Articles
https://doi.org/10.1038/s42256-020-00263-1

A soft robot that adapts to environments throughshape change
Dylan S. Shah 1,3, Joshua P. Powers
Rebecca Kramer-Bottiglio 1 ✉, Liana G. Tilton1, Sam Kriegman

2,3, Josh Bongard2 and2Many organisms, including various species of spiders and caterpillars, change their shape to switch gaits and adapt to different
environments. Recent technological advances, ranging from stretchable circuits to highly deformable soft robots, have begun
to make shape-changing robots a possibility. However, it is currently unclear how and when shape change should occur, andwhat capabilities could be gained, leading to a wide range of unsolved design and control problems. To begin addressing thesequestions, here we simulate, design and build a soft robot that utilizes shape change to achieve locomotion over both a flatand inclined surface. Modelling this robot in simulation, we explore its capabilities in two environments and demonstrate theautomated discovery of environment-specific shapes and gaits that successfully transfer to the physical hardware. We foundthat the shape-changing robot traverses these environments better than an equivalent but non-morphing robot, in simulation
and reality.

N

ature provides several examples of organisms that utilize
shape change as a means of operating in challenging, dynamic
environments. For example, the spider Araneus rechenbergi1,2 and the caterpillar of the mother-of-pearl moth (Pleurotyaruralis)3 transition from walking gaits to rolling in an attempt toescape predation. Across larger timescales, caterpillar-to-butterfly
metamorphosis enables land-to-air transitions, while mobile tosessile metamorphosis, as observed in sea squirts, is accompanied
by radical morphological change. Inspired by such change, engineers have created caterpillar-like rolling4, modular5–7, tensegrity8,9,plant-like growing10 and origami11,12 robots that are capable of somedegree of shape change. However, progress towards robots thatdynamically adapt their resting shape to attain different modes oflocomotion is still limited. Further, design of such robots and theircontrollers is still a manually intensive process.
Despite the growing recognition of the importance of morphology and embodiment on enabling intelligent behaviour in robots13,
most previous studies have approached the challenge of operatingin multiple environments primarily through the design of appropriate control strategies. For example, engineers have created robots
that can adapt their gaits to locomote over different types of terrain14–16, transition from water to land17,18 and transition from air
to ground19–21. Other research has considered how control policies
should change in response to changing loading conditions22,23, or
where the robot’s body was damaged24–26. Algorithms have also
been proposed to exploit gait changes that result from changing therelative location of modules and actuators27, or tuning mechanical parameters, such as stiffness28. In such approaches, the resting
dimensions of the robot’s components remained constant. These
robots could not, for instance, actively switch their body shape
between a quadrupedal form and a rolling-optimized shape.
The emerging field of soft robotics holds promise for building shape-changing machines29. For example, one robot switchedbetween spherical and cylindrical shapes using an external magnetic field, which could potentially be useful for navigating internal organs such as the oesophagus and stomach30. Robotic skins

wrapped around sculptable materials were shown to morph between
radially symmetric shapes such as cylinders and dumbbells to use
shape change as a way to avoid obstacles31. Lee et al. proposed a
hybrid soft–hard robot that could enlarge its wheels and climb onto
step-like platforms32. A simulated soft robot was evolved to automatically regain locomotion capability after unanticipated damage,by deforming the shape of its remnant structure33. With the exception of the study by Kriegman et al.33, control strategies and metamorphosis were manually programmed into the robots, thereby
limiting such robots to shapes and controllers that human intuitionis capable of designing. However, there may exist non-intuitive
shape–behaviour pairings that yield improved task performance ina given environment. Furthermore, manufacturing physical robots
is time consuming and expensive relative to robot simulators such as
VoxCad34, yet discovering viable shape–behaviour pairs and transferring simulated robots to functioning physical hardware remainsa challenge. Although many simulation-to-reality (‘sim2real’) methods have been reported24,25,35–43, none have documented the transferfrom simulation to reality of shape-changing robots.
To test whether situations exist where shape change improves arobot’s overall average locomotion speed within a set of environments more effectively than control adaptations, here we present a
robot that actively controls its shape to locomote in two different
environments: flat and inclined surfaces (Fig. 1). The robot had aninternal bladder, which it could inflate/deflate to change shape, and asingle set of external inflatable bladders that could be used for locomotion. Depending on the core’s shape, the actuators created different motions, which could allow the robot to develop new gaits andgain access to additional environments. Within a soft multi-material
simulator, an iterative ‘hill-climbing’ algorithm44 generated multiple
shapes and controllers for the robot, then automatically modified
the robots’ shapes and controllers to discover new locomotion strategies. No shape–controller pairs were found that could locomote
efficiently in both environments. However, even relatively smallchanges in shape could be paired with control policy adaptations toachieve locomotion within the two environments. In flat and even

Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT, USA. 2Department of Computer Science, University ofVermont, Burlington, VT, USA. 3These authors contributed equally: Dylan S. Shah, Joshua P. Powers. ✉e-mail: rebecca.kramer@yale.edu

1Nature Machine Intelligence | VOL 3 | January 2021 | 51–59 | www.nature.com/natmachintell

51Articlesa

NaTuRe MacHine InTelligence
External actuators
control behaviourcb Cannot roll uphilldSide view

Internal pressure
controls shapeefSide viewFig. 1 | Shape change can result in faster locomotion speeds than control adaptation, when a robot must operate in multiple environments. a, Using
inflatable external bladders, rolling was the most effective gait on flat ground. b, Rolling was ineffective on the inclined surface. c,d, Search discovered a flat
shape (achieved by deflating the inner bladder; c) and crawling gait (d) that allowed the robot to succeed in this environment. e,f, After discovering thesestrategies in simulation, we transferred learned strategies for rolling (e) and inchworm motion (f) to real hardware. Scale bars, 5 cm.

