to the contained fluid, or using an IR-transparent
pouch with an IR-absorber immersed in the working fluid. In
the latter case, the skin should be transparent to the primary
wavelengths of the heat source and opaque to the emissive
wavelengths of the robot’s operating temperature, to create a
greenhouse effect [26].
To select an appropriate IR-transparent plastic film, we
compared the transmittance of urethane, Mylar, and fluorinated
ethylene propylene (FEP) films (Figure 2) to the estimated
blackbody spectrum of our heater, as well as the black body
spectrum of an object at 307.15 K, which is the boiling point
of Novec 7000. Both the Mylar and FEP films show good
transmittance to the heat source wavelengths; however, Mylar
has the best durability and lowest gas permeability of the films
tested and thus was used throughout.
To test the effect of absorber configuration on response time,
we measured the time for a single pouch to transition from
fully deflated to fully inflated when fixed to a polystyrene
foam block positioned 76 cm away from the quartz heater.
Each pouch (7.0 cm ×3.7 cm) was heat sealed with equal
volumes of Novec 7000 inside. Four conditions were tested:
(A) clear Mylar pouch containing a black nonwoven microfiber
sheet (EonTex NW170-PI-20), (B) clear Mylar pouch with
the microfiber sheet adhered to the surface using double-
sided tape, (C) aluminized Mylar pouch with a microfiber
sheet adhered to its surface, (D) aluminized Mylar pouch with
the surface coated with matte black spraypaint (Krylon Ultra
Flat Camouflage). The response times of A, B, C, and D
were 95, 270, 105, and 150 seconds, respectively. The fastest
configuration, clear Mylar containing an internal microfiber
sheet, was selected for robot fabrication.
B. Robot Design
The robot is composed of a central spine comprised of a
pneumatically pressurized LDPE tube (lay-flat width, 5 cm)
that provides for overall growth, flanked by two Novec 7000
filled sPAMs (Figure 1). The sPAMs are small and supple
for eversion. Left-right steering is achieved by differential
Fig. 3. Schematic of fabrication steps. A: Cut Mylar to size. B: Fold in
half, length-wise, and heat-seal. C: Place absorber into sealed pouch; inject
Novec 7000. D: Heat seal previous pouch; repeat for five pouches. E: Tie off
pouches using spectra fiber. F: Inflated pouches show contraction.
inflation of the sPAMs. The sPAM on the heat source side
experiences a significantly higher radiative flux and thus a
higher temperature, and therefore inflates (i.e., contracts) more
than the one on the opposing side. In addition, the inclusion of
the internal absorbing sheet provides a means of ”shading” the
opposing-side sPAMs and the pneumatic LDPE spine offers
insulation between the two–enhancing this differential effect.
These design choices provide built-in feedback to the steering
of the robot. As such, the robot will tend to steer towards the
light source.
III. FABRICATION
The sPAMs were constructed from a 30 cm by 9 cm rect-
angular strip of clear Mylar folded onto itself length-wise,
and heat sealed along its length. 2.5 cm from the bottom, a
perpendicular heat seal creates a chamber with a width of
4.5 cm (3A, B). Next, a 3.8 cm diameter circle of heater fabric
was slipped in from the unsealed edge until it reached a heat
sealed edge. Thereafter, 1.5 mL of Novec 7000 was injected
into the chamber, and enclosed with a heat seal 4.5 cm from
the previous heat seal (3C,D). This process was repeated to
produce 5 flat pouches in series. Finally, Spectra fiber (Power
Pro 80 lb test) was tied onto the four seals separating each
pouch and at the two ends (3E). Multiple sets of these 5-pouch
sPAMs were then adhered to opposing sides of the pressurized
LDPE spine using double-sided tape.
IV. MODELING
Modeling the robot requires coupling mechanical and heat
transfer models. All processes are assumed to be quasistatic.
