Adv Materials Technologies - 2018 - Majidi - Soft‐Matter Engineering for Soft Robotics.pdf

PROGRESS REPORT
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Soft-Matter Engineering for Soft Robotics
Carmel Majidi
DOI: 10.1002/admt.201800477
and data-driven learning. In this respect,
existing materials and hardware technolo-
gies are good enough and do not represent
a crucial bottleneck for further progress
within current application domains.
So why the recent interest in soft
robotics and the sudden need to create
machines and electronics using elasto-
mers, fluids, and other soft matter? After
all, rigid materials have a variety of proper-
ties that make them well-suited for actua-
tion, sensing, signal processing, and robot
housing/packaging. In particular, the stiff
plastics, composites, metals, and ceramics
used for structural reinforcement, pack-
aging, motors, and printed circuit boards
(PCBs) exhibit the following advantages:
(i) highly load bearing and can support
large mechanical work or large inertial
forces; (ii) can maintain fixed mechanical
or electrical properties under extreme
forces; (iii) enable precision positioning
and motion control by rigidly transmitting
displacements. So why, then, replace these with materials that
have poor load capacity and for which it is difficult to precisely
control their motion and geometry?
The reason to engineer robots out of soft matter arises from
another fundamental aim within the field of robotics—creating
universal and customizable machines that are capable of per-
forming a wide variety of tasks and actively adapting themselves
to changing conditions within these tasks. While industrial
arms, surgical robots, and autonomous vehicles can perform
prescribed tasks with extraordinary precision, speed, or reli-
ability, they are not capable of adapting to other tasks (e.g.,
from precision manipulation to heavy-duty parts assembly) or
operating in fully unstructured environments (e.g., from a flat
paved road to a rocky mountainside). In contrast, natural organ-
isms present a proof-by-existence that it is possible to create
machines that are not only high performing, but also universal
and customizable. Within the field of soft robotics, cephalopods
like the octopus are an especially popular example due to its
astonishing ability to move in tightly confined spaces, manipu-
late objects, and camouflage itself through changes in shape,
color, and surface texture.[1]
While there are many factors that
contribute to the rich versatility and multifunctionality of nat-
ural organisms, the use of soft materials has a central role in
their ability to change their shape or how load is distributed so
that they can adapt to new tasks or changing environmental
conditions. More broadly, soft robots could help span the gap
between the high performance but specialized functionality of
conventional machines with the remarkable versatility of bio-
logical organisms (Figure 1A).
Since its inception, the field of robotics has aimed to create machines that
mimic the extraordinary capabilities of the human body. From as early as
the 1940s, this has included efforts to engineer actuators and electronics
out of elastomers, textiles, and other soft materials in order to mimic the
compliance and deformability of natural biological tissue. In the decades
since, there is extraordinary progress in the subdomain of soft robotics, with
recent efforts focused on novel methods of actuation, sensing, and manu-
facturing. In this progress report, recent advancements within this field
from the perspective of materials and mechanics are highlighted. Wherever
possible, efforts in soft robotics are connected to progress in the broader
field of soft-matter engineering, which relates to the application of principles
and practices in the soft-matter sciences to create machines, electronics,
and robotic systems out of fluids, elastomers, gels, and other soft materials.
To close, the current challenges and future opportunities within the field of
robotics are briefly discussed, with special attention toward the eventual goal
of autonomous soft robots that are capable of operating without dependency
on external hardware, tethers, or manual intervention.
Prof. C. Majidi
Soft Machines Lab
Carnegie Mellon University
Pittsburgh, PA 15213, USA
E-mail: cmajidi@andrew.cmu.edu
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/admt.201800477.
Soft Robotics
1. Introduction
The field of robotics as a scientific discipline emerged in the first
half of the 20th century as an effort to create fully autonomous
machines that are able to independently move and interact
with their environment and adapt their physical operation in
response to changing conditions. In the decades since, this has
led to extraordinary advancements in industrial automation,
surgical robots, and autonomous vehicles with machines con-
structed from hydraulics, motors, and electronics for sensing,
computing, and vision. Although engineered with materials
that have vastly different properties than biological tissue, these
robotic systems are capable of matching, and in many cases
exceeding, the performance of natural organisms for prescribed
tasks in manufacturing, precision manipulation, and transporta-
tion. While there are still opportunities for improved mechan-
ical and computing hardware within these domains, much
of the current research in robotics have focused on advanced
algorithms for sensing, vision, data fusion, decision making,
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1800477 (2 of 13)
In this progress report, the author will review some of the
recent advancements in soft robotics and describe some of
the open challenges that remain. As necessary, the author will
relate efforts within this subdomain to the emerging field of
soft-matter engineering. Soft-matter engineering represents
the practice of creating machines, electronics, and multifunc-
tional structures primarily out of soft materials and fluids
using principles and practices in polymer chemistry, condensed
soft-matter physics, soft lithography, and soft microfluidics
(Figure 1B). In this respect, many of the material technologies
used to create the artificial muscle, nervous tissue, and skin
used for soft robots fall within the domain of soft-matter engi-
neering since they are largely composed of elastomers, fluids,
and gels. In this report, the author will dedicate particular focus
on efforts toward autonomous soft robots that do not rely on
manual intervention or tethered hardware. Untethered soft
robots, unleashed from the constraints of bulky external hard-
ware, represent a necessary step toward the ultimate goal of
fully autonomous machines capable of independent mobility
and physical interaction with the environment.[4]
Before reviewing progress in untethered soft robots, the
author will begin by presenting a working definition of what a
robot is (Section 1.1). This will be helpful in evaluating current
trends and guiding future efforts within the subdomain of soft
robotics. Next, the author will highlight some of the features of
natural organisms, in particular soft organisms and biological
tissue, that are not present in conventional robotic systems and
hardware (Section 1.2). The purpose of this is to motivate the
need to revisit the materials and hardware architectures used in
robotics. Finally, the author will define what is meant by soft and
explain how the use of soft materials could enable machines to
become more universal and customizable. The remainder of the
progress report will explore current practices in soft robotics and
relate these to the ultimate goal of untethered, autonomous soft
robots that can match the robust mechanical properties, versa-
tility, multifunctionality, and adaptability of natural organisms.
This will begin with a discussion of relevant materials (Section 2),
including elastomers (2.1), polymer composites (2.2), fluids (2.3),
gels (2.4), and liquid metal (LM) embedded elastomer (LMEE)
composites (2.5). Next, the author will review various material
Carmel Majidi is the Adamson
Career Development
Professor of mechanical
engineering at Carnegie
Mellon University. He leads
the Soft Machines Lab, which
is a multidisciplinary research
group developing materials,
hardware architectures, and
fabrication methods that
enable robots and machines
to be mechanically compliant,
elastically deformable, and safe for physical interaction
with humans. Dr. Majidi is also active in the Pittsburgh
entrepreneurial community and is currently working
with local startups to commercialize some of his lab’s
research. Prior to joining Carnegie Mellon, Dr. Majidi was a
postdoctoral fellow at Princeton and Harvard Universities
and earned his Ph.D. at UC Berkeley, where he worked in
the domain of bioinspired engineering.
architectures for artificial muscle actuation (Section 3), with spe-
cial focus on fluidic actuators (3.1), dielectric elastomers (DE)
(3.2), and thermally responsive materials (3.3). This is followed
by an overview of current efforts in systems-level soft robotic
implementations as well as a brief discussion on remaining chal-
lenges and opportunities for future research (Section 4).
1.1. Robots: A Working Definition
Definitions of the term robot vary widely and have been used to
describe a broad range of systems, from complex anthropomor-
phic machines like the Honda Asimo and Boston Dynamics
Atlas to air-filled rubber structures that move or grip objects
when pneumatically actuated. For the purposes of this pro-
gress report, the author will adopt the following definition of a
Figure 1. A) Soft bioinspired robots have the potential to bridge the gap between conventional machines and natural organisms in balancing per-
formance with task specialization. B) Soft-matter engineering represents the applications of condensed soft-matter physics, polymer chemistry, and
lithography to applications in soft robotics (reproduced with permission.[2] Copyright 2016, Nature Publishing Group) and stretchable electronics
(reproduced with permission.[3] Copyright 2018, Springer Nature).

© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1800477 (3 of 13)
robot adapted from Peter Corke in his book Robotics, Vision and
Control:[5] a robot is a machine capable of
Sensing—gather information from its environment or about
its own physical state;
Planning—use this information to generate decisions on
how to change its state or act on its environment;
Action—perform a physical task based on its decision.