slightly inclined environments, the robot’s fastest strategy was toinflate and roll. At slopes above a critical transition angle, the robot
could increase its speed by flattening to exhibit an inchworm gait.
A physical robot was then designed and manufactured to achieve
similar shape-changing ability and gaits (Fig. 2). When placed inreal-world analogues of the two simulated environments, the physical robot was able to change shape to locomote with two distinct
environmentally effective gaits, demonstrating that shape change isa physically realistic adaptation strategy for robots.
This work points towards the creation of a pipeline that takes
as input a desired objective within specified environments, automatically searches in simulation for appropriate shape and control
policy pairs for each environment, and then searches for transformations between the most successful shapes. If transformations
between successful shapes can be be found, those shape–behaviour
pairs are output as instructions for designing the metamorphosing
physical machine. In this Article, we demonstrate that at least someshape–behaviour pairs, as well as changes between shapes, can betransferred to reality. Thus, this work represents an important step
towards an end-to-end pipeline for shape-changing soft robots thatmeet the demands of dynamic, real-world environments.

Results

The simulated robot. We initially sought to automate search for
efficient robot shapes and control policies in simulation, to test
our hypothesis that shape and controller adaptation can improve
locomotion speeds across changing environments more effectively
when given a fixed amount of computational resources, comparedwith controller adaption only. To verify that multiple locomotion
gaits were possible with the proposed robot design, we first used ourintuition to create two hand-designed shape and control policies:
one for rolling while inflated in a cylindrical shape (Fig. 1a), andthe other for inchworm motion while flattened (Fig. 1d). Briefly,
the rolling gait consisted of inflating the trailing-edge bladder to tip
52

the robot forward, then inflating one actuator at a time in sequence.
The hand-designed ‘inchworm’ gait consisted of inflating the four
upward-facing bladders simultaneously to bend the robot in anarc. We then performed three pairs of experiments in simulation.
Within each pair, the first experiment automatically sought robot
parameters for flat ground; the second experiment sought parameters for the inclined plane. Each successive pair of experimentsallowed the optimization routine to control an additional set of therobot’s parameters, allowing us to measure the marginal benefit ofadapting each parameter set when given identical computational
resources (summarized in Table 1 and Fig. 3). The three free parameter sets of our shape-changing robot are shape, orientation relative
to the contour (equal elevation) lines of the environment, and control policy (Fig. 3a). This sequence of experiments sought to determine whether optimization could find successful parameter sets ina high-dimensional search space, while also attempting to determine to what degree shape change was necessary and beneficial.
In all experiments, fitness was defined as the average speed therobot (measured in body lengths per second (BL s−1)) attained overflat ground or uphill, depending on the current environment ofinterest, during a fixed period of time. Parameters for the simulation were initialized based on observations of previous robots31,45
and adjusted to reduce the simulation-to-reality gap after preliminary tests with physical hardware (see Methods for additional
details). The results reported here are for the final simulations that
led to the functional physically realized robot and gaits.
In the first pair of experiments, we sought to discover whether
optimization could find any viable controllers within a constrained optimization space, which was known to contain the viablehand-designed controllers. Solving this initial challenge served totest the pipeline before attempting to search in the full search space,which has the potential to have more local minima. The shape andorientation were fixed (flat and oriented length-wise, θ = 90°, for
the inclined surface, cylindrical and oriented width-wise, θ = 0° for

Nature Machine Intelligence | VOL 3 | January 2021 | 51–59 | www.nature.com/natmachintell

Articles

NaTuRe MacHine InTelligence
Physical hardware

Simulation
Parameter sets
2

3

Succesfulsets x and y5

6

Incline4

Set xMorphing

Flat

1

Hardwareresults

Side view

Set y

Goal: locomote

Fig. 2 | Simulation revealed successful shapes and controllers, which we attempted to realize in hardware. Sets consisting of a shape, an orientation anda controller were generated for the robot in simulation. Each numbered sub-panel depicts a single automatically generated parameter set. After runningsimulations to determine the speed of each set, some were deemed too slow, while successful (relatively quick) sets were used to design a single physicalrobot that could reproduce the shapes and gaits found in simulation for both environments. During prototyping, actuator limits were measured andincorporated into the simulator to improve the accuracy of the simulation.

Table 1 | Simulation results, reported as the mean and maximum velocity attained for each test condition
Free parameters

Flat ground

Hill

Mean

Maximum

Mean

Maximum

Combined maximum

Orientation, shape, control

0.112

0.229

0.026

0.042

0.136

Shape, control

0.112

0.230

0.019

0.025

0.1275Control

0.114

0.202

0.010

0.023

0.112

Hand-designed rolling

NA

0.203

NA

−0.599−0.198Hand-designed inching

NA

0.093

NA

0.065

0.079

The simulator is deterministic, so no mean is reported for the hand-designed gaits (as they will always yield identical locomotion speed). Shape change allowed the robot to switch between dissimilar
locomotion gaits, outperforming the benchmark policies. Combined maximum was determined by averaging the maximum speed attainable in both environments. All values have units of body lengths
per second (BL s−1).