A. sPAM Model
To model the behavior of the sPAMs, we turned to pre-
vious modeling work on pleated pneumatic artificial muscles
(PPAMs) [24], which behave similarly to an individual unit of
the sPAM. For a given contraction ratio, γ, the force, Fγ, that
each sPAM produces is
Fγ=πP
gr21−2m
2mcos2(φr),2r
cos(φr)<2w
π(1)
P
gis the gauge pressure inside the sPAM, ris the radius of
the constriction, wis the flat tubing width used for the sPAM,
mand φrare parameters determined from the below system
of equations.
(F(φr|m)
√mcos(φr)=l
r
E(φr|m)
√mcos(φr)=l
r(1−γ
2)(2)
Fand Eare the first and second incomplete elliptic inte-
grals, respectively. The condition on the right hand side of
Equation 1 is the zero parallel force condition [23], [24]. For
further discussion and derivation of the force model, see [23],
[24], and [25].
The gauge pressure inside the sPAM can be described by
the inextensible textile model [27].
P
g=(P
PC(T) + nair RT
V−P
atm,P
PC(T) + nair RT
V>P
atm
0,P
PC(T) + nair RT
V≤P
atm
(3)
P
PC(T),T,nair ,R,V,P
atm are the Novec 7000 vapor pressure,
absolute temperature, moles of residual air, ideal gas constant,
sPAM volume, and atmospheric pressure, respectively. The
pressure terms on the right hand side are absolute pressures.
Ideally, there is no residual air inside the sPAM.
From these two models, we expect that increasing tempera-
ture increases force produced, an inverse relationship between
force and contraction ratio, and a pressure independent zero
force contraction ratio.
B. Heat Transfer
To fully model the heat transfer of the robot requires consid-
ering the three modes of heat transfer: conduction, convection,
and radiation. Modeling the radiation exchange is particularly
challenging because the radiative heat transfer is wavelength
and configuration dependent. For a simple heat transfer model,
we assume that each component can be modeled as a diffuse
surface and that the heat transfer of each component can be
described by an effective temperature, Ti. At equilibrium, the
energy balance is
hAi(Ti−T∞) =
N
∑
j=1
AiFi j(Jj−Ji)(4)
hrepresents the combined conductive and convective loss
coefficient to the environment, Aiis the effective area of the
component, Tiis the effective temperature, T∞is the effective
environmental temperature, Fi j is the effective view factor
from element ito element j, and Jis radiosity. Note that
AiFi j =AjFji and ∑Fij =1.
Assuming the dominant heat transfer is radiative, then the
best way to increase equilibrium temperature is to maximize
light source absorption and minimize radiative losses (i.e.,
maximize Jlightsource −Ji). This can be done via selective
absorption (see Section II-A).
The biggest source of uncertainty in the model is the
effective view factor. As the robot deforms, the flux that
each component sees is expected to change due to shielding,
reflection, and re-radiation. Figure 1B shows how the robot
alters the beam pattern of the light source. The best way to
determine the effect of illumination on robot performance is
through empirical measurements.
C. Kinematics Model
In order to determine the required steering forces and
understand how temperature affects the pose of the robot, we
created a simple kinematic model of the robot.
We discretize the robot into a series of Ntrapezoidal
sections, each consisting of three springs (Figure 4). The center
spring represents the pneumatic expansion force, and the two
outer springs represent the sPAMs. We assume there are no
forces between the trapezoidal sections, because we assume
the robot is free from external contacts (i.e., on frictionless
surface). We assume the torsion forces at the interfaces are
minimal since the robot is locally buckled.
Fig. 4. A: Trapezoidal kinematic model. B: Detail of forces and key
geometry.
The force and moment balances within the i-th component
are
P
gA=fi,1(γi,1) + fi,2(γi,2)(5)
fi,1(γi,1) = fi,2(γi,2)(6)
P
gis the gauge pressure of the pneumatic backbone and Ais
the crossectional area of the backbone.