While these conditions are necessary, they are not sufficient,
for example, many household appliances now have embedded
sensors and CPUs that enable the above capabilities, but few
would regard these as robots. It should be noted that many
would add programmability to the set of conditions. The author
has left this out since the notion of machine programmability
can be vague. While the concept of digital programmability, that
is, coded script with commands or rules uploaded to a micro-
controller, is unambiguous, it is less clear how to define pro-
grammability in the context of materials selection, mechanical
design, and structure. For example, a mechanical system can
have prescribed motions, stiffnesses, and resonant frequencies/
modes that can be programmed with reconfigurable linkages,
cams, or weights. Likewise, a microstructured material can be
patterned and actively reconfigured to program certain elastic,
tribological, or photonic properties.
Although the definition of what makes a machine a robot
can be further restricted, it can also be relaxed. Within the soft
robotics community, there are many examples of robots that are
not capable of sensing, decision making, or varying their physical
motion. Most of these robots use open-loop control and are often
limited to a single degree of freedom or single repetitive motion.
While it may be reasonable to think of these as robots, there is a
danger in broadening the definition too widely to the point that it
has not scientific meaning, that is, “if everything is a robot, then
nothing is a robot.” On the other hand, creating restrictive defini-
tions within a continuously evolving field may create unneces-
sary, artificial barriers that could cut out meaningful innovation.
Therefore, rather than judging whether a machine should or
should not be called a robot, it may be more meaningful to ask
what scientific lesson is learned from a given implementation
and whether it can be used to inform future practices in robotics.
1.2. Why Bioinspired?
Existing robotic systems can be engineered to match or outper-
form natural organisms for specialized mobility and manipu-
lation tasks. However, there is no single machine that comes
close to matching the versatility of animals in their ability to
adequately perform a wide range of tasks. This dichotomy has
led to the emergence of bionics to create humanoid robots,
robotic prostheses, artificial muscle, electronic skin, soft multi-
functional materials, and other technologies inspired by natural
organisms and biological tissue. Such efforts in bioinspired
design are based on the recognition that nature has solutions
to problems that we are still struggling to solve using existing
engineering methods. Indeed, nature has been a rich source of
inspiration to create robotic systems or materials with a com-
bination of properties not previously possible in engineered
systems. A popular example has been the gecko lizard, which
has inspired wall-climbing robots like the Stickybot[6]
and the
development of dry adhesives that mimic the setal arrays of
Anolis lizards in their ability to exhibit shear-controlled adhe-
sion[7] (Figure 2A).
Bioinspired engineering provides one potential roadmap,
but by no means represents the only approach for creating
robotic systems that are universal and customizable. None-
theless, while alternative design paradigms may eventually
emerge, they will likely incorporate many of the same princi-
ples observed in natural systems:
(i)
Choice of material and material geometry matter—the stiff-
ness and dimensions of a material will determine its load
capacity, deformation, and how stress is internally distrib-
uted (Figure 2B);
(ii)
Integrating materials with different stiffnesses can allow
systems to adapt their shape and internal stress distribu-
tion to support a wide range of loading conditions and geo-
metric constraints;
(iii)
Hierarchical gradations between soft and stiff materials can
help with translating the effects of physics at the nanoscale
to mechanics and motion at the mesoscale. An example of
this is the human musculoskeletal system, which uses a
combination of muscle fiber, tendons, and bone to translate
chemically driven interactions between actin and myosin
filaments into human motor tasks (Figure 2C).
In all these cases, the ability to incorporate soft and elastic
materials into the robotic system is crucial. Without these, the
system will not be capable of adapting its shape, stiffness, or
internal load distribution for accomplishing new tasks or to
accommodate changes in environmental conditions.
Of course, it is natural to question why it would be better
to have one universal machine capable of all tasks rather than
having a collection of specialized machines dedicated to each
task. After all, modern households are full of appliances that
cover a wide range of tasks and it is not obvious why it would
be useful to replace these with a single device. However, the
conditions within a household are largely known and static. In
contrast, applications of robotics to field exploration, healthcare,
and human–machine interaction typically require physical inter-
action in unknown or changing environments. Moreover, as the
demands for robotic automation and machine assistance con-
tinue to increase, these systems will be exposed to a wider range
of scenarios where it is not always known a priori what the robot
is supposed to do or how it is meant to respond. An example
could be a healthcare robot that is capable of giving immediate
aid to a patient who experienced an unexpected fall during a rou-
tine activity. With a collection of specialized machines, the patient
might not get the necessary aid because only a certain number of
preselected devices might be on hand at any given time.
Another context in which it may make sense to replace a col-
lection of specialized machines with a single bioinspired robot
is in resource- or space-limited environments. These include
the International Space Station (ISS), sea vessels, aircraft, and
remote field operations. In the case of ISS, the need to cut down
on collections of specialized tools, equipment, and machines
has led to interests in 3D printers and humanoid robots like the
Robonaut.[8]
Similarly, the military has long expressed interest
in programmable matter in which a single volume of material
can reconfigure itself into various tools, for example, a clay-like

© 2018 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim
1800477 (4 of 13)
material that can reversibly transform itself from a screwdriver
to a pair of pliers. Even in the household, there is a prolifera-
tion of appliances and Internet of Things (IoT) technologies
designed to further improve quality of life through automa-
tion. This could eventually result in the need for multitasking
humanoids or healthcare robots that would replace these spe-
cialized technologies.
1.3. Why Soft?
To date, much of the effort in bioinspired robotics have focused
on piecewise-rigid systems composed of motors, PCBs, and
semirigid plastics, carbon-fiber composites, or cardboard.
These robots are able to walk, crawl, fly, and swim in a manner
similar to natural organisms without reliance on soft or highly
deformable materials. Given the success of bioinspired robotics
with rigid and semirigid materials, why bother to create soft
robots?
Despite promising achievements in the field of bioinspired
robotics, there are still several critical issues that can only be
addressed by using soft materials:
• Mobility in confined spaces—Semirigid robots can have ad-
equate compliance to collapse their shape through folding or
bending. However, they are limited in their ability to squeeze
and move through tightly confined spaces. In contrast, soft
robots can passively deform in order to adapt to the shape of
their surroundings.[9,10]
• Impact resistance—When subject to large loads, stiffer mate-
rials tend to generate high stress concentrations that can lead
to permanent mechanical damage. In contrast, soft materi-
als use their compliance and deformability to distribute loads
over a large area, allowing for uniform stress distribution and
low peak stress. Likewise, soft materials are better at absorb-
ing dynamical loads and shock.[11,12]
• Design complexity—In order to be mechanically compliant
at the device level, piecewise rigid systems require carefully
selected geometries. An example is the Softworm peristaltic
robot, which achieves compliance using a helical mesh struc-
ture for its body.[13] However, these so-called deterministic
compliant architectures can introduce significant complexity
or limitations to the design. Because soft robots are made
of intrinsically compliant materials, such deterministic archi-
tectures do not need to be incorporated into their design.
While the last item is not a fundamental technical barrier,
it nonetheless represents an important reason to adopt soft
materials into robot design. This is because manufacturing
represents a significant bottleneck for creating bioinspired
robots and so anything that can simplify design will relieve the
burden on having to adopt prohibitively complicated fabrication
methods.
Another reason to use soft materials is that they are more
compatible with the mechanics of the human body. Elasto-
mers and stretchable textiles can be worn on the skin without
causing discomfort or interfering with natural motion. When
used as an electronic skin for machines used in human–robot
interaction, the material can conform to the body and not result
in painful stress concentrations or point contacts. Such com-
patibility is especially important for wearable assistive robots,
orthoses, and even implants. An example of the latter is a soft
robotic ventricular assist device for help with pumping the
heart.[14]
For the purposes of this progress report, soft is defined as any
fluid, gel, or material with a shear modulus less than 10 MPa.
This includes most elastomers along with soft polymer com-
posites that contain a dispersion of nano- or microscale parti-
cles. Although not a significant focus of this report, biological
materials used in tissue engineering and biohybrid materials
also largely fall within the definition here of soft matter.
