Progress Reportwww.advmat.deShape Changing Robots: Bioinspiration, Simulation, andPhysical Realization
Dylan Shah, Bilige Yang, Sam Kriegman, Michael Levin, Josh Bongard,
and Rebecca Kramer-Bottiglio*
are specialized for a single task, and cannot
adapt their body to accomplish additional
tasks
after
manufacture.
Moreover,biological bodies are often highly regenerative, and able to repair and reconfigure
their large-scale architecture in the faceof significant damage or radical changes
to their components.[3] For example, salamanders regenerate amputated limbs,[4]and fragments cut from arbitrary portionsof planaria flatworms can rebuild (andrescale) their bodies to recover a full, correct anatomy.[3] Remarkably, many of thesesystems are able to retain information,such as learned memories, despite drastic
reconfiguration or total replacement of theirbrains.[5] In these integrated living systems,
intelligence, memory, learning, behavior,and body structure are all intertwined andemerge from the multiscale dynamics of the same robust andhighly fault-tolerant medium.
Evolution did not result in hard-coded body plans purely determined by genetic factors, but rather produced diverse examples ofintelligent self-modifying systems which adapt to numerous extragenomic influences.[6] In this way, biology serves as an important
proof-of-principle, and design challenge, for artificial intelligence andshape changing robots. Despite having access to this extensive set ofmodel systems, the realization of general-purpose, adaptive robots
has remained elusive. Researchers have proposed modular robots
that can be attached to each other to expand functionality,[7] passively
conforming universal grippers,[8] reconfigurable robotic skins,[9]self-assembling robot swarms,[10] gait-switching mechanisms[11] andcontrollers,[12,13] and algorithms that quickly re-adapt to multiple
distinct tasks.[14] Such approaches succeed at adaptation but operate
under the assumption that the robot’s body is only reconfigured or
reshaped due to external forces, and do not explore the possibility ofsynthetic machines that actively grow, regenerate, deform, or otherwise change the resting shape of their constituent components.
With the introduction of a conformable gripper by Hirose
in 1978,[15] followed by continuum robot arms,[16] silicone
grippers,[17] and variable stiffness actuators,[18] robots that canadapt to real-world environments by changing their shape are
becoming closer to reality. In particular, the idea of passively
conforming around objects during grasping has been quite successful.[17,19,20] Soft robots have shown potential in other applications, including human–robot interaction and exploration,
as reviewed by Kim et al.,[21] Rus et al.,[22] and others.[23,24] For
a comprehensive review of the role of deformation in singlefunction soft robots, the reader is referred to Wang et al.[25]One of the key differentiators between biological and artificial systems isthe dynamic plasticity of living tissues, enabling adaptation to different
environmental conditions, tasks, or damage by reconfiguring physicalstructure and behavioral control policies. Lack of dynamic plasticity is asignificant limitation for artificial systems that must robustly operate in thenatural world. Recently, researchers have begun to leverage insights fromregenerating and metamorphosing organisms, designing robots capable ofediting their own structure to more efficiently perform tasks under changing
demands and creating new algorithms to control these changing anatomies.
Here, an overview of the literature related to robots that change shape toenhance and expand their functionality is presented. Related grand challenges,
including shape sensing, finding, and changing, which rely on innovations
in multifunctional materials, distributed actuation and sensing, and somatic
control to enable next-generation shape changing robots are also discussed.

1. Introduction
Biological organisms are able to adjust their body structure,
stiffness, and behavior toward a complex anatomy that accommodates a variety of environmental demands and external perturbations. For example, octopuses have been observed to squeeze
through apertures that are much smaller than their body, hydrostatic caterpillars use peristaltic shape change to locomote acrossnumerous environments,[1] and moth larvae have been observed
to curl up to roll away from predators.[2] In contrast, robots often
D. Shah, B. Yang, Prof. R. Kramer-Bottiglio
School of Engineering & Applied Science
Yale University
9 Hillhouse Avenue, New Haven, CT 06511, USA
E-mail: rebecca.kramer@yale.edu
S. Kriegman, Prof. J. Bongard
Department of Computer Science
University of Vermont
E428 Innovation Hall, Burlington, VT 05405, USA
Prof. M. Levin
Department of Biology
Allen Discovery Center at Tufts University
Tufts University
200 Boston Ave. Suite 4604, Medford, MA 02155, USA
Prof. M. Levin
Wyss Institute for Biologically Inspired Engineering
Harvard University
3 Blackfan Cir, Boston, MA 02115, USA
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adma.202002882.