Fig. 5. Schematic showing an image the temperature-controlled experimental
setup, with sPAM position indicated by red dotted lines.
This model implies that fi,1(γi,1) = f2(γi,2) = P
gA/2. The
i-th angle can be determined from the relation
l0(1−γi,2) + d
tan(θi−1)+d
tan(θi)=l0(1−γi,1)(7)
l0is the free length of the section and drepresents the width
spacing between the two sPAMs. For simplicity, we assume
this value is constant. To initialize the problem, we assume
θ0=π/2.
The coordinates of the points on the 1 side (e.g., heater side)
of the robot are:
yi,1=
i
∑
j=1l1,icos
i−1
∑
k=0
(π−2θk)(8)
xi,1=
i
∑
j=1l1,isin
i−1
∑
k=0
(π−2θk)(9)
A similar expression can be derived for the 2 side of the robot.
This model tells us that at equilibrium the force exerted
by each sPAM is independent of temperature and depends
solely on the pressure of the robot’s spine. However, the
exact strain state (i.e., γ) requires temperature information.
Interestingly, this model suggests that such a robot can be
used for thermometry applications. By knowing the pose
of the robot and the spine pressure, we can determine the
temperatures seen by the robot, because at constant force each
strain state corresponds to a unique temperature.
V. EX PE RI ME NTAL RE SU LTS
Heat transfer in radiative systems is often environmen-
tally and configurationally dependent. To characterize the
performance of our actuators, we varied the strain on the
actuator and measured the corresponding force under different
environmental conditions. We first tested them in a constant-
temperature environment (Figure 5) before testing them in a
relatively uncontrolled environment (lab space) under different
illumination conditions (Figures 8,7). For each actuation test,
we used sPAMs comprised of five pouches to minimize the
effects of any potential manufacturing variations in a single
pouch.
Fig. 6. Force vs. contraction ratios for different temperatures.
Fig. 7. A: Flux as a function of distance. The circles are the experimentally
measured points and the solid line is an exponential fit to the data. B: IR
image of the heat source on a polystyrene foam floor. The contours represent
isotherms, which we interpret as isoflux lines.
A. Force vs. Contraction Ratio at Fixed Temperatures
For this test, a sPAM was placed in a temperature controlled
box, and suspended by two pieces of Spectra fiber. One end
of the fiber was pinned and the other was attached to a
force gauge (Mark-10 M3-5) on a translating stage (Figure
5). To find the free length of the actuator, we translated the
linear stage at room temperature (∼20 °C) until the sPAM
transitioned from slack (0 N) to slightly tensioned (2.8 N). The
contraction ratio was varied by translating the linear stage to
differing positions. Figure 6 shows the force-contraction ratio
relations produced by the sPAMs at two different temperatures.
As predicted, force increases with temperature and varies
inversely with contraction ratio, and the zero force contraction
ratios are nearly the same.
B. Contraction Ratio vs. Flux at Fixed Force Level
The second set of tests measured the contraction ratio at
different flux levels and a predetermined force level.
We estimated the flux experienced by the robot by mea-
suring the equilibrium temperature, Tplate , of a black-painted
aluminum plate (∼1.6 cm ×1.6 cm). The center of plate
was placed 2 cm above the polystyrene floor, which is
approximately level with sPAMs on the robot. For simplicity,
we assume the plate is a blackbody and use a vertical flat
plate convection model [26] to estimate the flux as: Qlight =
σT4
plate −h(Tpl ate −Tamb). As expected, the flux roughly obeys
the inverse square law. Using IR imaging (FLIR E60) we
Fig. 8. Image of heat flux testing setup.
determined spatial distribution of heat around the lamp and
found good agreement with the model (Figure 7).
To measure contraction ratio versus flux, we used a similar
test setup as above, except now heat was provided by a
quartz heater with no enclosure (Figure 8). The sPAM was
backed with a 5 cm diameter LDPE tubing to simulate the heat
transfer effects of the central spine. In each test, the system
was equilibrated for 12 minutes to reach steady state and
the screw displacement required to produce 5 N of force was
measured. This allowed the contraction ratios to be measured
as a function of distance and flux (Figure 9), where the flux
values were derived from the fitted curve in Figure 7A.