the flat surface). In the second pair of experiments, the algorithm
was allowed to simultaneously search for an optimal shape andcontroller pair. Finally, in the third pair of experiments, all threeparameter sets were open to optimization in both environments,
allowing optimization the maximum freedom to produce novel
shapes, orientations and controllers for locomoting in the two different environments. For each experiment, we ran 60 independent‘hill climbers’ (instantiations of the hill-climbing search algorithm44,
not to be confused with a robot that climbs a hill) for 200 generations, thus resulting in identical resource allocation for each experiment (Fig. 3b,c). In addition, we ran a control experiment in which
we fixed the shape of the robot to be fully inflated and oriented
width-wise (θ = 0°) for the inclined surface, to determine whether
shape change was necessary. The best the robot could do was prevent itself from rolling backward, and it attained a fitness value of−0.001 BL s−1.
When shape and orientation were set as fixed parameters, optimization found a control policy that had a similar behaviour tothe hand-designed control policies. Rolling was successful on flatground (maximum fitness 0.202 BL s−1), and performing inchworm
motion was the most effective gait discovered over inclined ground(maximum fitness 0.023 BL s−1), confirming that successful controllers could be found with the proposed pipeline (Table 1). For
reference, other robots that exclusively utilize inchworm gaits havewidely varied speeds, ranging from 0.013 BL s−1 (for a 226-mm-longrobot)46 to 0.16 BL s−1 (for a centimetre-scale robot)47.
For the second pair of experiments (orientation fixed), the bestrobots produced inflated shapes that rolled over flat ground (maxfitness 0.230 BL s−1) and flat shapes that performed inchworm
motion on the inclined ground (maximum fitness 0.025 BL s−1). The

increased complexity of the search space caused by allowing shapechange did not hinder the search process, allowing the algorithm todiscover efficient solutions without any a priori knowledge of theviability of the attainable shape–controller pairs.
In the last pair of experiments (all parameters open), the algorithm again discovered that cylindrical rolling robots were the mosteffective over a flat surface. However, over the inclined surface, theoptimization algorithm found better designs with a semi-inflated
shape capable of shuffling up the hill when oriented at an angle(maximum fitness 0.042 BL s−1). Using this strategy, the robot
achieved combined locomotion of 0.136 BL s−1, outperforming thehand-designed strategy of using crawling on inclines and rollingon flat ground. The deflated shape increased the surface area ofthe robot in contact with the ground, increasing friction between
the robot and the ground, while the non-standard orientation
reduced the amount of gravitational force opposing the directionof motion, thereby requiring less propulsive force and reducing the
likelihood of the robot rolling back down the hill. However, when
we attempted to replicate this behaviour in physical hardware, therobot could not shuffle, and rather rocked in place. Thus, the besttransferable strategy for moving up the incline was to attain the
flattened shape and traverse the hill using an inchworm-like gait. In
all the experiments, the policies found were less finely tuned thanthose that were hand-designed. Thus, even though optimization
produced similar overall behaviours and performance (inching
and rolling), these behaviours also included occasional counterproductive or superfluous actuations (Supplementary Video 1). Suchunhelpful motions could probably be overcome via further optimization and by adding a fitness penalty for the number of actuators
used per time step.

Nature Machine Intelligence | VOL 3 | January 2021 | 51–59 | www.nature.com/natmachintell

53Articles

NaTuRe MacHine InTelligence

a

Shape

Orientation

Controller

θ

f

Goal

Actuator

ϕ

tion

direc

t

b

c

Flat surface

Inclined surface
1.0

0.8
Normalized fitness

Normalized fitness

1.0

0.6

0.4

0.2

0

50

100

150

200

0.9

Free parameters
Orientation, shape, control
Shape, control
Control

0.8

0.7

0

50

100

150

200

Generations

Generations

Fig. 3 | Automated search discovered increasingly successful gaits in both environments. a, For each simulation, the algorithm could adjust theorientation, shape and/or controller of the robot. Orientation (θ) was measured by the angle between the robot’s leading edge and a constant-elevationline on the surface. Shape was parameterized as the inner bladder’s pressure, resulting in a family of shapes between the cylinder and flat shape shown.
Control of each actuator was parameterized as the number of timesteps (t) until its first actuation (ϕ) and the number of timesteps between actuations(f). Here we show an example controller for the eight main bladders, with green shaded squares illustrating inflation and white squares showing deflation.
b,c, Results on a flat surface (b) and on an inclined surface (c). Shaded regions represent 1 s.d. about the mean (solid line) and dashed lines represent
maximum fitness. The legend indicates which parameters were to open to optimization, the others being held constant.

Our control experiment, where the robot was constrained to be oriented width-wise against the inclined surface and fully inflated, tested
whether optimization could find a way to move up the hill withoutchanging shape, thereby determining whether shape change was necessary to move up the inclined surface at all. Here the most successfulof the discovered policies exploited the simulator in ways similar tothe physically infeasible robots in the previous experiment, and shuffled uphill. Thus, there were no transferable strategies that allowed
locomotion uphill in the control experiment. We ran a Welch’s t-test
comparing the solutions found through optimization during the threeprevious pairs of experiments against the transferable solutions in thisexperiment. The optimized solutions were found to be significantly
better, P < 0.05, providing strong evidence of the necessity of shapechange and showing that increasing the dimensionality of the search
space helped, rather than hindered, the optimization algorithm.
A similar trend is shown in Fig. 3b,c, where the best robot foreach environment was discovered by the pair of experiments inwhich the hill-climbing algorithm had the most control over the
optimization of the robot (increase in maximum fitness of 13.6%
over flat ground, 78.9% on the incline), despite the larger numberof trainable parameters, and thus an increased likelihood of getting
stuck in a local minimum. In addition, the population of simulated
robots continued to exhibit similar (and often superior) mean performance compared with the control-only experiments (Fig. 3).
These observations suggest that the robots avoided local minima,
and that more parameters should be mutable during automateddesign of shape-changing robots. We hypothesize that maximizing the algorithm’s design freedom would be even more importantwhen designing robots with increased degrees of freedom, using
more sophisticated optimization algorithms that can operate in an
exponentially growing search space.
54