DOI: 10.1002/adma.202002882

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Several recent works have begun to explore the idea of using
the resting (non-actuated) shape of a robot’s body as a way to
expand the robot’s functionality. For example, one robot could
switch between spherical and cylindrical shapes for medical
applications such as navigating the digestive system.[26,27]
Another robot used origami techniques to change the diameterof its wheels to crawl over steps and under overhangs.[28] Nygaard
et al. introduced a quadrupedal robot that adjusted its leg length
to maximize locomotion speed across different surfaces.[29] In
another recent study, robotic skins were attached to sculptablematerials to create a robot that could change its shape to navigate over an obstacle, rather than searching for a path aroundthe obstacle.[30] Shape change can also be used to allow robots torecover from damage, sometimes outperforming adaptations incontrol policy.[31] In such examples, even relatively small changes
in resting body shape proved useful, pointing toward future general-purpose robots that leverage shape change to adapt to challenging real-world environments, as envisioned in Figure 1.
Despite the intense interest in the genesis and implicationsof shape for many fields, including medicine,[32] developmental
biology,[33] swarm robotics,[34] and evolutionary robotics,[35] aconsensus on how to quantify changes in shape has not beenreached. Taha et al., for instance, reported that 20 distinct shape
metrics are commonly used for 3D medical image segmentation.[32] For robots, one natural approach to measure shapechange is calculating a virtual “elastic deformation energy,”
which can be thought of as the energy required to stretch anelastic membrane from one shape to another.[36] However, formany robots, it is difficult to generate meshes or analytic expressions to represent their shape in real time, and it is common
in robotics to quantify shape-estimation errors using a small
subset of surface points and evaluating root-mean-squared
error (RMSE) or mean absolute error.[37–42] Several other discrete measurements of shape similarity have been proposed in
the robotics community, including Procrustes analysis (a modification of RMSE that is invariant to rotation, scaling, and translation errors),[40] a “shape index” (S = Perimeter/ (2 π × area ),which does not define a true metric),[10] and the Hausdorff
distance.[43]Here, we will use the term “shape changing robots” to referto robots that actively change their shape to adapt to their environment or gain new functionalities. Although this definition does not divide robots into two mutually exclusive sets, it
provides a framework to critically evaluate the state-of-the-art
design paradigms and materials used in robotics. Throughsuch introspection, and by observing biological mechanisms forshape change, we present several avenues where fundamental
advances in materials science can enable the next generationof adaptive, shape changing robots, potentially one day rivaling
biological systems that locally encode shape information to
enable dynamic plasticity and regeneration.[33]2. Biological Control of ShapeIn organisms ranging from flatworms to mammals, hierarchical processes regulate shape throughout development
to ensure the organism can succeed in its ecological nichethroughout its life cycle.[33] Each normal fertilized egg reliably

Adv. Mater. 2020, 2002882

Michael Levin is interested
in embodiments of mind
at multiple scales of
biology and engineering.
He received B.S. degrees
in computer science andbiology, followed by a Ph.D.
(Harvard University). After a
post-doc (Harvard Medical
School), he started his
independent lab focusing
on the biophysics of cell:cellcommunication during
embryogenesis, regeneration, and cancer. His group at
Tufts uses biophysical and computational approaches tostudy decision-making and basal cognition in cells, tissues,
and artificial living machines. He holds the Vannevar Bushchair, and directs the Allen Discovery Center, working
to crack the morphogenetic code for applications inregenerative medicine and machine learning.
Josh Bongard is the Veinott
Professor of computerscience at the University ofVermont and director of theMorphology, Evolution andCognition Laboratory. His
work involves automateddesign and manufactureof soft-, evolved-, andcrowd-sourced robots, aswell as computer-designed
organisms. He is the authorof the book How the Body
Shapes the Way We Think, the instructor of a Reddit-based
evolutionary robotics MOOC, and director of the robotics
outreach program Twitch Plays Robotics.
Rebecca Kramer-Bottiglio
is the John J. Lee AssistantProfessor of mechanicalengineering and materials
science at Yale University.
Working at the intersectionof materials, manufacturing,and robotics, her group isderiving new multifunctional
materials that will allow
next-generation robots toadapt their morphology andbehavior to changing tasks
and environments. She is recognized for her approach to
manufacturing liquid metals through printable dispersions
and scalable sintering methods and her developmentof robotic skins that turn inanimate objects into
multifunctional robots.

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www.advmat.deFigure 1. Next-generation shape changing soft robots will sense their environment and adjust their shape and behavior to accommodate environmental
or terrain changes.

self-assembles a default 3D anatomical structure with very
precise tolerances to a standard “target morphology” for thatspecies. This process is remarkably robust—for example, mammalian embryos can be cut in half and each will result in acomplete, normal body. In another example, land-based mammalian embryos thrive in an aqueous environment during fetal
development, yet prior to birth grow skeletal structures moresuitable for terrestrial locomotion.
Regenerative animals provide a unique example of how
shape change can be used to recover from damage. Whenthe limbs of a salamander are amputated, the cells are called
upon to proliferate, perform morphogenesis, and stop whena correct salamander limb is complete.[4] How the cells areable to ascertain the current morphology of the much larger
limb, and continually compare it to an intrinsic model of thetarget limb morphology to control individual cell behaviors
toward self-limiting repair, is largely unknown.[44] However,
it is clear that this somatic decision-making is an ancient,pre-neural example of intelligence and distributed computation in biological systems.[45–47] The tissue undergoing
dynamic shape change is the same tissue that is processing
information on-the-fly and making decisions about growthand form. Regenerative systems thus challenge engineers
to implement a kind of integrated, robust computational
medium that can continue to guide its own shape even as itis being deformed.
Recent progress in genomics and molecular biology haveshed crucial light on the origin of biological hardware: genes
encode signaling and structural components (proteins) at
the sub-cellular level. However, the genome does not directlyencode the target morphology, nor the algorithms sufficientto perform the kind of error correction seen during regeneration.[6] The search for the biological software that runs on
the genome-specified hardware has only begun, and two key
features are now apparent. First, the software is biophysical in
implementation. Bioelectric networks[48] enable cell collectives
to store pattern memories, generate spontaneous symmetrybreaking morphogenesis, recognize patterns, and integrate
information across large distances in the body[49]—all occurring outside the brain. Second, this embodied software strategy
enables dynamic plasticity. For example, caterpillars that learn