2. Materials
The soft robotic systems covered in this report are largely com-
posed of soft polymers and elastomers-like silicone rubber. The
elastomers are typically used for the limbs or fingers of the
robot as well as its housing or carrier medium for embedded
electrical circuitry. Soft robots also typically contain fluids for
actuation or stretchable circuitry. These fluids can be filled
into chambers or incorporated as microfluidic channels or dis-
persion within an elastomer matrix or gel. In the case of flu-
idic actuation, the hydrostatic pressure of the fluid also has a
central role in the mechanics of the soft. Although relatively
small compared to the maximum stresses in the surrounding
elastomer, they must nonetheless be included in the poten-
tial energy used to determine the mechanical response of the
robot. For certain dynamical loading conditions, fluid rheology
can also have a role. However, most applications involve low
shear rates such that the fluidic shear stresses are
negligible
Figure 2. A) Bioinspired engineering has led to advancements at multiple length scales, exemplified by the gecko-inspired Stickybot (reproduced with
permission.[6] Copyright 2006, Company of Biologists) and microfibrillar adhesive engineered to mimic the setae in the Anolis lizard. Reproduced with
permission.[7] Copyright 2008, The Royal Society Publishing. B) Material stiffness matters in determining how a system deforms and supports load.
C) The musculoskeletal system represents a classical example of how robust mechanical functionality can be achieved by combining soft and rigid
materials at a variety of length scales (Credit: National Cancer Institute/SEER Training Modules).

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compared to the hydrostatic pressure or elastic stresses. Finally,
soft robots may contain smart materials like shape-memory
alloy (SMA) and liquid crystal elastomers (LCEs), which change
shape in response to electrical current or heat. An example of a
recent soft robot gripper that contains all three of these material
classes—silicone for housing, liquid metal for circuit wiring,
and SMA for the actuators—is presented in Figure 3.[15] It is sig-
nificant to recognize here that, as with many robotic implemen-
tations, the gripper also contains conventional microelectronics
for sensing, signal processing, and radio communication.
For the various materials used in soft robots, it is useful to
review the constitutive relationships that relate applied stresses
with internal pressure and deformation. In the case of conduc-
tive elastomers, it also helps to have a sense of the electrome-
chanical coupling between stretch and electrical resistance.
These relationships are then used in Section 3 to better under-
stand the principles of actuation and how material properties
and geometric dimensions influence their functionality.
2.1. Elastomers
Elastomers are rubbery polymers that are mechanically compliant
and have a high elastic strain limit. Compliance is commonly
related to Young’s modulus (E), which scales with the tensile
stress required to stretch a material by a prescribed amount. In
conventional engineering applications, strain is typically small
and E can be determined for small deformations in the regime
where stress and strain have an approximately linear relation-
ship. However, elastomers and other soft polymers used in soft
robotics typically undergo large strains. In this regime, their
the stress response is typically nonlinear. More generally, addi-
tional elastic coefficients are required to capture the stress–strain
behavior of elastomers. Nonetheless, Young’s modulus is still a
useful measure for comparing the stiffness of materials since
the full nonlinear response will converge with the linearized rela-
tionship at small strain. In general, elastomers have a modulus
between 0.1 and 10 MPa, although soft robots tend to be com-
posed of soft polysiloxanes (silicone) and polyacrylate elastomers,
which typically have a modulus between 0.1 and 1 MPa.
A material is elastic if it returns to its original length after it
has been stretched under an applied tensile load. Elastomers
are considered to be hyperelastic since they exhibit an elastic
response over a broad range of strains and have a stress–strain
relationship that can be derived from a strain energy density
W.[16] Typically, W is expressed in terms of a stretches λi where
the index i ∈ {1,2,3} corresponds to the orthonormal directions
associated with the principle directions of elastic deformation.
For a volumetric element with edges oriented along the prin-
ciple directions, stretch is defined as the final length of the edge
(ℓi) divided by its initial length (ℓ0). Likewise, (Cauchy) stress σi
is defined as the internal pressure (in Pascals) acting along the
corresponding principle direction. For a hyperelastic solid that
is incompressible, that is, volume remains fixed; λ1λ2λ3 = 1,
the stress is calculated as σi = λi{∂W/∂λi} − p.[17] The value p is
called the hydrostatic pressure and is typically unknown when
first deriving the constitutive relationship. It can be determined
from the boundary conditions for σi or λi along with the incom-
pressibility constraint.
The elastic strain energy density W can be derived from the
Helmholtz free energy of a solid. For most soft elastomers,
it is dominated by entropy of the polymer chains and can be
obtained from first principles using statistical mechanics.
This includes the commonly used Neo-Hookean constitutive
model: W = C1{λ1
2
+ λ2
2
+ λ3
2
− 3}, where the elasticity coef-
ficient C1 = E/6. The form of the strain energy function can
also be obtained from experimental measurements. One such
phenomenological representation of a hyperelastic solid is the
Ogden model.[17]
In soft robotics, there are a wide range of elastomers that
have become popular for their compliance, stretchability, and
elastic resilience. Polysiloxanes such as poly(di-methylsiloxane)
(PDMS) are commonly used for soft microfluidics and robotics
due to their low modulus, high strain limit, and relatively low
hysteresis between loading and unloading cycles. Pt-cured
PDMS elastomers like Ecoflex 30 (Smooth-On) and Sylgard 184
(Dow Corning) are especially popular because they are clear,
inert, and mechanically robust. There has also been interest
in soft polyurethanes, polyacrylates (e.g., 3M VHB), and block
copolymer elastomers like styrene ethylene butylene styrene.
When selecting an elastomer, engineers typically focus on prop-
erties like strain limit, modulus, and manufacturing process-
ability. However, it is also important to consider factors like
creep, stress relaxation, and other forms of inelastic deforma-
tion that can lead to hysteresis and energy loss during consecu-
tive loading and unloading. A more complete examination of
elastomers for various robotics and stretchable electronics
applications have been reported in recent literature.[18–20]
Figure 3. Soft robots are typically composed of elastomers, fluids, and smart materials that respond to electrical or thermal stimulation. An example
of this is a soft robot gripper that has a silicone elastomer body, liquid metal circuitry to support embedded microelectronic components, and shape
memory alloy for electrical actuation. Reproduced with permission.[15]
Copyright 2018, Institute of Electrical and Electronics Engineers.

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2.2. Polymer Composites
Elastomers are naturally insulating—both electrically and
thermally. In order to introduce electrical and/or thermal con-
ductivity, elastomers are typically filled with nano/micropar-
ticles or fluidic inclusions. The dispersion phase is typically
conductive, resulting in a substantial enhancement in thermal
conductivity and electric permittivity. For high filler concen-
trations, the dispersion phase forms a percolating network
with long-range connectivity. This results in a composite that
is electrically conductive. Conductive elastomers typically con-
tain percolating networks of acetylene carbon black, exfoliated
graphite, carbon nanotubes, silver nanoflakes, silver nano-
wires, and other or metal nano/microparticles. An example
of a soft sensing skin with traces of carbon-filled conductive
elastomer is shown in Figure 4A.[21] Electrically conductive
elastomers can also be produced by blending elastomers with
conductive polymers like polyaniline (PANI) or poly(3,4-eth-
ylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS).[22]
Conductive elastomer composites typically exhibit signifi-
cant electromechanical coupling and hysteresis, that is, greater
electrical resistance during unloading compared to loading.
While several theories exist for explaining electromechanical
coupling in conductive elastomer composites, one possible
explanation is related to electrical tunneling between conduc-
tive particles. Rather than forming direct physical contact,
nanoparticles in a percolating network are separated from their
neighbors by an Å-scale gap, with the contact resistance is
controlled by electrical tunneling. As the gap increases during
stretch, the interparticle resistance increases dramatically,
resulting in a decrease in the effective volumetric conductivity
of the composite.[23]
2.3. Fluids
The earliest soft robots used pneumatic artificial muscles
(PAMs) for actuation. These actuators are composed of an elas-
tomer shell lined with braided textile that would contract when
filled with compressed air. They are called artificial muscle due
to the similarities with natural muscle in force output, contrac-
tion, stiffness change, and speed.[24] Another early example of
soft biocompatible technology was the Whitney strain gauge,
which was composed of a rubber tube filled with LM.[25] Strain
was determined by measuring the change in the conductivity
of the LM channel as the tube was stretched. Because of its
compliance and elasticity, the strain gauge could wrap around
a human limb and measure muscle contraction or joint motion
without interfering with the natural mechanics of the body.
In addition to compressed air and LM, there have been
a variety of other fluids commonly used in soft robotics over
the subsequent decades. These include carbon grease, water,
aqueous electrolytic solutions, and O2 gas produced through
fuel decomposition. The role of fluids in soft actuators is
analogous to that in conventional pneumatic and hydraulic
machinery. Although performance can be influenced by
chemical reactions, rheology, gas dynamics, and other kinetic
or rate-dependent properties, this section will focus on static
and quasistatic fluid properties.