While optimization found intuitive shapes and behaviours forthe given environments (rolling on flat ground, inching on moderate inclines), we further sought to discover optimal shape–behaviour pairs in very slightly inclined environments, where it was not
obvious whether the robot would favour rolling or inching. We thus
relied on evolution to discover where shape and behavioural transitions should occur across an incline sweep, and whether a graduallychanging environment should require a correspondingly gradualchange in robot shape. A state-of-the art evolutionary algorithm(distance-weighted exponential natural evolutionary strategies, or
DX-NES48; see Methods for further details) revealed that gradualchanges are not advantageous. Instead, the simulated robot switchedbetween a relatively inflated and deflated core, with a corresponding switch between rolling and inching gaits, at a critical incline
angle of 2.5° (Fig. 4). This result suggests that the fitness landscapeof shape-changing robots may not be smooth, and that the optimal
shape and gait of a robot can be sensitive to slight environmental
changes (for example, when the incline angle is just below or justabove the critical incline angle). Robots might therefore benefit
from being able to detect sudden decreases in performance to allow
them to respond by transitioning to a different, more appropriate
shape–policy strategy. We further note that the exact critical incline
angle, or transition angle, is dependent on the friction between the
robot and the surface it is traversing.
Overall, this sequence of experiments showed that automatedsearch could discover physically realistic shapes and controllers
for our shape-changing robot in a given environment (a prescribedground incline). In addition, when faced with an incline sweep,
evolutionary algorithms could discover the transition point where
shape change is necessary. Although the hand-designed controllers each performed comparably to the best discovered controllers

Nature Machine Intelligence | VOL 3 | January 2021 | 51–59 | www.nature.com/natmachintell

Articles

NaTuRe MacHine InTelligence90

90°

Rolling Transition

Inchworm
14.0

0°Orientation (°)

45°

45

7.0

Pressure (kPa)

10.5

3.5

0

0
0

2.5

5.0
7.5
Angle of incline (°)

10.0

Fig. 4 | Optimal orientation and pressure found in simulation, as afunction of the angle of incline. Between 2° and 3°, the best robots switchfrom being inflated with rolling-like gaits, to deflated with inchworm-likegaits. Error bars represent 1 s.d. over 11 evolutionary trials.

in a single environment, by changing shape, the robot had a better
combined average speed in both environments. Concretely, the best
shape–controller pair found by hill climbing locomoted at a speedof 0.229 BL s−1 on flat ground and 0.042 BL s−1 on incline, resulting
in an average speed across the two environments of 0.136 BL s−1,
compared with the average speed of −0.198 BL s−1 for the roundshape with a rolling gait and 0.079 BL s−1 for the flat shape with aninchworm gait (Table 1).
Transferring to a physical robot. Transferring simulated robots toreality introduces many challenges. For perfect transferal, the simulation and hardware need to have matching characteristics, including: material properties, friction modelling, actuation mechanisms,
shape, geometric constraints and range of motion. In practice, hardware and software limitations preclude perfect transferal, so domain
knowledge must be used to achieve a compromise between competing discrepancies. Here we sought to maximize the transferal ofuseful behaviour, rather than strictly transferring all parameters. In
simulation, we found that the same actuators could be used to create
different locomotion gaits. When restricted to the cylindrical shape,
successful controllers typically used sequential inflation of the bladders to induce rolling. The flatter robots employed their actuators
to locomote with inchworm motion. To transfer such shape change
and gaits to a physical robot, we created a robot that had an inflatable core, eight pneumatic surface-based actuators for generating
motion and variable-friction feet on each edge to selectively grip theenvironment (Fig. 1). This suite of features allowed the robot to mirror the simulated robot’s gaits, including rolling and inching. The‘hand-designed controllers’ from simulation were transferred toreality by sending the same command sequence from a PC to digitalpressure regulators49 that inflated the bladders, resulting in forward
motion. However, it was found that different bladders expanded at
different rates and had slightly different maximum inflation before
failure, so in the experiments shown in this manuscript, the robots
were manually teleoperated to approximate the hand-designed controllers with non-uniform timesteps between each actuation state.
Further details on the robot hardware are presented in Methods.
Mirroring simulation, rolling was achieved by inflating thetrailing-edge bladder to push the robot forward, exposing new bladders that were then inflated one at a time, sequentially (Fig. 1a andFig. 5a). Each inflation shifted the robot’s centre of mass forward
so the robot tipped in the desired direction, allowing the robot toroll repeatedly. This motion was effective for locomoting over flatground (average speed 0.05 BL s−1). When we attempted to command the robot to roll up inclines, the slope of the incline and therobot’s seam made it difficult for the robot to roll. These observa-