Adv. Mater. 2020, 2002882

conditioned responses to a chemical in their environment
retain that information as butterflies, despite complete brain
reconstruction during metamorphosis.[50] Planaria retain theirmemories across total brain removal and regeneration.[51,52]
Oviedo et al. showed a technique for creating two-headed
flatworms whose pieces continue to regenerate as two-headed
forms in subsequent rounds of damage and regrowth without
further treatment.[53] Tadpoles made to have eyes only on theirtails can see quite well, despite this unprecedented change
in sensory system architecture.[54] Next-generation robots
can learn from these examples of basal cognition coupled tophysical shape change,[45,55] perhaps embedding informationprocessing tools that guide shape change directly into therobot’s body.[56,57]

3. Simulated Shape Changing Robots
Although numerous organisms successfully exploit shapechange as a mechanism for adaptation and survival, it isunclear when and how robots should change their shape. To
address these questions, it would be useful to evaluate a large
number of diverse shape changing robots in different environments. However, manufacturing and deploying multiple robots
can be expensive, time consuming, and even dangerous. Thus,
simulations are often used to weed out undesirable designs
before attempting to build them in reality.[43,58–60]
Yet, under realistic design conditions, simulations cannot
exhaustively search the design space. Even using a small
number of mechanical parts, the size of the design space isenormous. For example, in voxel-based robot simulators,[61,62]
which use voxels as structural building blocks, there are
4.5 × 108 unique ways to arrange 12 voxels to form a robot, andthe design space (the number of possible designs) increases
exponentially with each additional block.[63] As a result, evolutionary[64–67] and learning[68,69] algorithms are usuallyemployed to efficiently explore the vast space of possible robot
designs.[70]Directly incorporating biologically inspired mechanisms ofshape change—for example, slowly extruding limbs during
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4. Shape Changing Robots

Figure 2. Simulations can automatically generate complex shape changing
robots, including ones that recover from damage through shape change.
The quadrupedal robot shown here discovered that, after being damaged,
it was more advantageous to change its shape than adapt its control
policy. Adapted with permission.[31] Copyright 2019, Sam Kriegman.

final, legged form of the robot—has been shown to speed theevolution of robust, adaptive behavior in simulated robots.[71]In other cases, evolved robots have rediscovered natural strategies on their own. For example, simulated soft robots evolved
control policies that allowed them to squeeze their bodies
through small apertures.[72] In another study, a simulated
quadruped had all four of its legs simultaneously amputated;
subsequently, evolution discovered that specific deformation
to the resting shape could recover the robot’s function more
effectively than re-adapting its control policy for its new body
(Figure 2),[31] which is analogous to biological regeneration,although using different mechanisms (mechanical deformation versus regrowth).
Computational design can also discover novel ideas notknown to occur in nature. For example, regeneration was not
the only successful adaptation strategy discovered by evolution in the experiments reported by Kriegman et al.[31] Whenthe simulated robot was cut in half, evolution sometimes
decreased the damaged robot’s surface area by compressing theremaining limbs, and other times it expanded the robot’s limbs,
compressed its spine, and flipped over to recover an inverted
locomotion strategy. Within and across nine different damage
scenarios, the best shape-shifting strategies were diverse andcreative: very few were a recapitulation of a familiar biologicalexample. Thus, simulation can provide non-intuitive designs
beyond those inspired by natural systems.