2.3.1. Compressed Air
The ideal gas law is typically used to model the mechanics of
air in PAMs and other soft pneumatic systems. For compressed
air with a fixed pressure p, defined relative to atmospheric
Figure 4. A) Soft sensing skin with traces of carbon-filled conductive elastomer. Reproduced with permission.[21] Copyright 2016, Wiley-VCH. B) Stretch-
able capacitor with channels of EGaIn liquid metal in a soft silicone film. Reproduced with permission.[20] Copyright 2018, American Chemical Society.
C) Tactile skin with ionically conductive gel. Reproduced with permission.[40] Copyright 2014, Wiley-VCH. D) Liquid metal embedded elastomer (LMEE)
composite, which exhibits high electrical permittivity and thermal conductivity. Reproduced with permission.[43] Copyright 2016, Wiley-VCH; reproduced
with permission.[44] Copyright 2017, National Academy of Sciences.

1800477 (7 of 13)
pressure, the potential energy is Up = −pV, where V is the
enclosed volume. To maintain this pressure as the volume
changes, air must flow in or out of the enclosure. When the
enclosure is sealed, with the air trapped inside, the ratio
p/V becomes fixed and the potential energy is computed as
Up = p0V0ln(V/V0). Here, the subscript 0 denotes the initial
value prior to volume change. Gas pressure is typically con-
trolled with electrically powered pumps or valves that are con-
nected to a compressor or pressurized supply.
Recently, there has been interest in using pressurized air
created through combustion and fuel decomposition in order
to power soft pneumatic actuators. One approach has been to
use platinum to catalyze the decomposition of hydrogen per-
oxide[2,26] or the combustion of butane and oxygen.[11] Such
reactions can lead to significant gas pressures (e.g., 50 kPa for
H2O2 decomposition) that are sufficient for actuator motion.
Robots powered with combustion are capable of jumping
and require functionally graded materials with gradations in
mechanical compliance in order to distribute internal stresses
during impact landings.
2.3.2. Water
Soft fluidic actuators are also powered with water instead of air,
as water can allow for greater load bearing and a more rapid
actuator response.[27] As with the surrounding elastomer, the
water is treated as incompressible and so slight displacements
to the boundaries of the fluid or surrounding elastomer will
typically lead to rapid changes in fluidic pressure and actuator
stiffness. There has also been recent interest in underwater soft
actuators with hydrogels that allow water to flow out into the
surrounding fluidic media.[28] Because the hydrogel has similar
density and transparency to seawater, the soft actuators are both
optically and acoustically transparent. This could have poten-
tial advantages for engineering underwater soft robots that do
not interfere with the natural behavior of surrounding marine
organisms.
2.3.3. Conductive Fluid
Electrically conductive fluids are commonly used for soft robotic
skin and DE technologies. Conductive grease, such as carbon
black mixed with silicone oil, has been especially popular for
dielectric elastomer actuator (DEAs) and other DE-based tech-
nologies.[29]
Despite their relatively high electrical resistivity
(ρ ≈ 0.1–1 Ω m), these greases have adequate conductivity to
function as capacitive electrodes for actuators and capacitive
sensors. DE films can also be coated with liquid metals[30]
like
eutectic gallium indium (EGaIn), which are nontoxic and have
much lower resistivity (ρ ≈ 3 × 10−7
Ω m).[31]
They oxidize in air,
forming a nm-thick Ga2O3 skin that holds the liquid in place
and helps it wet to most polymer surfaces, including soft poly-
acrylate and silicone.[32]
Ga-based LM alloys are also popular as stretchable circuit
wiring and transducers for soft microfluidic electronics. An
example of EGaIn microchannels in a soft silicone is presented
in Figure 4B.[20]
As shown in the figure, the fluidic channels
remain intact as the surrounding elastomer is stretched. They
can be used to map strain or pressure into changes in electrical
resistance. In fact, commercial versions of the Whitney strain
gauge are presently made with EGaIn rather than mercury. The
resistance (R) of LM channels can be predicted with Ohm’s law,
that is, R = ρL/A, where L and A are the channel length and
cross section, respectively. Soft microfluidic electronics have
also been engineered using aqueous electrolytic solutions.[33,34]
These ionic conductors are nonetheless useful for sensors or
electrodes that provide AC field and are not capable of sup-
porting DC current for digital circuit functionality.
2.4. Gels
Gels have been emerging as a popular material for soft robot
actuation and electronics. By definition, gels are binary fluid-
solid systems that have colloidal dimensions, that is, nanom-
eter or micrometer-scale distances between the boundaries of
the fluid and solid phases.[35] Gels can be thought of as com-
bining the material properties of soft polymers and fluids, with
the polymer treated as the continuous dispersion medium and
the fluid as the dispersion phase. The polymer typically repre-
sents only a small volume fraction of ≈1–10%, with just enough
material to give the gel structural integrity, and the gel is usu-
ally bicontinuous, with both the solid and fluid phases forming
connected networks.
Gels can be infused with a variety of different fluids. These
can range from water, as in the case of hydrogels,[36] to ionic
solution[37] and gas (i.e., aerogels[38]). Gels with ionic solutions
have been used to create optically transparent DEAs[39] and
tactile skin, as shown in Figure 4C.[40] The solid phase typi-
cally exhibits elastic properties that enable swelling and large
mechanical deformation. It can be synthetic, for example,
polyethylene oxide, polyvinyl alcohol,[36] or naturally derived
using agarose, alginate, or collagen. There has also been recent
interest in double network gels that exhibit a remarkable com-
bination of high mechanical compliance (tensile modulus
≈ 0.1–1 MPa) and fracture toughness (≈0.1–10 kJ m−2).[41,42]
Gels are an attractive material system for applications in soft
robotics due to their potential to combine ionic conductivity
with high tear resistance and skin-like elasticity.
2.5. LM-Embedded Elastomers
While gels are predominately composed of fluid, it is also
possible to engineer fluid-elastomer composites in which the
fluid dispersion makes up less than half of the volume. One
approach is to embed elastomers with a suspension of Ga-
based LM microdroplets (Figure 4D).[43,44]
Compared to con-
ductive polymer composites that have rigid filler, these LMEEs
exhibit significantly reduced electromechanical coupling.[3,45]
Depending on the concentration and microstructure of the
embedded LM droplets, the LMEE composites can be thermally
conductive and electrically insulating or electrically conduc-
tive. In the case of electrically conductive LMEE, the droplets
make direct physical contact and the contact resistance has only
limited dependency on stretch. This is due to the ability of the

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liquid metal to flow between the droplets and preserve the con-
tact resistance of each droplet–droplet interface. Because the
total number of contacts does not change during stretch, the
absolute electrical resistance remains unchanged.
Soft silicones and urethanes have typically been used as the
matrix material for LMEEs, although the LM droplets can be
suspended in a much wider range of polymers or deposited as
a thin-film coating on an elastomer substrate. To create electri-
cally conductive networks, the droplets can be ruptured through
mechanical or laser scribing.[46,47] Interestingly, this same
scribing process enables new conductive pathways to form in
circuits that have been mechanically damaged. This results in
an autonomous self-healing property in which the electrical
wiring within a soft robot can form new routes to conduct elec-
tricity as the robot is punctured with holes.[3]
LMEEs that have not been scribed remain electrically insu-
lating and exhibit an enhanced electrical permittivity.[43] The
increased electric permittivity (εr) arises from the polarization
of the embedded droplets and can be predicted with effec-
tive medium theory (EMT), which provides reasonable agree-
ment with experimental measurements.[48] The field equations
for heat transfer have the same differential form as those for
electrostatics. Therefore, EMT can also be used to predict the
relative enhancement in thermal conductivity (k) of an LMEE
composite. The prediction can be further modified to account
for stretch in the composite, which leads to elongation of the
droplets into needle-like ellipses. Such theoretical predictions
have been shown to be in good agreement with experimental
measurements of LMEEs stretched to 400% strain.[44] In gen-
eral, thermally conductive elastomer composites can function
as heat dissipating elastomer substrates for heat generating
electronics or thermal actuators such as shape-memory alloy.