tions suggest the existence of a transition regime on the physicalrobot, where the ideal shape–locomotion pair switches from arolling cylinder to a flat shape with inchworm gait, similar to thesimulated robot. However, the boundary is not cleanly defined on
the physical hardware: at increasing inflation levels approaching thestrain limit of the silicone, the robot could roll up increasingly steep
inclines up to ~9°. After just a few such cycles, the bladders would
irreversibly rupture, causing the robot to roll backward to the startof the incline.
By accessing multiple shapes and corresponding locomotion
modes, shape-changing robots can potentially operate within multiple sets of environments. For example, when our robot encountered
inclines, it could switch shapes (Fig. 5a–c and Supplementary Video1). To transition to a flattened state capable of inchworm motion,
the robot would deflate its inner bladder, going from a diameter of
7 cm (width-to-thickness ratio γ = 1) to an outer height of ~1.2 cm(γ ≈ 8.3) (Fig. 5b). The central portions of the robot flatten to ~7 mm,
which is approximately the thickness of the robot’s materials, resulting in γ ≈ 14. During controlled tests, an average flat-to-cylindermorphing operation at 50 kPa took 11.5 s, while flattening with avacuum (−80 kPa) took 4.7 s (see Methods for additional details).
Flattening reduced the second moment of area of the robot’s
cross-section, allowing the bladders’ inflation to bend the robot inan arc (Fig. 5c). At a first approximation, body curvature is given asMκ ¼ EI, where M is the externally induced moment, E is the effective
modulusand I is the axial cross-section’s second moment of area.
I
Thus, flatter robots should bend to higher curvatures for a given
pressure. However, even for the flattest shape, bending was insufficient to produce locomotion: on prototypes with unbiased frictional
properties, bending made the robot curl and flatten in place.
Variable-friction ‘feet’ were integrated onto both ends of therobot and actuated one at a time to alternate between gripping infront of the robot and at its back, allowing the robot to inch forward (average speed of 0.01 BL s−1 on flat wood). The feet consisted of a latex balloon inside unidirectionally stretchable silicone
lamina50, wrapped with cotton broadcloth. When the inner latex
balloon was uninflated (−80 kPa), the silicone lamina was pulled
into its fabric sheath, thus the fabric was the primary contact withthe ground. When the balloon was inflated (50 kPa), it pushed thesilicone lamina outward and created a higher-friction contact withthe ground (Fig. 6a). To derive coefficients of static friction (μ) for
both the uninflated (μu) and the inflated (μi) cases, we slid the robot
over various surfaces including acrylic, wood and gravel. As therobot slid over a surface, it would typically exhibit an initial linear
regime corresponding to pre-slip deformation of the feet, followed
by slip and a second linear kinetic friction regime (Fig. 6b). Fromthe pre-slip regime, we infer that on a wood surface μu = 0.56 andμi = 0.70—an increase of ~25% (Fig. 6c). On acrylic, μu = 0.38 andμi = 0.51, which is an increase of 35%, yielding an inching speedof 0.007 BL s−1. When the difference in friction (Δμ = μi − μu) for
the variable-friction feet was too low (such as on gravel), inchworm motion was ineffective, as predicted by simulation (Fig. 6d).
Similarly, when the average friction (μm = (μi + μu)/2) was too high,it would overpower the actuators and lead to negligible motion (Fig.
6e). On wood, the inchworm gait was effective on inclines up to~14°, at a speed of 0.008 BL s−1 (Fig. 5 and the Supplementary Video1). Thus, the robot could quickly roll over flat terrain (0.05 BL s−1)then flatten to ascend moderate inclines, attaining its goal of maximizing total travelled distance.

Discussion

In this study, we tested the hypothesis that adapting the shape of arobot, as well as its control policy, can yield faster locomotion acrossenvironmental transitions than adapting only the control policy ofa single-shape robot. In simulation, we found that a shape-changing
robot traversed two test environments faster than an equivalent but

Nature Machine Intelligence | VOL 3 | January 2021 | 51–59 | www.nature.com/natmachintell

55

Articles

NaTuRe MacHine InTelligencea Rollingt = 0:00

0:03

0:05

0:08

0:23

0:32

0:37

2:38

3:31

b Morphingc Crawlingd Attempt to crawl

Morph and rollt = 0:00

0:23

0:41

1:25

Fig. 5 | Shape change allowed the physical robot to operate in previously inaccessible environments. a, When round, the robot’s actuators createda rolling gait that was effective on flat ground. b, By deflating its inner bladder, the robot could flatten. c, When flat, the outer bladders induced aninchworm-like gait, allowing the robot to ascend inclines up to ~14°. d, The inchworm gait gripped the ground to crawl forward, making it ineffective on
granular surfaces. When faced with such a situation, the robot could expand its inner bladder to begin rolling. For length-scale reference, the robot is 10 cm
by 15 cm when flattened, and 7 cm diameter by 15 cm when round. Times are given in the format of minutes:seconds. Panels a–c correspond to times froma single trial, while panel d is from a different trial and has a separate start time.

non-morphing robot. Then, we designed a physical robot to utilize
the design insights discovered through the simulation, and foundthat shape change was a viable and physically realizable strategy
for increasing the robot’s locomotion speed. We have also shown
progress towards an automated sim2real framework for realizing metamorphosing soft robots capable of operating in different
environments. In such a pipeline, simulated shape-changing robots
would be designed to achieve a desired function in multiple environments, then transferred to physical robots that could attain similar shapes and behaviours. We demonstrated each component of thepipeline on a representative task and set of environments: locomotion over flat ground and an incline. Starting with an initial robot
design, the search method sought valid shapes and control policies that could succeed in each environment. The effective shapes
and gaits were then transferred to physical hardware. However, thesimulation was able to generate some non-transferable behaviour by
exploiting inaccuracies of some simulation parameters. For example, when the friction coefficient was too low, the robot would makeunrealistic motions such as sliding over the ground. Other parameters, such as modulus, timescale, maximum inner bladder pressure,resolution of the voxel simulation (that is, the number of simulated
voxels per bladder) and material density, could be adjusted withoutcausing drastic changes in behaviour. Developing a unified framework for predicting the sim2real transferability of multiple shapes
and behaviours to a single robot remains an unsolved problem.
56

Insights from early physical prototypes were used to improve thesimulator’s hyperparameters (such as physical constants), resulting
in more effective sim2real transferal. Pairing hardware advanceswith multiple cycles through the sim2real pipeline, we plan to systematically close the loop such that data generated by the physicalrobot can be used to train a more accurate simulator, after whicha new round of sim2real transfers can be attempted. This iterative
process will be used to reduce the gap between simulation and reality in future experiments.
With advances such as increased control of the physical robots’shape and more efficient, parallelized soft-robot simulators, thepipeline should be able to solve increasingly challenging robot
design problems and discover more complicated shape–controller
pairs. While the sim2real transfer reported in this manuscript primarily tested intermediate shapes between two extremal shapes—
a fully inflated cylinder and a flattened sheet—future robots may
be able to morph between shapes embedded within a richer, but
perhaps less intuitive morphospace. For example, robots could be
automatically designed with a set C of Nc inflatable cores and corresponding constraining fabric outer layers. To transition between
shapes, a different subset C could be inflated, yielding 2N c distinct
Irobot morphologies. Designing more sophisticated arrangementsof
actuators and inflatable cores could be achieved using a multilayer
evolutionary algorithm, where the material properties of robots aredesigned along with their physical structure and control policies51.