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While biological and simulated systems alike indicate thateven small shape adaptations can enable recovered or new
functionalities, realizing shape changing robots in hardware
presents its own set of unique challenges. However, we see
immense potential in the convergence of multifunctional materials and soft robotics toward the goal of shape changing robots,and some promising examples already exist. Here, we focus
on examples of physical robots that employ shape change toenhance, recover, or expand their capabilities.
Several robots have leveraged functional materials to change
shape, to attain new gaits, and avoid obstacles, thereby solving
problems that are traditionally in the realm of mechanics[73]and computer science.[74] For example, Shah et al. proposed arolling soft robot that uses a cable-driven robotic skin to sculpt
an inner clay body into a different morphology (Figure 3a).[30]Initially cylindrical, the robot could roll on flat ground; when
it encountered an obstacle in its path, the robot changed into
a dumbbell shape to roll over the obstacle without changing its
gait or path. While the robot was designed with 20 independent
degrees of freedom (DoFs) for shape changing, it was foundthat only a single DoF was necessary to perform the required
obstacle avoidance. In another example, a caterpillar-inspired
robot called GoQBot changed its shape to switch between controlled crawling and ballistic rolling gaits (Figure 3c).[75] Using
shape memory alloy (SMA) coils to deform its silicone body insmall arches, the robot could crawl forward. Upon rapid activation of the SMA actuators, the robot curled into a ball shapeand initiated rolling in under 250 ms. Such a maneuver could
be useful for escaping predation, rolling downhill in an energyefficient manner, and increasing the robot’s effective dimensions to enable it to easily overcome obstacles larger than its
flattened shape. In yet another example, Lee et al. proposed arobot that folds fabric and sheets of poly(ethylene terephthalate)(PET) to enlarge its wheels and climb onto step-like platforms(Figure 3d).[28] The robot was then able to collapse its wheels
to roll under narrow gaps, allowing the robot to operate over awide range of terrains and environmental conditions. Despite
being primarily made of flexible materials, the robot was able touse cleverly designed folding patterns to support a payload 400×
the weight of its wheels. To adapt to changing flow conditions
underwater, Ishida et al. developed a quadruped with a 4-DoF
morphing top that could change its drag and lift coefficients togain assistance from the current when the flow aligned with its
direction of motion, and reduce drag when walking against theflow.[76] Similar to the rest of the robots in this category, only a
few DoF for shape change were required to allow these robots
to continue operation, without searching for complex control
strategies to deal with changes in its environment.
Other soft robots have used shape change to switch between
locomotion on land, in air, and/or in water. Baines et al.
recently demonstrated a life-size turtle- and tortoise-inspired
morphing limb that could change between flipper and leg
shapes, as a step toward amphibious robots which can accomplish both aquatic and terrestrial locomotion (Figure 3f).[77,78]
The transformation from flipper to leg occurred via coupledvariable stiffness and actuation materials distributed along thelength of the morphing limb. Initially in a flipper shape, fluidic

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www.advmat.deactuators inflated, causing a change in limb cross-sectional
geometry to transition to the load-bearing leg shape. The variable stiffness material, a thermoset polymer with embedded
heaters, controllably softened and stiffened the limb to lockand unlock the geometries. Hawkes et al. designed an origami robot that could fold between shapes resembling a boat

and a plane (Figure 3e).[79] Although these structures were
not demonstrated moving through air or water, locomotion
could potentially be achieved through integration of additional
actuators. For example, other lightweight origami robots[80]attained controlled flight resembling the locomotion paths ofinsects.[81,82]

Figure 3. Shape changing soft robots. a) Cable-driven clay morphing robot changing shape to avoid an obstacle. Adapted with permission.[30] Copyright
2019, IEEE. b) Cylindrical rolling robot flattens to switch from a rolling gait to a crawling gait. Reproduced with permission.[87] Copyright 2020, The
Authors. c) Caterpillar robot changing from inching to rolling. Adapted with permission.[75] Copyright 2011, IOP Publishing. d) Variable diameter origami
wheel. Adapted with permission.[28] Copyright 2017, Mary Ann Liebert, Inc. e) Programmable origami robot transitioning between a “boat” and a “plane”
shape. Adapted with permission.[79] Copyright 2010, National Academy of Sciences. f) Variable stiffness morphing limb for an amphibious legged robot.
Adapted with permission.[78] Copyright 2020, IOP Publishing. g) Magnetically actuated soft capsule for drug delivery. Adapted with permission.[26]Copyright 2012, IEEE. h) Tissue engineered robot with light-activated morphing wings. Reproduced with permission.[83] Copyright 2019, Wiley-VCH.

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www.advmat.deFigure 4. Sheets that can sense their 3D shape. Recent advances in shape-sensing e-skins use several sensing modalities, ranging from discrete
to continuous approaches. Left to right: hexagonal PCBs with integrated accelerometers, sensor network with accelerometers and magnetometers,
optical fibers in silicone foam, fiber Bragg gratings in silicone. Image for Hexagonal PCBs: Adapted with permission.[40] Copyright 2012, IEEE. Image forsensor network: Reproduced with permission.[37] Copyright 2012, IEEE. Image for opical fiber: Adapted with permission.[91] Copyright 2018, The Authors,published by American Association for the Advancement of Science. Image for fiber Bragg grating: Adapted with permission.[41] Copyright 2019, IEEE.