At low flux values, the required contraction ratio varies
nearly linearly with flux, then saturates at higher flux values to
an upper limit that is determined by the pressure-independent
zero force contraction ratio. Thus higher fluxes, which result in
higher equilibrium temperatures and pressures, cannot increase
contraction ratios indefinitely.
Fig. 9. Contraction ratios required to achieve 5 N of force as a function of
(A) distance and (B) flux.
C. Kinematic Model Verification
We tested the kinematic model by comparing the predicted
deformation of a short section of a 5-pouch robot to the
experimentally-determined values (Figure 10). With respect to
the center of the sPAM on the heater side, the robot was placed
55 cm away from the heater. The center body was inflated to
about 12 kPa, so that the required deformation force is 5 N. To
estimate the contraction ratio at this distance, we interpolated
Fig. 10. Model verification on a section of robot. The predicted shape is
drawn in orange. Inset shows the infrared image of a similar test setup.
the data presented in Figure 9A to find γ=0.163. Setting l0=
4.1 cm, d=5.0 cm, and θ0=π/2, we computed the expected
sPAM shape. When the computed shape is overlaid on the
experimental image, there is good agreement, validating the
utility of the model. In this approach, the sPAM positioned
away from the heater is assumed to be sufficiently insulated
that γ=0, while the sPAM on the heater side is uniformly
illuminated, which is consistent with infrared imaging results
of a similar test (inset). We attribute the small discrepancies to
unmodeled dimensional variations in the constructed sPAMs
and heat transfer to the antagonistic side. It is possible that the
changes in view factors and flux as the robot deforms, which
are assumed to be small, also contribute to some extent.
D. Demonstration
We demonstrate the robot growing via internal pressure and
steering with the heat-sensing sPAMs to find the heat source
in three different scenarios. Figure 11A shows that the robot
can find the heat source even if it is initially growing away
from it. Figure 11B and C shows the robot navigating around
simple obstacles. It is possible to increase the steering speed by
placing the robot closer to the heat source (∼35 cm), as shown
in Figure 12 where ∼90 s reorientation times are achieved.
Notably, in this case, we demonstrate the turning process
without eversion. Since the robot is significantly stiffer when
there are sPAMs inside the spine, a higher actuation force is
required, which takes longer to achieve.
VI. CONCLUSIONS AND FUTURE WORK
This work demonstrates the design, testing, modeling, and
deployment of a heat-sensing vine-inspired robot capable of
autonomous thermotropic motion. The robot makes use of
a central pneumatically-pressurized spine for support and to
drive eversion, while all sensing, control and actuation is
achieved locally at a material level without central control or
human intervention. We present models of the mechanical and
heat transfer properties of the robot with sufficient resolution
Fig. 11. Demonstrations of thermotropic eversion in unknown environments
(obstacles outlined). In this timeseries, the heat source is visible at the middle
right of each image. A: Eversion towards heater from behind. Here the vine-
robot emerges from the lower right corner, with no discernable curvature along
the body. As the tip grows further, the sPAMs actuate asymmetrically under
thermal activation, bending and growing in a curved path toward the heat
source. B: Eversion between two styrofoam barriers , which provide thermal
shielding and define the growth path. C: Eversion through a simple styrofoam
maze toward the heat source.
Fig. 12. The robot can steer towards the heat source within 90 s
to describe the robot’s kinematic response to an external
heat source. These models are validated through experimental
analysis of heat-activated sPAMs, which are then incorporated
into a soft robot capable of heat-sensing and thermotropic
motion in unknown environments.