Nature Machine Intelligence | VOL 3 | January 2021 | 51–59 | www.nature.com/natmachintell

Articles

NaTuRe MacHine InTelligence
a

d
0.03

–80 kPa

Speed (BL s–1)

0.02
Primary contact with ground
50 kPa

0.01

0

–0.01

b

Acrylic–80 kPa
50 kPa1.4

Wood–80 kPa
50 kPac

Gravel–80 kPa
50 kPa

0.2

0.4
0.6
Δµ (N N–1)

0.8

1.0

0
0.5

0.7

0.9
1.1
µm (N N–1)

1.3

1.5

e
1.0
0.020
Speed (BL s–1)

0.9

1.2

µ

0.8
Force (N)

0

0.8

0.7
0.6
0.5

0.4

0.015
0.010
0.005

0.4
0

0

5

10

15

Displacement (mm)

20

25

0.3

Acrylic

Wood

GravelSurface material

Fig. 6 | The variable-friction feet change their frictional properties when inflated. a, When the robot’s feet are inflated, silicone bladders protrude fromtheir fabric sheath to contact the ground. Blue scale bar on inset represents 1 cm. b, Force versus displacement when the robot was slid over wood, acrylic
and gravel. Each shaded region represents ±1 s.d. about the mean (solid line). c, Coefficient of static friction. The boxes denote 25th and 75th percentiles,
and the bars represent the median. d, Speed (in simulation) as a function of the difference between friction values, Δμ = μi − μu (where μi is friction while
the foot is inflated to 50 kPa, and μu is friction while uninflated at −80 kPa). e, Speed (in simulation) as a function of average friction value, μm = (μi + μu)/2.
In d and e, the hand-tuned inchworm gait was used.

In addition, it is unclear how to properly embed sensors into thephysical robot to measure its shape, actuator state and environment. Although some progress has been made towards intrinsicallysensing the shape of soft robots52 and environmental sensing53, it
remains an open challenge for a robot to detect that it as encountered an unforeseen environment and edit its body morphology andbehavioural control policy accordingly.
Future advances in hardware and search algorithms could be
used to design shape-changing robots that can operate across morechallenging environmental changes. For example, swimming or
amphibious robots could be automatically designed using underwater soft-robot simulation frameworks54, and changing shapewithin each gait cycle might allow robots to avoid obstacles31 or
adapt to environmental transitions. We have begun extending ourframework to include underwater locomotion, where locomoting
between terrestrial and aquatic environments represents a more
extreme environmental transition than flat-to-inclined surface environments. Our preliminary results suggest that multiple swimming
shape–gait pairs can be evolved using the same pipeline and robot
presented herein (Supplementary Information). While recent work
has shown the potential advantages of adapting robot limb shapeand gait for amphibious locomotion55, closing the sim2real gap on
shape-changing amphibious robots remains largely unstudied.
Collectively, this work represents a step towards the closed-loop
automated design of robots that dynamically adjust their shape
to expand their competencies. By leveraging soft materials, suchrobots potentially could metamorphose to attain multiple grasping
modalities, adapt their dynamics to intelligently interact with theirenvironment and change gaits to continue operation in widely different environments.

Methods

Simulation environment. The robots were simulated with the multi-material
soft-robot simulator Voxelyze34, which represents robots as a collection of cubic
elements called voxels. A robot can be made to move via external forces or throughexpansion of a voxel along one or more of its three dimensions.
Voxels were instantiated as a lattice of Euler–Bernoulli beams (Supplementary
Fig. 1a). Thus, adjacent voxels were represented as points connected by beams(Supplementary Fig. 1b). Each beam had length l = 0.01 m, elastic modulus
E = 400 kPa, density ρ = 3,000 kg m−3, coefficient of friction μ ¼ 0:6 and damping
I typically has
coefficient ζ = 1.0 (critically damped). For comparison, silicone
a modulus of ~100−600 kPa and density of ~1,000 kg m−3. These parameters
were initially set to E = 100 kPa and ρ = 1,000 kg m−3, but were iteratively
changed to increase the speed and stability of the simulation while maintaining
physically realistic behaviour. We simulated gravity as an external acceleration(g = 9.80665 m s−2) acting on each voxel. For the flat environment, gravity wasin the simulation’s negative z direction. Since changing the direction of gravity
is physically equivalent to and computationally simpler than rotating the floor
plane, we simulated the slope by changing the direction of gravity. The robot
could change shape by varying the force pushing outward, along to the interior
voxels’ surface normals, representing a discrete approximation of pressure(Supplementary Fig. 1c). The maximum pressure was set at 14 kPa (1.4 N per voxel)
after comparison with previous results (for example, the robotic skins introduced
by Shah et al. inflated their pneumatic bladders to under 20 kPa (ref. 31)) andafter initial experiments with hardware revealed only 10–35 kPa was necessary.
The robots’ external bladders were simulated via voxel expansion such that avoxel expanded along the z-dimension of its local coordinate space at 3 × 10−4 m
per simulation step and 1.5 × 10−5 m along the x dimension. Expansion in the ydimension created a bending force on the underlying skin voxels. This value waschanged on a sliding scale from 1.76 × 10−4 m to 3 × 10−5 m based on the pressureof the robots’ core, such that bladder expansion created minimal bending force

Nature Machine Intelligence | VOL 3 | January 2021 | 51–59 | www.nature.com/natmachintell