Shape change has also been used in human-centered applications. Yim and Sitti proposed a millimeter-scale, magnetically actuated capsule that can locomote and switch between aspherical and cylindrical shape (Figure 3g).[26,27] Although therobot could locomote in each shape, the robot used shape change
to improve the precise positioning of its endpoints, and deliver
simulated drugs inside of a synthetic stomach model. Anotherproposed millimeter-scale robot had oscillating cardiac muscle
cells attached to the back of airplane-shaped “wings” to propel it
across the surface of the liquid medium in a cell culture, simulating applications in targeted drug delivery in the human body
(Figure 3h).[83] When the “wings” absorbed near-infrared radiation, heat spread to their attached temperature-sensitive hydrogel
actuators to induce curling. The curled shape had a higher
bending stiffness that prevented further swimming motions,allowing the robot to stop directly above a target location andrelease anticancer drugs onto cancer cells. Finally, researchers
have demonstrated that shape change can alter our perception ofrobots during human–robot interactions,[84–86] thereby improving
these exchanges and increasing the operational value of the robot.
Researchers have also explored the potential for automatically designing shape changing robots in simulationand transferring successful designs to reality. Kriegman et al.
developed a scalable method to create physical shape changing
voxel-based modular robots, and successfully transferred two
strategies of shape change discovered in simulation to reality;
however, functionality (locomotion) did not transfer.[31] Later,
locomotion was transferred from simulation to reality using
an improved version of the same system (silicone-based pneumatic voxels), however these locomoting physical robots did notchange shape.[43] Another simulated shape changing robot used
an inflatable core to transition between a cylindrical shape anda flattened sheet-like shape to adapt its locomotion to different
environments.[87] Initially a rolling cylinder on flat terrain, therobot changed to the flattened shape with an inchworm gait
to maintain efficient locomotion up an incline. This simulated
robot design was successfully transferred to reality, thereby realizing a physical robot that utilizes shape change to gain accessto additional environments (Figure 3b).

5. Grand Challenges
The examples given herein highlight how shape change
can allow a robot to enhance or expand its functionality via
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adaptation or regeneration. However, to develop robots rivaling
biological systems, several challenges need to be addressed.
First, it is unclear how to optimally embed proprioception andintelligence into such machines to enable robots to sense theirshape. Additionally, to design robots for tasks more complicatedthan can be solved through human intuition, it is imperative toautomate the design of shape changing robots. Finally, transferring highly functional designs to reality requires functional
materials that can be integrated into systems that can attainprecise control over shape.
5.1. Shape Sensing
Next-generation shape changing robots will rely on proprioception to determine when a target morphology has been reached,
optimize shape change through intermediate shapes, anddecouple deformation-driven task performance from global
shape change. During regeneration, an organisms’ cells compare
their body’s current state to the target morphology, although theexact mechanisms for these processes are poorly understood.[4]Techniques exist for measuring the deformation of fixed-shaperobots, which generally rely on a comparison to the reference
body shape at rest. For example, continuum manipulator modeling relies upon assumptions about cross-sectional geometry,[88]while traditional robot kinematics assume each component is arigid body.[89] However, if the reference body shape is changing,such an approach is no longer applicable. Thus, intrinsically(i.e., without external components) measuring the state of shapechanging robots largely remains an unsolved problem.[90]There have been several attempts to detect the shape of nonstretchable robot “skins” (Figure 4). Many studies treat the skinas an inextensible sheet of rigid elements joined by known
axes of rotation (Figure 4, left). Hoshi and Shinoda arranged
24 printed circuit boards (PCBs) into a mesh and estimatedinter-PCB rotations using accelerometers and magnetometers.[39]
Building upon this work, Mittendorfer et al. developed rigid
sensorized PCBs that could be connected and wrapped aroundrobots.[40] Hermanis et al. then used a grid-like arrangement ofaccelerometers and gravitometers on a flexible fabric sheet.[37]In these studies, no attempt was made to estimate the true
shape of the underlying object; the objective was to measure
the location of the PCBs’ centers with high precision.
Other proposed approaches leveraged techniques frommachine learning and statistics to process sensor signals and2002882 (6 of 12)© 2020 Wiley-VCH GmbH

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www.advmat.deextract a continuous estimate of the shape of the skins (Figure 4,
right). Such an approach is more general, and could potentiallylead to more accurate estimations of the state of shape changing
soft robots. Rendl et al. used data from 16 piezoelectric bend
sensors, which experience a potential difference on their electrodes during bending, on a PET sheet to estimate the sheet’s
shape as a combination of several shape primitives.[38] Anotherstudy used neural networks to estimate the shape of a silicone
plate using inextensible optical fiber Bragg gratings strain sensors (coated with ORMOCER inorganic–organic hybrid polymers).[41] Van Meerbeek et al. embedded an array of opticalfibers inside an open-celled elastomeric foam and used their
output to predict the mode of deformation and angle of deformation of the foam, using machine learning algorithms.[91]Several challenges emerge from inspection of these works.
Some shortcomings arise from material limitations: none ofthe proposed approaches could accommodate or detect in-planestrains. There are solutions to making stretchable strain sensors[92–94] and stretchable circuits,[95,96] but is is unclear how totransfer these advances to sense a variety of dissimilar shapes.
For instance, how many sensors, and what type of sensors, areneeded to detect the shape of each robot in Figure 3? Biologicalorganisms, such as humans, distribute multimodal sensing
capabilities across their skin and at multiple depths,[97] andthroughout their musculoskeletal system.[98] The efficiency ofthis approach is unclear, as evolution selects for survival, andbiological constraints do not map perfectly to the constraints
and cost–benefit relationships relevant in robotics. Additionally,
how can sensors be developed to decouple large in-plane strainsfrom transverse strain (pressure), at sufficiently high resolution? Some progress has been made toward independent multimodal sensing for robots with a fixed resting shape,[99] but thesemethods have yet to be tested in shape changing robots. Finally,
the proprioceptive sensors used in shape changing robots should
be simultaneously robust to repeated applications of externalstrain, able to withstand undesired local shear forces, and easy
to manufacture at the densities needed to detect the complicateddeformations experienced during typical operations.
Other challenges are algorithmic: each proposed sensing
approach—broadly, what we classify as discrete versus continuous approaches—has drawbacks. The discrete method insufficiently handles continuously deformable surfaces, while thedata-driven continuous approach only operates under limited
deformation conditions. Solutions in this regard could involve
applying techniques from differential geometry to fuse rotationand strain data to generate smooth surface estimates.[100–103] In
the work by Stanko et al.,[100] a single algorithm was used toestimate the shape of objects as dissimilar as a mushroom, achair, and a guitar. The only required input was distance estimates between successive orientation measurements. Whenpaired with stretchable strain sensors[92–94] and stretchable
circuits,[95,96] such algorithms could provide solutions to theoverall problem of estimating the shape of a morphing robot.