In the current iteration, the response of the robot is relatively
slow. A heat source, such as a fire, would have much higher
heat flux at equivalent or even greater distances, resulting in
much faster response times. Materials with higher melting
temperatures would need to be used in such cases. Another
possible variation of the proposed design is to use carbon
dioxide as the working fluid. Carbon dioxide absorbs strongly
at the wavelengths emitted by fire, meaning the robot could
selectively sense fire rather than other hot objects [28].
Overall, this demonstration represents a significant step
forward in our understanding of how to incorporate material-
level sensing and actuation into vine-inspired robots and soft
robots generally. Future robots that build on the presented
concepts could provide enhanced capabilities in search and
rescue and firefighting applications.
VII. ACKN OWLEDGEMENTS
We thank Professor Michael Gordon’s research group for
performing the transmittance measurements in Figure 2, and
David Haggerty for his editing help.
REFERENCES
[1] E. W. Hawkes, C. Majidi, and M. T. Tolley, “Hard questions for soft
robotics,” Science robotics, vol. 6, no. 53, p. eabg6049, 2021.
[2] D. Mishima, T. Aoki, and S. Hirose, “Development of pneumatically
controlled expandable arm for search in the environment with tight
access,” in Field and Service Robotics. Springer, 2003, pp. 509–518.
[3] T. Viebach, F. Pauker, G. Buchmann, G. Weiglhofer, and R. Pauker, “Ev-
erting sleeve system,” Patent, July 5, 2006, european Patent 1676598A2.
[4] H. Tsukagoshi, N. Arai, I. Kiryu, and A. Kitagawa, “Smooth creep-
ing actuator by tip growth movement aiming for search and rescue
operation,” in 2011 IEEE International Conference on Robotics and
Automation. IEEE, 2011, pp. 1720–1725.
[5] ——, “Tip growing actuator with the hose-like structure aiming for
inspection on narrow terrain,” IJAT, vol. 5, no. 4, pp. 516–522, 2011.
[6] A. Sadeghi, A. Tonazzini, L. Popova, and B. Mazzolai, “Robotic
mechanism for soil penetration inspired by plant root,” in 2013 IEEE
International Conference on Robotics and Automation. IEEE, 2013,
pp. 3457–3462.
[7] E. W. Hawkes, L. H. Blumenschein, J. D. Greer, and A. M. Okamura,
“A soft robot that navigates its environment through growth,” Science
Robotics, vol. 2, no. 8, p. eaan3028, 2017.
[8] M. M. Coad, L. H. Blumenschein, S. Cutler, J. A. R. Zepeda, N. D.
Naclerio, H. El-Hussieny, U. Mehmood, J. Ryu, E. W. Hawkes, and
A. M. Okamura, “Vine robots: Design, teleoperation, and deployment
for navigation and exploration,” in preparation.
[9] B. Mazzolai, “Growth and tropism,” Living Machines: A Handbook of
Research in Biomimetics and Biohybrid Systems; Prescott, TJ, Lepora,
N., Verschure, PFMJ, Eds, pp. 99–104, 2018.
[10] A. Sadeghi, A. Mondini, E. Del Dottore, V. Mattoli, L. Beccai, S. Tac-
cola, C. Lucarotti, M. Totaro, and B. Mazzolai, “A plant-inspired robot
with soft differential bending capabilities,” Bioinspiration & biomimet-
ics, vol. 12, no. 1, p. 015001, 2016.
[11] F. Bullo, J. Cort´
es, and S. Martinez, Distributed control of robotic
networks. Princeton University Press, 2009.
[12] B. Forde and H. Lorenzo, “The nutritional control of root development,”
Plant and soil, vol. 232, no. 1, pp. 51–68, 2001.
[13] V. Krishnan and S. Martinez, “Distributed control for spatial self-
organization of multi-agent swarms,” SIAM Journal on Control and
Optimization, vol. 56, no. 5, pp. 3642–3667, 2018.
[14] S. Bandyopadhyay, S.-J. Chung, and F. Y. Hadaegh, “Probabilistic and
distributed control of a large-scale swarm of autonomous agents,” IEEE
Transactions on Robotics, vol. 33, no. 5, pp. 1103–1123, 2017.