3. Architectures
Over the decades since the inception of robotics, PAMs and
LM-based sensing have been used in humanoids,[49] exo-
skeletons,[50] industrial automation,[51] and clinical physi-
ology.[25] In recent years, there has been increasing interest in
extending pneumatic actuation and LM electronics to create
miniaturized systems using emerging methods in soft-matter
engineering.[52,53]
This includes soft lithography fabrication
methods, soft microfluidic architectures, micro/nanocomposite
synthesis, and soft polymer engineering. Soft-matter engi-
neering has also been used to create electrostatic actuators, sen-
sors, and energy-harvesting transducers. In the case of DEAs,
an insulating elastic film is coated with conductive liquid (e.g.,
carbon grease or liquid metal) and its deformation is coupled to
the electrical capacitance between the liquid electrodes. While
the properties of DE transducers have been known since the
late 19th century,[29]
recent efforts have focused on soft robotic
implementations using polyacrylate films and tape, silicone
elastomer, conductive grease, and conductive elastomers.[54]
In contrast to conventional robotic hardware, these soft mate-
rial systems can be incorporated into a host robot or interfaced
with the human body without adding bulk, weight, or stiffness.
Perhaps the most successful applications of soft material archi-
tectures to date are the inflatables used in balloon angioplasty
and blood pressure monitoring. While these are not robotic
implementations, they do share many of the same design prin-
ciples that are popular within soft robotics and may represent
a starting point for more widespread adoption of soft robotics
into commercial or medical products.
As soft materials become increasingly used in robotics and
human–machine interaction, there will be continued need for
improvements in the performance and functionality of soft
matter circuits, sensors, and actuators. This requires progress
in not only materials engineering and device-level design, but
also advancements in manufacturing for precision materials
patterning and robust multimaterial integration. Moreover, as
soft robotic technologies continue to mature, there will be an
increasing demand for predictive theoretical models that can
inform design and operation. As in other areas of robotics and
engineering, these models can enable rapid design decisions
with reduced dependency on prototype iterations and testing.
Moreover, they can furnish design rules and scaling laws that
are particularly useful in early stages of design where it is
impractical to explore a vast materials space using experimental
or computationally intensive finite element techniques. Where
possible, the following subsections will apply the constitutive
models presented in Section 2 to derive approximate algebraic
expressions that relate device performance with material prop-
erties, geometry, and external loading conditions. Such models
are not only helpful for making early stage design decisions but
also can be used to identify the relevant governing physics that
can be subsequently incorporated into a more detailed compu-
tational simulation.
This section presents an overview of only a few classes of
soft robot actuators and is by no means exhaustive. The catego-
ries of actuators reviewed here have been selected because of
their current popularity in soft robotic implementations. For
a more complete discussion of soft actuators used in robotics,
the interested reader should refer to recent review papers in the
literature.[55,56]
3.1. Fluid-Elastomer Structures
Much of the current work in fluidic soft robots and electronics
build on fabrication methods and architectures for soft micro-
fluidics used in biotechnology and medicine.[57–60]
These devices
are typically produced using soft lithography fabrication tech-
niques to create networks of microfluidic channels embedded
in a soft polymer matrix.[61–63]
Recent applications include soft
microfluidics for organ-on-a-chip devices,[64,65]
soft robotics,[66]
and resistive strain gauges and pressure sensing with liquid
metal.[67]
In some cases, the deformation of the elastic medium
and embedded microfluidic channels are coupled and this can
be exploited to achieve unique functionalities that are not pos-
sible with a rigid device. Examples include soft robot actuators
that couple fluidic pressure with the contraction, inflation, or
bending of an elastic shell; sensors composed of liquid metal
or ionic fluid[34]
microchannels that change electrical resistance
in response to applied pressure or stretch; pressure-controlled
microfluidics that filter or capture nanoparticles;[68,69]
and
microfluidic “Quake” valves that use pressurized control lines
to manipulate the flow of fluid within a device.[62]

1800477 (9 of 13)
Theoretical studies have been performed that establish
fluid–elastomer coupling for a wide range of soft microfluidic
systems. These include studies of PAM actuators that relate
internal fluid pressure (p) with various modes of actuator
deformation.[70,71] Examples include the pneumatically actu-
ated gripper in Figure 5A,[72] 3D-printed flexural actuator in
Figure 5B,[73] and contractile vacuum-controlled actuator in
Figure 5C.[74] In general, these relationships are established by
finding the shape (i.e., contraction length, bending curvature,
or twist angle) that minimizes the total Gibbs free energy (Π) of
a system. For PAMs and other pressure-controlled mechanical
systems, Π is equivalent to the potential energy of a system and
accounts for the stored elastic energy of the material (W⋅V0,
where V0 is the fixed volume of the rubber), mechanical work
of the pressurized fluid (p⋅Ve, in the case of air, where p is fixed,
Ve is the enclosed air volume), and mechanical work of the
applied load (F⋅L, in the case of length change under a fixed
force F, where L is the actuator length). In the case of the McK-
ibben PAM actuator, the stored elastic energy has negligible
contribution compared to the mechanical work of the pressur-
ized air and applied force. For this special case, the length and
diameter (D) of the actuator are coupled by the inextensibility
of the braided nylon that make up the actuator’s fabric shell:
D = b{1 − L2/b2}1/2/nπ, where b is the fiber length and n is the
number of turns.[70] It follows that Π ≈ −pπD2L2/4 − FL. At
static equilibrium, the condition that Π is minimized (i.e., dΠ/
dL = 0) implies
4
3 3
2 2
π
≈ +
L
n F
p
b
(1)
As with most PAMs, another feature of the McKibben actu-
ator is that it increases in stiffness when pressurized. This cou-
pling of contraction and stiffening is similar to that of natural
skeletal muscle and is a reason why McKibben actuators are
referred to as artificial muscle. A corresponding spring con-
stant η can be defined that relates displacement with applied
force, that is, F = ηΔL. In the limit as ΔL goes to zero, it follows
that η ≈ {b√3/2πn2}p. This suggests that stiffness increases lin-
early with increased internal air pressure.
The theoretical approach presented above for relating
internal air pressure and actuator deformation can also be
extended to flexural pneumatic actuators that bend rather than
contract. Studies have examined such coupling in so-called
Suzumori[75]
and Pneu-Net actuator,[76]
which are composed of
soft air chambers that are bonded to flexible but inextensible
strain limiting elements that control the direction of actuator
bending. Although highly simplified, these analytic approxi-
mations provide reliable order-of-magnitude estimate for how
bending curvature increases with pressure and can be used to
inform how material selection and geometric dimensions can
influence flexural response.[77]
3.2. Dielectric Elastomers
While fluidic actuators exhibit contractions and stiffnesses that
are in the range of natural muscle, their application in soft
robotics is limited by their dependency on bulky pneumatic
or hydraulic hardware. A promising alternative is to use DEAs
and transducers since these can be powered electrically using
a portable power supply. The DE technologies used in soft
robotics can be thought of as soft capacitors in which capaci-
tance C is coupled to stretch in the plane (λ1, λ2) and thickness
(λ3) of the elastic film. In general, C = λ1λ2C0/λ3, where C0 is
the natural capacitance of the undeformed film. For the spe-
cial cases of uniaxial stretch and biaxial stretch, it follows that
C/C0 = λ and λ4, respectively, and for pure compression through
the thickness (i.e., λ3 = λ 1), C/C0 = λ−2. This electrome-
chanical coupling can be used both for capacitive sensing and
energy harvesting. For a balloon-like transducer (Figure 5D),[78]
energy harvesting is governed by biaxial stretch (i.e., C/C0 = λ4)
while for a stacked DE capacitor with alternating layers of insu-
lating and conductive silicone (Figure 5E),[79] the electrome-
chanical coupling is C/C0 = λ−2. When a voltage (Φ0) is supplied
to the capacitor, a pressure or force is required to maintain a
fixed initial capacitance C0. In this configuration, the capacitor
is loaded with charge q0 = C0Φ0, where C0 is the capacitance of
the undeformed transducer. Next, as the electrodes are momen-
tarily disconnected from the power supply and the pressure or
force increases, the voltage will also increase. This is due to the
increase in capacitance and the fact that the surface charges
must remain fixed (due to being disconnected from the power
supply). Subsequently removing charge at this higher voltage
allows for net electrostatic energy to be delivered to the power
supply.
For DE generators, mechanical deformation is used to
manipulate internal electric field and produce electrostatic
energy. However, the reverse is also possible—electric field can
induce mechanical deformation. This arises from the Maxwell
stress that is generated from the electrostatic attraction of the
surface charges on the opposing surfaces of the dielectric film.