solutions, there are many unresolved fundamental questionsin this area. For example: How will a robot know that its current shape is no longer optimal, and it should search for a newshape and behavioral policy? How should robot shapes andbehaviors be generated given only environmental inputs? Here,
we explore how the state-of-the-art could be improved to create
automated pipelines for finding effective shapes and designingsophisticated shape changing robots.
The application of evolutionary algorithms to simulated
robots has begun to address the questions above, but only
within empirical studies with one or two objectives for the
robots to solve.[31,87,104] Further, higher-level and/or transenvironmental tasks have been largely unexplored. Althoughevolved simulated robots have transitioned between terrestrial
and aqueous environments,[64] no general understanding of
how shape change can equip a machine to travel through air,water, or over land yet exists. Transitioning between shapes tosolve widely varied tasks such as locomotion and grasping has
not been considered, nor has changing shape in real time to
avoid damage. To address these scenarios, the major challenges
of catastrophic forgetting,[105] transferability,[106,107] simulation
inaccuracies, system identification,[65] and the limited efficiency and sub-optimality of search algorithms likely need tobe considered.
Most existing studies on simulated morphing ignored thecosts of shape change. Although shape change is sometimes
more computationally efficient than searching for control policies,[31,87] in hardware implementations, there is an energetic
cost associated with changing shape. Energy must be expended
to power actuators (e.g., SMAs and shape memory polymers,[108,109] dielectric elastomer actuators,[110] or various othersoft actuators[111]) and materials may need to be replaced during
regeneration or growth (e.g., via inflation,[31,112] additive manufacture,[113] etc.). Quantifying both the computational and energetic costs of shape change will be important to the realizationof shape changing robots that operate in the real world.
Additionally, it is challenging to specify algorithmic constraints that guarantee that the shape and behavior solutions
found are physically realizable. While it is possible to stretch
any two homeomorphic shapes into each other, generating
designs which are robust to simulator inaccuracies requires
sufficiently realistic constraints, and algorithms that can navigate a constrained, likely highly non-convex, search space.
Numerous methods to navigate the simulation–reality gap
have been proposed, including injecting noise into the simulations[106] and estimating an assumed transferability function.[107]Other approaches for crossing the simulation–reality gap in soft
robotics include reducing the robot to quasi-static motions[60]and simplifying the search space.[104] However, these simplifications dramatically reduce the range of capabilities that can be
evolved and limit the scope of tasks that can be completed.
5.3. Shape Changing

5.2. Shape Finding
It is not obvious which shape a robot should assume in a given
environment. While evolutionary robotics[35] may yield potential

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Most morphing robots in the literature have been designed toattain a limited set of shapes as a proof-of-concept. Increasing
the controllable degrees of freedom should generally improve
the shape changing abilities of robots (Figure 5), but such

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www.advmat.deFigure 5. Additional controllable degrees of freedom will allow shape changing robots to approach the capabilities of biological systems. Current
shape changing robots leverage relatively few controllable degrees of freedom (DoFs) to adapt, while some biological organisms leverage dozens of
independent DoFs during normal motions, and growth allows organisms countless independent DoFs for changing their shape. Left to right: Morphing
wheel; clay-sculpting morphing robot; voxel-based robots; octopus squeezing through a 1-inch diameter hole; tadpole-to-adult transition for a Microhyla
fissipes frog. Image for morphing wheel: Adapted with permission.[28] Copyright 2017, Mary Ann Liebert, Inc. Image for morphing robots: Adaptedwith permission.[30] Copyright 2019, IEEE. Image for voxel-based robots: Adapted with permission.[31] Copyright 2019, Sam Kriegman. Octopus image:Reproduced with permission.[114] Copyright 2012, James B. Wood. Frog image: Reproduced under the terms of the CC-BY Creative Commons Attribution
International License (https://creativecommons.org/licenses/by/4.0/).[142] Copyright 2019, The Authors, published by Frontiers.