[15] H. Yamaguchi, T. Arai, and G. Beni, “A distributed control scheme
for multiple robotic vehicles to make group formations,” Robotics and
Autonomous systems, vol. 36, no. 4, pp. 125–147, 2001.
[16] S. Wang, R. Zhang, D. A. Haggerty, N. D. Naclerio, and E. W. Hawkes,
“A dexterous tip-extending robot with variable-length shape-locking,”
in 2020 IEEE International Conference on Robotics and Automation
(ICRA). IEEE, 2020, pp. 9035–9041.
[17] J. D. Greer, T. K. Morimoto, A. M. Okamura, and E. W. Hawkes, “A soft,
steerable continuum robot that grows via tip extension,” Soft robotics,
2018.
[18] M. Selvaggio, L. Ramirez, N. D. Naclerio, B. Siciliano, and E. W.
Hawkes, “An obstacle-interaction planning method for navigation of ac-
tuated vine robots,” in 2020 IEEE International Conference on Robotics
and Automation (ICRA). IEEE, 2020, pp. 3227–3233.
[19] Z. Shen, F. Chen, X. Zhu, K.-T. Yong, and G. Gu, “Stimuli-responsive
functional materials for soft robotics,” Journal of Materials Chemistry
B, vol. 8, no. 39, pp. 8972–8991, 2020.
[20] Y. Zhao, M. Hua, Y. Yan, S. Wu, Y. Alsaid, and X. He, “Stimuli-
responsive polymers for soft robotics,” Annual Review of Control,
Robotics, and Autonomous Systems, vol. 5, 2021.
[21] J. Han, W. Jiang, D. Niu, Y. Li, Y. Zhang, B. Lei, H. Liu, Y. Shi,
B. Chen, L. Yin, et al., “Untethered soft actuators by liquid–vapor phase
transition: remote and programmable actuation,” Advanced Intelligent
Systems, vol. 1, no. 8, p. 1900109, 2019.
[22] S. M. Mirvakili, A. Leroy, D. Sim, and E. N. Wang, “Solar-driven soft
robots,” Advanced Science, vol. 8, no. 8, p. 2004235, 2021.
[23] J. D. Greer, T. K. Morimoto, A. M. Okamura, and E. W. Hawkes,
“Series pneumatic artificial muscles (spams) and application to a soft
continuum robot,” in 2017 IEEE International Conference on Robotics
and Automation (ICRA). IEEE, 2017, pp. 5503–5510.
[24] F. Daerden and D. Lefeber, “The concept and design of pleated pneu-
matic artificial muscles,” International Journal of Fluid Power, vol. 2,
no. 3, pp. 41–50, 2001.
[25] F. Daerden, “Conception and realization of pleated pneumatic artificial
muscles and their use as compliant actuation elements,” Vrije Univer-
siteit Brussel, p. 176, 1999.
[26] T. L. Bergman, F. P. Incropera, D. P. DeWitt, and A. S. Lavine,
Fundamentals of heat and mass transfer. John Wiley & Sons, 2011.
[27] V. Sanchez, C. J. Payne, D. J. Preston, J. T. Alvarez, J. C. Weaver, A. T.
Atalay, M. Boyvat, D. M. Vogt, R. J. Wood, G. M. Whitesides, et al.,
“Smart thermally actuating textiles,” Advanced Materials Technologies,
vol. 5, no. 8, p. 2000383, 2020.
[28] R. Linares, G. Vergara, R. Guti´
errez, C. Fern´
andez, V. Villamayor,
L. G´
omez, M. Gonz´
alez-Camino, and A. Baldasano, “Gas and flame
detection and identification using uncooled mwir imaging sensors,” in
Thermosense: Thermal Infrared Applications XXXVII, vol. 9485. SPIE,
2015, pp. 385–390.