The electromechanical coupling between Maxwell stress and
elastic deformation has been exploited for a wide variety of DEA
architectures. The simplest of these is the annular diaphragms
that were used in the early years of DEA research.[80] Mini-
mizing the potential energy Π of these systems with respect to
film thickness yields a highly nonlinear relationship between
biaxial stretch and voltage. In addition to being nonlinear, such
coupling typically exhibits a limit point instability where the
film will undergo sudden wrinkling or creasing when voltage
exceeds a critical value.[81,82]
At these high voltages, the elas-
tomer may also fail due to dielectric breakdown, which occurs
when the applied electric field reaches the electric breakdown
strength of the elastomer.[83]
Such failures are sometimes dif-
ficult to avoid since DEAs only undergo significant deformation
at voltages close to these critical values.
The principle of minimum potential energy used to model
DEAs and fluidic actuators can also be extended to more
complex structures that combine dielectric elastomers with
semirigid frames constructed from flexural elements. These
so-called dielectric elastomer minimum energy structures
(DEMES) are composed of thin dielectric membranes that are
stretched and bonded to a flexible (but inextensible) frame.[84,85]
An example of a flexural DEMES actuator with liquid metal
electrodes is presented in Figure 5F. Applying electric field acts
to relieve the residual membrane stresses and allows the frame
to return to its natural shape. Another recent development

1800477 (10 of 13)
has been to combine DEAs with fluidic actuators in order to
improve work density and load capacity.[86]
3.3. Thermal Actuators
Although DEAs can operate with mobile electronics, the cir-
cuitry need for high-voltage operation can still be bulky and
incompatible with miniaturized soft robotic systems. Another
alternative for electrically powered actuation is to use thermal
actuators like SMAs. Nickel-titanium (nitinol) has been pop-
ular for soft actuation because of their high work density and
ability to undergo large changes in stiffness and shape when
electrically activated. Actuation is controlled by a reversible
change from the martensite to austenite crystal phase, which
can be induced through resistive (Ohmic) heating of the alloy.
Depending on the natural shape of the SMA actuator, this tran-
sition can be used to induce bending (Figure 5G),[87]
twisting,
or contractions, as in the case of an SMA wire that is coiled into
the shape of a spring.[88] Since the martensite-austenite phase
transition is controlled by temperature, SMA actuation requires
careful attention to thermal management. To prevent over-
heating, researchers have explored techniques ranging from
precise voltage control[89]
to the use of active cooling[90,91]
and
integration of thermally conductive soft elastomer[44]
for passive
heat dissipation.
Other thermal actuators utilize shape-memory poly-
mers that deform in response to applied heat. This includes
the twisted and coiled polymer muscle composed of a nylon
6 fishing line originally introduced in ref. [92]. As shown in
Figure 5H, the actuator is capable of lifting a 100 g load with
a 53% actuation stroke.[93]
Another approach to thermal actua-
tion, presented in Figure 5I, involves the integration of micro-
fluidics with LCEs.[94]
In this design, the microfluidic channels
supply hot or cold water to the LCE in order to rapidly heat
it up or cool it down. Compared to external heating and pas-
sive cooling, this vascular LCE-based artificial muscle (VLAM)
exhibits relatively fast actuation and shape recovery. In addition
Figure 5. Pneumatic soft robot actuation: A) soft robot gripper produced using direct write printing. Reproduced with permission.[72]
Copyright 2018,
Wiley-VCH; B) 3D-printed pneumatic flexural actuator. Reproduced with permission.[73]
Copyright 2017, Wiley-VCH; C) contractile vacuum-controlled
actuator. Reproduced with permission.[74]
Copyright 2016, Wiley-VCH. Dielectric elastomer technologies: D) inflation-controlled energy harvesting.
Reproduced with permission.[78]
Copyright 2012, Royal Society of Chemistry; E) stacked dielectric elastomer actuator (DEA). Reproduced with per-
mission.[79]
Copyright 2009, Elsevier; F) flexural dielectric elastomer minimum energy structure (DEMES) with liquid metal electrodes. Thermally
responsive actuators: G) bending actuator with shape memory alloy (SMA). Reproduced with permission.[87]
Copyright 2017, Elsevier. Reproduced with
permission.[108]
Copyright 2019, Elsevier Books; H) twisted and coiled polymer muscle composed of a nylon 6 fishing line. Reproduced with permis-
sion.[93]
Copyright 2018 Wiley-VCH; vascular LCE-based artificial muscle powered by injecting with hot and cold water. Reproduced with permission.[94]
Copyright 2018, Wiley-VCH.

1800477 (11 of 13)
to shape-controlled actuation, thermally responsive polymer
also exhibits reversible stiffness-tuning properties that are also
important for artificial muscle applications. Stiffness tuning
polymers for robotics has recently been demonstrated in
ref. [95] using conductive thermoplastic elastomers and a more
general review of stiffness tunable materials for robotics has
been presented in ref. [96].
4. Applications and Outlook
The materials and artificial muscle architectures described
above have been applied to a wide range of soft robotic systems.
Most of these robots are tethered and require external hard-
ware for supplying pressurized air to power pneumatic actua-
tors, high voltage to activate DEAs, or electrical current to heat
SMAs. However, progress toward fully autonomous soft robots
requires implementations that are untethered and capable
of mobility with on-board or embedded hardware. One chal-
lenge has been to develop actuators that are powerful enough
to carry their own power supply. Some groups have addressed
it by significantly scaling up their actuators and creating large
soft robots like the 0.65 m long pneumatic quadruped created
by Tolley et al.,[97] which is capable of carrying batteries, com-
pressors, valves, and microprocessor. Other attempts at unteth-
ered soft robots are engineered to swim or move in an aqueous
medium, which reduces load on the actuators through buoy-
ancy and the absence of dry friction. Examples include a fast-
moving untethered fish that is actuated using hydrogel-based
DEAs that are activated with a built-in high-voltage supply[98]
and an autonomous soft robotic fish that swims using hydraulic
actuators that are powered with hardware contained within the
body.[99,100]
SMA has become popular as an actuator for untethered soft
robots due to its low mass, high work density, and ability to
be activated using portable electronics for electrical power and
control. This has resulted in several recent examples of SMA-
powered soft robots that contain an on-board power supply
and microcontroller.[101–103] Although promising, the use of
SMA for untethered soft robots is limited by the high power
consumption and low efficiency of electrical power input to
mechanical power output. Moreover, SMA actuators have lim-
ited bandwidth due to the time required for the alloy to cool
and return to the martensite phase after electrical current is
removed. Successful use of SMA in soft robotics therefore
requires careful geometric design and choice of surrounding
materials in order to ensure adequate thermal management
for reliable high-frequency response over extended operating
times and lower weight for reduced cost of transport and
longer battery life.
Another approach to creating untethered soft robots has been
to use combustion. This has led to jumping robots capable of
producing large forces.[11,104,105]
More recently, controlled com-
bustion has been employed to create an untethered soft octopus
robot that does not contain any electronics.[2]
Although the
robot is not capable of locomotion, it represents a rare example
of a fully soft-matter machine that contains absolutely no rigid
materials. Other attempts to create fully soft-matter robots typi-
cally contain biological tissue, such as the jellyfish-inspired bio-
hybrid robot reported in ref. [106] which can be controlled by
applying small electrical charges to the environment. This is
accomplished using muscle microtissue that is engineered in
a soft elastomer substrate. However, the robots are not autono-
mous, since the muscle is stimulated using external electrodes
or light.
Despite recent successes with engineering untethered soft
robots, there is significant room for improvement. In general,
creating completely untethered robotic systems is challenging
due to issues with materials compatibility and integration. This
is because the soft materials used for actuation, sensing, and
circuit wiring are not enough for autonomous functionality.
These soft material systems also need to interface with rigid
microelectronic components for signal processing, communi-
cation, and power regulation. Some groups have attempted to
create more universal frameworks for creating hybrid mate-
rial systems that combine soft elastomers and fluids with rigid
miniaturized components.[15,107] Improved materials inte-
gration can also be accomplished through advancements in
functional-graded materials with smooth transitions in mate-
rial stiffness. This can eliminate the damage-causing stress
concentration that often arise at the interface between soft and
rigid materials.
Untethered functionality represents just one step toward
soft robot autonomy. Referring back to the definition presented
in Section 1.1, soft robots must eventually be capable of under-
standing their physical state and environment or about its
own physical state and perform physical task based on deci-
sions that use this information. Soft-matter engineering pro-
vides a framework for engineering machines that have the
actuators, sensors, and electronics to achieve this autonomy.