complexity comes with trade-offs and limitations. For example,
origami robots[80] are typically designed to attain a limited set ofshapes by folding at discrete locations (Figure 5, left).[28] Additional shapes could be achieved by adding or utilizing additional
folds, but would increase the system’s complexity. The claysculpting robotic skins[30] were designed to stretch with theirsurface to attain a continuous range of shapes; however, they
were restricted to shapes with circular cross-sections (Figure 5,
second from left). Adding additional cables to this design, more
complicated profiles could be attained, but the robot could not
attain, for example, a quadrupedal shape. The field needs fundamentally new approaches to shape change, including novel
actuators and growth mechanisms, paired with complementary
technologies to control surface strain.
Typically, a robot’s components are optimally placed for its
morphology and target function. Yet, for a shape changing robot,
optimal component placement will differ between morphologies.
One solution to this problem is to increase the sensor and actuator component density throughout the robot to increase its controllable degrees of freedom. Potential ways to increase sensor
and actuator density include multifunctional materials,[115–117]
3D circuits,[95] skins with tightly integrated sensing and actuation,[118] and multimodal sensing arrays.[97] However, numerous
issues arise when increasing component density, including
cross-talk, data processing, and complicated wiring schemes.[90]Communication protocols for large numbers of sensors or actuators is another challenge. Pneumatic robots, for example, usually require one three-state (inflate, hold, release) valve set per
actuator. Although pneumatic multiplexing has been shown to
independently control large arrays of actuators,[119] multiplexers
often result in a lower attainable actuation frequency.
To further expand the range of shapes that morphing robots
can attain, additional actuation modes need to be introduced.
Many shape changing robots utilize a single actuation mode,for example, tension,[30] volumetric expansion,[120] origami
folding,[28] or bending.[83] In contrast, many shape changing
organisms exploit multiple actuation modes. For example, thetentacles of cephalopods and many species’ tongues tightly
integrate muscles with different orientations to achieve torsion,
extension, and bending (Figure 5, second from right).[121,122]
Integration of multiple actuation modes has largely been
unexplored in the context of shape changing robots, and is aAdv. Mater. 2020, 2002882

major unsolved challenge. Much can be learned from the fieldof microrobotics, where many robots have been built using
stimuli-responsive polymers. Often these robots contain several
actuation modes in addition to novel functionalities, such as
camouflage.[123–126] Stimuli used in these micro-machines (magnetic fields,[123,125] chemical vapor,[124] light,[123] and solvent[126])
are usually less practical for larger-scale soft robots due to unfavorable strength-to-weight ratios at larger length scales. With
additional advances in fundamental materials science, implementation of stimuli-responsive polymers in large-scale robots
may become viable.
Combining novel actuators, robot-simulators, and shapesensing technologies, robots could then utilize 3D “shape servoing,” or closed-loop control of shape, to converge on a desired
shape. In a 2D shape servoing application, an external visionsystem was paired with a robot arm to deform materials into
a desired shape.[127] Building upon such extrinsic methods ofshape control, it is conceivable that there will be optimal ways to
use a robot’s actuators to smoothly shift between desired shapes.
Insight into how to efficiently change shape could come fromobserving how sculptors smoothly sculpt clay between manyhighly dissimilar shapes.[30] Formalizing intuition and observation into computationally tractable shape-control loops could
come from mechanics-based modeling and solving an inverse
problem (i.e., calculating the required control sequence to attaina desired shape), or using data-driven reinforcement learningmodels to solve problems in an automated, closed-loop fashion.
As a robot undergoes large changes in shape, the surface
stress can often approach the maximum available actuator
stress and restrict further motion. To overcome these limitations, one solution is to design robots that can reversibly
undergo large deformations.[21,24] In contrast, many biologicalorganisms experience large-scale, growth-driven shape change
in response to numerous stimuli,[6,33] promoting long-term viability of the organism (Figure 5, right). It is hypothesized that
control of these factors could eventually lead to synthetic organisms with programmable growth from varied initial states into
target morphologies. Recent studies have proposed continuum
robots that can grow along an arc-like path, using eversion[79]and tip-based additive manufacturing.[113] Progress is also being
made in related fields, such as biohybrid robots,[128] expanding
polymers[129] and hydrogels,[130] and simulating growing

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www.advmat.deFigure 6. Variable modulus materials can allow robots to tune their morphing trajectories and selectively maintain desirable shapes. a) Granular jamming allowed an air-filled robot to selectively control its expansion (left) and generate a wide range of shapes (right) for locomotion. Adapted withpermission.[132] Copyright 2009, IEEE. b) Low-melting-point-alloy inclusions in a silicone matrix allowed reversible morphing and shape memory inarbitrary geometries. The images show how the “switchable stretchability” material could tune the trajectory of a single inflatable actuator. Reproducedwith permission.[136] Copyright 2019, Wiley-VCH. c) Variable stiffness material embedded in a morphing limb was used for softening during shapechange, and stiffening to hold either a flipper or leg shape in aquatic and terrestrial environments, respectively. Tortoise and flipper images on theright: Adapted with permission.[78] Copyright 2020, IOP Publishing. The turtle image is from Pixabay.