57

Articles

NaTuRe MacHine InTelligencewhen the robot was inflated, simulating the expansion of physically realizable soft
robots. Concretely, the y-dimension expansion was computing using a normalizing
equation (b − a)((P − PMIN)/(PMAX − PMIN)) + a where a = 1.7, b = 10, PMAX is the
maximum outward force per voxel in the robot’s core (1.4 N), PMIN is the minimum
outward force per voxel (0 N) and P is the current outward force per voxel. These
values were adjusted iteratively, until simulated and physical robots with the same
controllers exhibited similar behaviour in both the inclined and flat environments.
Lastly, to prevent the robot from slipping down the hill, and to enable othernon-rolling gaits, the robot was allowed to change the static and kinetic frictionof its outer voxels between a low value (μ = 1 × 10−4) when inactive and high value(μ = 2.0) when active.
Optimization. The optimization algorithm searched over three adjustable aspectsof the robots: shape (parameterized as inner bladder pressure), orientation of
the robot relative to the incline and actuation sequence. The algorithm searchedover a single number p ∈ [0, 1.4] (N per voxel) for shape and θ ∈ [0°, 90°] fororientation (see Supplementary Fig. 3a for illustrations of each parameter). The
robot’s actuation sequence S over T actuation steps was represented by a binary
10 × T matrix where 1 corresponds to bladder expansion and 0 corresponds to
bladder deflation. Each of the first eight rows corresponded to one of the inflatable
bladders, and the last two rows controlled the variable-friction feet. Each column
represented the actuation to occur during a discrete amount of simulation
timesteps t, resulting in a total simulation length of t × T. t was set such that an
actuation achieved full inflation, followed by a pause for the elastic material tosettle. Actuating in this manner minimizes many effects of the complex dynamics
of soft materials, reducing the likelihood of the robots exploiting idiosyncrasies ofthe simulation environment. In this study, we used t ≈ 11,000 timesteps of 0.0001 seach and T = 16 for all simulations, for a total simulation time of 17.6 s. To populate
S, the algorithm searched over a set of parameters (frequency f and offset ϕ) for
each of the ten actuators. Both of these parameters were kept in the range 0−T
where in our case we set T = 16. f determined the number of columns between
successive actuator activations, where f = 0 created a row in the actuation matrixof all 1s, f = 1 created a row with every other column filled by a 1, f = 2 every twocolumns filled by a 1, and so on. ϕ specified the number of columns before that
actuator’s first activation.
We optimized the parameters of shape, orientation and actuation using ahill-climber method. This method was chosen for computational efficiency, as asingle robot simulation took considerable wall-clock time (approximately 2.5 min
on a 2.9 GHz Intel Core i7 processor). The hill-climber algorithm needs only one
robot evaluation per optimization step, in contrast to more advanced optimization
algorithms that often require multiple evaluations per optimization step. The
current set of parameters C was initialized to randomly generated values andevaluated in the simulation, where fitness was defined as the distance travelled overflat ground, or distance travelled up the incline. A variant V was made by mutatingeach of the parameters by sampling from a normal distribution centred aroundthe current parameters of C. V was then tested in the simulation, and if it travelledfarther, the algorithm replaced C with V and generated a new V. The process ofgenerating variations, evaluating fitness and replacing the parameters was done for
200 generations. To determine the repeatability of such an algorithm, we ran 60
independent hill climbers for each of the six experiments, as described in Results.
Parallelized simulations for critical angle experiment. To enable the extensive
batch of simulations used in the distance-weighted exponential natural
evolutionary strategies (DX-NES48) trials, changes were made to the simulator
that allowed it to be more stable and efficient. First, the physics simulator was
updated for parallel computation of the voxel physics. This allowed us to decrease
the inflation rate of the outer bladders and increase the timestep (increasing thein-simulation time from 17.6 s to approximately 70 s), while still lowering thewall-clock time per robot simulation. We also decreased the robot’s elastic modulus(from 400 kPa to 300 kPa) along with the maximum pressure of the inner core. Thisset of improvements had the net effect of increasing the stability of the voxel–voxel
interactions, while enabling a larger number of physically realistic simulations to
be run. We then ran 11 independent evolutionary trials using DX-NES, each witha population size of 100 for 100 generations, for each of six different environments,
placing particular emphasis on the region around where the hand-tuned rolling
gait began to consistently roll backward (between 2° and 4°).
Manufacturing the physical robot. The physical robot was designed toenable transfer of function, shapes and control policies from simulation, while
maximizing locomotion speed and ease of manufacture. In summary, the inner
bladder was silicone (Dragon Skin 10, abbreviated here as DS10, Smooth-On Inc.),
the cylindrical body was cotton dropcloth, and the outer bladders were made witha stiffer silicone (Dragon Skin 30, abbreviated here as DS30, Smooth-On Inc.) for
higher force output. The variable-friction feet were made out of latex balloons,unidirectionally stretchable lamina (STAUD prepreg, described in ref. 50) andcotton dropcloth. Complete manufacturing details follow.
First, the outer bladders were made (Supplementary Fig. 2a). Two layers of
DS10 were rod coated onto a piece of polyethylene terephthalate (PET). After
curing, the substrate was placed in a laser cutter (ULS 2.0), PET-side up, and58