However, autonomous functionality also depends on advance-
ments in algorithms for sensing, planning, adaptive learning,
and control that are specialized to the unique mechanics of
soft material systems. Therefore, although many of the near-
term efforts in soft robotics should remain focused on mate-
rials integration, future efforts must broaden the research to
address machine intelligence, planning, and other aspect of
robot autonomy.
Acknowledgements
This article is part of the special series on Advanced Intelligent Systems
that showcases the outstanding achievements of leading international
researchers on intelligent systems.
Conflict of Interest
The authors declare no conflict of interest.
Keywords
artificial muscle, biological inspiration, soft-matter engineering, soft robotics
Received: September 26, 2018
Revised: October 23, 2018
Published online: December 13, 2018

1800477 (12 of 13)
[1] R. T. Hanlon, J. B. Messenger, Cephalopod Behavior, Cambridge
University Press, Cambridge, UK 2018.
[2] M. Wehner, R. L. Truby, D. J. Fitzgerald, B. Mosadegh,
G. M. Whitesides, J. A. Lewis, R. J. Wood, Nature 2016, 536, 451.
[3] E. J. Markvicka, M. D. Bartlett, X. Huang, C. Majidi, Nat. Mater.
2018, 17, 618.
[4] S. I. Rich, R. J. Wood, C. Majidi, Nat. Electron. 2018, 1, 102.
[5] P. Corke, Robotics, Vision and Control: Fundamental Algorithms in
MATLAB, 2nd ed., Springer-Verlag, Berlin, Germany 2017.
[6] K. Autumn, A. Dittmore, D. Santos, M. Spenko, M. Cutkosky,
J. Exp. Biol. 2006, 209, 3569.
[7] J. Lee, C. Majidi, B. Schubert, R. S. Fearing, J. R. Soc., Interface
2008, 5, 835.
[8] M. A. Diftler, J. Mehling, M. E. Abdallah, N. A. Radford,
L. B. Bridgwater, A. M. Sanders, R. S. Askew, D. M. Yamokoski,
F. Permenter, B. K. Hargrave, R. Piatt, R. T. Savely, R. O. Ambrose,
Proc. IEEE Int. Conf. Rob. Autom. (ICRA) 2011, 2178.
[9] E. W. Hawkes, L. H. Blumenschein, J. D. Greer, A. M. Okamura,
Sci. Rob. 2017, 2, eaan3028.
[10] R. F. Shepherd, F. Ilievski, W. Choi, S. A. Morin, A. A. Stokes,
A. D. Mazzeo, X. Chen, M. Wang, G. M. Whitesides, Proc. Natl.
Acad. Sci. USA 2011, 108, 20400.
[11] N. W. Bartlett, M. T. Tolley, J. T. B. Overvelde, J. C. Weaver,
B. Mosadegh, K. Bertoldi, G. M. Whitesides, R. J. Wood, Science
2015, 349, 161.
[12] S. Seok, C. D. Onal, K. J. Cho, R. J. Wood, D. Rus, S. Kim, IEEE/
ASME Trans. Mechatronics 2013, 18, 1485.
[13] A. S. Boxerbaum, K. M. Shaw, H. J. Chiel, R. D. Quinn, Int. J. Rob.
Res. 2012, 31, 302.
[14] E. T. Roche, Sci. Transl. Med. 2017, 9, eaaf3925.
[15] T. Hellebrekers, B. O. Ozutemiz, J. Yin, C. Majidi, Proc. IEEE/RSJ
Int. Conf. Intell. Robot. Syst. (IROS) 2018.
[16] G. Marckmann, E. Verron, Rubber Chem. Technol. 2006, 79, 835.
[17] R. W. Ogden, Non-linear Elastic Deformations, Dover, Mineola, NY
1997.
[18] J. C. Lötters, W. Olthuis, P. H. Veltink, P. Bergveld, J. Micromech.
Microeng. 1997, 7, 145.
[19] J. C. Case, E. L. White, R. K. Kramer, Soft Rob. 2015, 2, 80.
[20] S. Park, K. Mondal, R. M. TreadwayIII, V. Kumar, S. Ma,
J. D. Holbery, M. D. Dickey, ACS Appl. Mater. Interfaces 2018, 10,
11261.
[21] A. Charalambides, S. Bergbreiter, Adv. Mater. Technol. 2017, 2,
1600188.
[22] Y. Wang, Sci. Adv. 2017, 3, e1602076.
[23] M. Knite, V. Teteris, A. Kiploka, J. Kaupuzs, Sens. Actuators, A 2004,
110, 142.
[24] F. Daerden, D. Lefeber, Eur. J. Mech. Environ. Eng. 2002, 47, 11.
[25] R. J. Whitney, J. Physiol. 1953, 121, 1.
[26] C. D. Onal, X. Chen, G. M. Whitesides, D. Rus, in Robotics
Research (Eds: H. I. Christensen, O. Khatib), Springer-Verlag,
Berlin, Germany 2017, pp. 525–540.
[27] A. D. Marchese, R. K. Katzschmann, D. Rus, Soft Rob. 2015, 2, 7.
[28] H. Yuk, S. Lin, C. Ma, M. Takaffoli, N. X. Fang, X. Zhao, Nat.
Commun. 2017, 8, 14230.
[29] F. Carpi, S. Bauer, D. De Rossi, Science 2010, 330, 1759.
[30] J. Wissman, L. Finkenauer, L. Deseri, C. Majidi, J. Appl. Phys. 2014,
116, 144905.
[31] M. D. Dickey, R. C. Chiechi, R. J. Larsen, E. A. Weiss, D. A. Weitz,
G. M. Whitesides, Adv. Funct. Mater. 2008, 18, 1097.
[32] R. C. Chiechi, E. A. Weiss, M. D. Dickey, G. M. Whitesides, Angew.
Chem. 2008, 120, 148.
[33] K. Noda, E. Iwase, K. Matsumoto, I. Shimoyama, Proc. IEEE Int.
Conf. Rob. Autom. (ICRA) 2010, 4212.
[34] J. B. Chossat, Y. Tao, V. Duchaine, Y. L. Park, Proc. IEEE Int. Conf.
Rob. Autom. (ICRA) 2015, 2568.
[35] G. W. Scherer, Cem. Concr. Res. 1999, 29, 1149.
[36] J. L. Drury, D. J. Mooney, Biomaterials 2003, 24, 4337.
[37] W. Hong, X. Zhao, Z. Suo, J. Mech. Phys. Solids 2010, 58, 558.
[38] K. H. Kim, M. Vural, M. F. Islam, Adv. Mater. 2011, 23, 2865.
[39] C. Keplinger, J. Y. Sun, C. C. Foo, P. Rothemund, G. M. Whitesides,
Z. Suo, Science 2013, 341, 984.
[40] J. Y. Sun, C. Keplinger, G. M. Whitesides, Z. Suo, Adv. Mater. 2014,
26, 7608.
[41] J. P. Gong, Y. Katsuyama, T. Kurokawa, Y. Osada, Adv. Mater. 2003,
15, 1155.
[42] J.-Y. Sun, X. Zhao, W. R. K. Illeperuma, O. Chaudhuri, K. H. Oh,
D. J. Mooney, J. J. Vlassak, Z. Suo, Nature 2012, 489, 133.
[43] M. D. Bartlett, A. Fassler, N. Kazem, E. J. Markvicka, P. Mandal,
C. Majidi, Adv. Mater. 2016, 28, 3726.
[44] M. D. Bartlett, N. Kazem, M. J. Powell-Palm, X. Huang, W. Sun,
J. A. Malen, C. Majidi, Proc. Natl. Acad. Sci. USA 2017, 114, 2143.
[45] A. Fassler, C. Majidi, Adv. Mater. 2015, 27, 1928.
[46] J. W. Boley, E. L. White, R. K. Kramer, Adv. Mater. 2015, 27, 2355.
[47] Y. Lin, C. Cooper, M. Wang, J. J. Adams, J. Genzer, M. D. Dickey,
Small 2015, 11, 6397.
[48] T. C. Choy, Effective Medium Theory: Principles and Applications,
Oxford University Press, Oxford, UK 2015.
[49] I. Boblan, A. Schulz, Proc. 41st Int. Symp. 2010 6th German Conf.
Rob. (ROBOTIK) 2010, pp. 1–6.
[50] H. R. Luce, Life Mag. 1960, 48.
[51] Rubber Dev. 1984, 37, 117.
[52] D. Trivedi, C. D. Rahn, W. M. Kier, I. D. Walker, Appl. Bionics
Biomech. 2008, 5, 99.