robots.[34] However, the load-bearing capabilities of many ofthese systems are low, and the remaining systems have limited
controllability and ability to grow into unplanned geometries.
Variable modulus materials (reviewed by Manti et al.[131])can also potentially be used to control the deformation of sections during shape change, improve load-bearing capabilities, and reduce energy requirements. For example, one robot
selectively stiffened sections of its outer membrane to direct
deformation when the inner chamber was inflated, producing
locomotion (Figure 6a).[132] Granular jamming, used in thisexample, is stretchable but generally has low tensile modulus
relative to other state-of-the-art variable stiffness materials,
including conductive epoxies[133] and laminar jamming.[134,135]
Unfortunately, these alternative materials do not perform wellover tensile strains larger than a few percent. Recent advancessuch as cutting serpentine patterns in layer jamming sheets
to allow stretch in one direction,[18] and low-melting-pointalloy inclusions in a silicone matrix[136] (Figure 6b) have thepotential to allow robots to control their stiffness while controlling large strains during shape change. By leveraging variable stiffness strategies such as layer jamming,[134,135] granularjamming,[8,18] or variable stiffness materials such as thermoset
polymers,[133] robots could also increase their load-bearing

Adv. Mater. 2020, 2002882

capabilities in each attained shape, without requiring readaptation of control strategy. For example, in the turtle- andtortoise-inspired morphing limb proposed by Baines et al., therobot could hold a flipper-like shape for hydrodynamically efficient swimming, and switch to a load-bearing leg-like shapefor walking using a softening/stiffening thermoset epoxy(Figure 6c).[77,78] Stiffening could also allow a robot to lockin its shape and disengage its morphing actuators, to reduceenergy requirements. Researchers have shown this concept
in various applications, including using a variable stiffness
conductive epoxy composite to selectively soften and stiffen agripper to maintain the position of its payload without additional energy input or control loops.[133] In other examples,
researchers employed layer[137] and granular jamming[138] toselectively soften and stiffen continuum manipulators to holda pose.

6. Conclusions and Outlook
We have surveyed the literature related to shape changing
robots, from bioinspiration to simulation and hardware
implementation. By actively morphing into different shapes,

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many state-of-the-art robots have been shown to expand theircapabilities by gaining new locomotion modes,[28,75] avoiding
obstacles,[30] or transitioning between body shapes suitable
for swimming or walking.[77,78] Increased closed-loop control
of morphology and material properties could eventually allow
robots to rival the dynamic plasticity attained by natural systems. However, many open questions remain regarding when,how, and to what degree shape change is useful.
The phenomenon of shape change overlaps with considerations of adaptation at differing spatial and temporal scales.
Spatially, for example, a rigid robot may experience local shapechange at a joint, but none within the rigid segments fromwhich it is comprised. In contrast, a soft robot may change
its shape at all relevant length scales, globally and locally.
Organisms[6] or robots[120] capable of physical developmental
change may change their body plans slowly over their lifetimes,
while faster, local deformations may occur at joints during
specific behaviors. Consideration of how to seamlessly modeland integrate such capabilities into the design of robots acrosslength scales, while simultaneously balancing traditional design
goals such as velocity, payload, and force output, remains alargely unsolved problem.
Much can be gained in future research by exploiting lessons of robustness from biology. A key component of biological embedded control is its multiscale goal-seeking nature.[139]Functional swarms—for example, termite colonies that maintain a shared nest—are made of individual bodies that eachbuild and repair to their particular target morphology. This isdone by organs that maintain specific physiological and functional specifications, and tissues which deform to maintainhistological targets. These are, in turn, made of cells which optimize various parameters as they migrate, proliferate, and differentiate. Inside the cells are genetic and metabolic networks that
also have degrees of memory, robustness, and homeostasis.
The ability of each nested level to have its own local morphogenetic goals (in the cybernetic sense) contrasts with today’s
robots, which are largely made of unintelligent parts, althoughsome early examples of embedded distributed computation andsoft logic gates are emerging.[140,141]
As demonstrated by this progress report, innovations in
multifunctional materials, soft robotics, and evolutionary
robotics are converging to make shape changing robots more
viable. Such shape changing robots should be viewed as important model systems for evolutionary biology and regenerative
medicine,[10] providing simplified “bodies” in which to test theories of tissue computation, brain–body control, and regenerativealgorithms, and in which to abstract the profound lessons oflife-as-it-could-be from evolutionary contingencies.[33,34] Indeed,
control of morphology is an unsolved problem in medicine—from fixing birth defects to traumatic injury repair, aging, andcancer. Thus, the question of shape and its dynamic control isan emerging new science at the intersection of evolution, biomedicine, machine learning, and robotics.

Acknowledgements
This work was supported by an NSF Emerging Frontiers in Researchand Innovation grant (# 1830870). D.S. was supported by a NASA SpaceTechnology Research Fellowship (80NSSC17K0164).
Adv. Mater. 2020, 2002882

Conflict of Interest
The authors declare no conflict of interest.

Keywords
anatomical homeostasis, evolutionary robotics, morphing robots,reconfigurable robots, regeneration, smart materials, soft robotics,
synthetic morphogenesis
Received: April 28, 2020
Revised: June 1, 2020
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