[53] M. D. Dickey, Adv. Mater. 2017, 29, 1606425.
[54] G. Y. Gu, J. Zhu, L. M. Zhu, X. Zhu, Bioinspiration Biomimetics
2017, 12, 011003.
[55] D. Chen, Q. Pei, Chem. Rev. 2017, 117, 11239.
[56] L. Hines, K. Petersen, G. Z. Lum, M. Sitti, Adv. Mater. 2017, 29,
1603483.
[57] H. A. Stone, A. D. Stroock, A. Ajdari, Annu. Rev. Fluid Mech. 2004,
36, 381.
[58] T. M. Squires, S. R. Quake, Rev. Mod. Phys. 2005, 77, 977.
[59] G. M. Whitesides, Nature 2006, 442, 368.
[60] E. K. Sackmann, A. L. Fulton, D. J. Beebe, Nature 2014, 507, 181.
[61] Y. Xia, G. M. Whitesides, Annu. Rev. Mater. Sci. 1998, 28, 153.
[62] S. R. Quake, A. Scherer, Science 2000, 290, 1536.
[63] D. Qin, Y. Xia, G. M. Whitesides, Nat. Protoc. 2010, 5, 491.
[64] D. Huh, H. J. Kim, J. P. Fraser, D. E. Shea, M. Khan, A. Bahinski,
G. A. Hamilton, D. E. Ingber, Nat. Protoc. 2013, 8, 2135.
[65] S. N. Bhatia, D. E. Ingber, Nature 2014, 201, 4.
[66] S. Wakimoto, K. Ogura, K. Suzumori, Y. Nishioka, Proc. IEEE Int.
Conf. Rob. Autom. (ICRA) 2009, 556.
[67] R. K. Kramer, C. Majidi, R. J. Wood, Proc. IEEE Int. Conf. Rob.
Autom. (ICRA) 2011, 1103.
[68] D. Huh, K. Mills, X. Zhu, M. A. Burns, M. Thouless, S. Takayama,
Nat. Mater. 2007, 6, 424.
[69] W. Sparreboom, A. Van Den Berg, J. Eijkel, Nat. Nanotechnol.
2009, 4, 713.
[70] C. P. Chou, B. Hannaford, IEEE Trans. Rob. Autom. 1996, 12, 90.
[71] S. Wakimoto, J. Misumi, K. Suzumori, Sens. Actuators, A 2016, 250,
48.
[72] B. J. Cafferty, V. E. Campbell, P. Rothemund, D. J. Preston, A. Ainla,
N. Fulleringer, A. C. Diaz, A. E. Fuentes, D. Sameoto, J. A. Lewis,
G. M. Whitesides, Adv. Mater. Technol. 2018, 3, 1800299.
[73] B. A. W. Keong, R. Y. C. Hua, Adv. Mater. Technol. 2018, 3, 1700172.
[74] D. Yang, M. S. Verma, J.-H. So, B. Mosadegh, C. Keplinger, B. Lee,
F. Khashai, E. Lossner, Z. Suo, G. M. Whitesides, Adv. Mater.
Technol. 2016, 1, 1600055.
[75] K. Suzumori, S. Iikura, H. Tanaka, Proc. IEEE Conf. Micro Electro
Mech. Syst. (MEMS) 1991, 204.

1800477 (13 of 13)
[76] F. Ilievski, A. D. Mazzeo, R. F. Shepherd, X. Chen, G. M. Whitesides,
Angew. Chem. 2011, 123, 1930.
[77] K. M. de Payrebrune, O. M. O’Reilly, Extreme Mech. Lett. 2016, 8,
38.
[78] C. Keplinger, T. Li, R. Baumgartner, Z. Suo, S. Bauer, Soft Matter
2012, 8, 285.
[79] G. Kovacs, L. Düring, S. Michel, G. Terrasi, Sens. Actuators, A 2009,
155, 299.
[80] R. Pelrine, R. Kornbluh, Q. Pei, J. Joseph, Science 2000, 287, 836.
[81] T. Li, C. Keplinger, R. Baumgartner, S. Bauer, W. Yang, Z. Suo,
J. Mech. Phys. Solids 2013, 61, 611.
[82] Q. Wang, L. Zhang, X. Zhao, Phys. Rev. Lett. 2011, 106, 118301.
[83] R. Pelrine, R. Kornbluh, J. Joseph, R. Heydt, Q. Pei, S. Chiba,
Mater. Sci. Eng., C 2000, 11, 89.
[84] S. Rosset, O. A. Araromi, J. Shintake, H. R. Shea, Smart Mater.
Struct. 2014, 23, 085021.
[85] O. A. Araromi, I. Gavrilovich, J. Shintake, S. Rosset, M. Richard,
V. Gass, H. R. Shea, IEEE/ASME Trans. Mechatronics 2015, 20,
438.
[86] E. Acome, S. K. Mitchell, T. G. Morrissey, M. B. Emmett,
C. Benjamin, M. King, M. Radakovitz, C. Keplinger, Science 2018,
359, 61.
[87] H. Rodrigue, W. Wang, D. R. Kim, S. H. Ahn, Compos. Struct. 2017,
176, 398.
[88] S. Kim, E. Hawkes, K. Cho, M. Joldaz, J. Foleyz, R. Wood, Proc.
IEEE/RSJ Int. Conf. Intell. Robot. Syst. (IROS) 2009, 2228.
[89] H. Jin, Smart Mater. Struct. 2016, 25, 085026.
[90] S. S. Cheng, Y. Kim, J. P. Desai, IEEE Trans. Rob. 2017, 33, 986.
[91] J. O. Alcaide, L. Pearson, M. E. Rentschler, Proc. IEEE Int. Conf.
Robot. Autom. (ICRA) 2017, 4338.
[92] C. S. Haines, M. D. Lima, N. Li, G. M. Spinks, J. Foroughi,
J. D. W. Madden, S. H. Kim, S. Fang, M. J. de Andrade, F. Göktepe,
Ö. Göktepe, S. M. Mirvakili, S. Naficy, X. Lepró, J. Oh, M. E. Kozlov,
S. J. Kim, X. Xu, B. J. Swedlove, G. G. Wallace, R. H. Baughman,
Science 2014, 343, 868.
[93] L. Wu, I. Chauhan, Y. Tadesse, Adv. Mater. Technol. 2018, 3,
1700359.
[94] Q. He, Z. Wang, Z. Song, S. Cai, Adv. Mater. Technol. 2018, 3,
1800244.
[95] S. Rich, S. H. Jang, Y. L. Park, C. Majidi, Adv. Mater. Technol. 2017,
2, 1700179.
[96] L. Wang, Y. Yang, Y. Chen, C. Majidi, F. Iida, E. Askounis, Q. Pei,
Mater. Today 2018, 21, 563.
[97] M. T. Tolley, Soft Rob. 2014, 1, 213.
[98] T. Li, Sci. Adv. 2017, 3, e1602045.
[99] A. D. Marchese, C. D. Onal, D. Rus, Soft Rob. 2014, 1, 75.
[100] R. K. Katzschmann, A. D. Marchese, D. Rus, in Experimental
Robotics (Eds: M. A. Hsieh, O. Khatib, V. Kumar), Springer-Verlag,
Berlin, Germany 2016, pp. 405–420.
[101] S.-H. Song, Bioinspiration Biomimetics 2016, 11, 036010.
[102] H.-T. Lin, G. G. Leisk, B. Trimmer, Bioinspiration Biomimetics 2011,
6, 026007.
[103] J. Cao, L. Qin, H. P. Lee, J. Zhu, Proc. SPIE 2017, 10163,
101631X.
[104] M. T. Tolley, Proc. IEEE Int. Conf. Intell. Robot. Syst. (IROS) 2014,
561.
[105] M. Loepfe, C. M. Schumacher, U. B. Lustenberger, W. J. Stark, Soft
Rob. 2015, 2, 33.
[106] J. C. Nawroth, H. Lee, A. W. Feinberg, C. M. Ripplinger,
M. L. McCain, A. Grosberg, J. O. Dabiri, K. K. Parker, Nat. Bio-
technol. 2012, 30, 792.
[107] K. B. Ozutemiz, J. Wissman, O. B. Ozdoganlar, C. Majidi, Adv.
Mater. Interfaces 2018, 5, 1701596.
[108] C. Majidi, Mechanics of fluid-elastomer systems in soft robotics. In
Robotic Systems and Autonomous Platforms, Woodhead Publishing
2019, pp. 425–448.

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