an outline of the eight bladders were cut into the PET layer. The substrate wasremoved from the laser cutter and the PET not corresponding to the bladders (thatis, the outer ‘negative’ region) was removed. Two layers of DS30 were rod coatedonto the substrate. DS30 is stiffer than DS10, and was used to increase the outer
actuators’ bending force, while DS10 was used in all other layers to keep the robot
flexible. Using ethanol as a loosening agent, the encased PET was then removed
from all eight bladders. Finally, a layer of DS10 was cast over the bladders’ DS10
side for attaching broadcloth to begin manufacturing of the inner bladder.
The inner bladder was made by first soaking cotton broadcloth (15 cm by
20 cm) with DS10, and placing it on the uncured layer on top of the outer bladders(Supplementary Fig. 2b). PET was then laid on the robot, and the inner bladderoutline was lasercut into the PET. Again, the outer PET was removed, and DS10
was rod coated to complete the inner bladder. The PET was removed using ethanol
and tweezers, and silicone tubing (McMaster-Carr) was inserted into each bladderand adhered with DS10.
To make the variable-friction feet, rectangular slits were lasercut into
broadcloth, and unidirectionally stretchable laminate50 was attached using Sil-Poxy(Smooth-On Inc.) (Supplementary Fig. 2c). Latex balloons were attached using
Sil-Poxy, and the feet were sealed in half with Sil-Poxy to make an enclosed
envelope for each foot. When at vacuum or atmospheric pressure, the fabric would
contact the environment, leading to a low-friction interaction. When the feet were
inflated, the silicone would contact the environment, allowing the feet to increase
their friction.
Finally, the robot was assembled by attaching the feet to the main robot
body using Sil-Poxy, and the robot was folded to bond the inner bladder to thebladderless half, using DS10 (Supplementary Fig. 2d).
Experiments with the physical robot. To test the robot’s locomotion capabilities,
we ran the physical robots through several tests on flat and inclined ground.
The pressure in the robots’ bladders was controlled using pneumatic pressure
regulators49. The robots were primarily operated on wood (flat and tipped to angles
up to ~15°), with additional experiments carried out on a flat acrylic surface and aflat gravel surface (Fig. 5 and Supplementary Video 1).
The variable-friction feet were assessed by pulling the robot across threematerials (acrylic, wood, gravel) using a materials testing machine (Instron 3343).
The robot was placed on a candidate material and dragged across the surface at
100 mm min−1 for 130 mm at atmospheric conditions (23 °C, 1 atm). This process
was repeated ten times for each material, at two feet inflation pressures: vacuum(−80 kPa) and inflated (50 kPa). The static coefficient of friction, μs, was calculatedby dividing the force at the upper end of the linear regime by the weight of
the robot.
The robot’s shape-changing speed was assessed by manually inflating anddeflating the robot’s inner core for 20 cycles. For each cycle, the robot body was
inflated to a cylindrical shape with a line pressure of 50 kPa, and the time required
to attain a diameter of ~7 cm was recorded. The body was then deflated with a linepressure of −80 kPa, and the time required to flatten to a height of ~1.2 cm wasrecorded.
Reporting Summary. Further information on research design is available in the
Nature Research Reporting Summary linked to this article.

Data availability

The data that support the findings of this study are available from thecorresponding author upon reasonable request.

Code availability

A public repository at https://doi.org/10.5281/zenodo.4067077 contains the codenecessary to reproduce the soft-robot simulations.

Received: 31 March 2020; Accepted: 22 October 2020;
Published online: 30 November 2020

References

1. Jager, P. Cebrennus Simon, 1880 (Araneae: Sparassidae): a revisionary up-datewith the description of four new species and an updated identification key for
all species. Zootaxa 3790, 319–356 (2014).
2. Bhanoo, S. N. A desert spider with astonishing moves. The New York Times
D4 (2014).
3. Armour, R. H. & Vincent, J. F. V. Rolling in nature and robotics: a review.
J. Bionic Eng. 3, 195–208 (2006).
4. Lin, H.-T., Leisk, G. G. & Trimmer, B. GoQBot: a caterpillar-inspired
soft-bodied rolling robot. Bioinspir. Biomim. 6, 026007 (2011).
5. Christensen, D. J. Evolution of shape-changing and self-repairing control forthe atron self-reconfigurable robot. In Proc. 2006 IEEE International
Conference on Robotics and Automation (ICRA) 2539–2545 (IEEE, 2006).
6. Yim, M. et al. Modular self-reconfigurable robot systems [grand challenges ofrobotics]. IEEE Robot. Autom. Mag. 14, 43–52 (2007).

Nature Machine Intelligence | VOL 3 | January 2021 | 51–59 | www.nature.com/natmachintell

Articles

NaTuRe MacHine InTelligence
7. Parrott, C., Dodd, T. J. & Groß, R. HyMod: A 3-DOF Hybrid Mobile andSelf-Reconfigurable Modular Robot and its Extensions. In Distributed
Autonomous Robotic Systems (eds. Groß, R. et al.) 401–414 (Springer, 2018).
8. Paul, C., Valero-Cuevas, F. J. & Lipson, H. Design and control of tensegrity
robots for locomotion. IEEE Trans. Robot. 22, 944–957 (2006).
9. Sabelhaus, A. P. et al. System design and locomotion of superball, anuntethered tensegrity robot. In 2015 IEEE International Conference on
Robotics and Automation (ICRA) 2867–2873 (IEEE, 2015).
10. Sadeghi, A., Mondini, A. & Mazzolai, B. Toward self-growing soft robots
inspired by plant roots and based on additive manufacturing technologies.
Soft Robot. 4, 211–223 (2017).
11. Miyashita, S., Guitron, S., Ludersdorfer, M., Sung, C. R. & Rus, D. An
untethered miniature origami robot that self-folds, walks, swims, anddegrades. In 2015 IEEE International Conference on Robotics and Automation(ICRA) 1490–1496 (IEEE, 2015).
12. Rus, D. & Tolley, M. T. Design, fabrication and control of origami robots.
Nat. Rev. Mater. 3, 101–112 (2018).
13. Pfeifer, R., Lungarella, M. & Iida, F. Self-organization, embodiment, andbiologically inspired robotics. Science 318, 1088–1093 (2007).
14. Saranli, U., Buehler, M. & Koditschek, D. E. Rhex: a simple and highly mobile
hexapod robot. Int. J. Robot. Res. 20, 616–631 (2001).
15. Raibert, M., Blankespoor, K., Nelson, G. & Playter, R. BigDog, therough-terrain quadruped robot. IFAC Proc. Vol. 41, 10822–10825 (2008).
16. Kuindersma, S. et al. Optimization-based locomotion planning, estimation,and control design for the atlas humanoid robot. Auton. Robot. 40,
429–455 (2016).
17. Ijspeert, A. J., Crespi, A., Ryczko, D. & Cabelguen, J.-M. From swimming towalking with a salamander robot driven by a spinal cord model. Science 315,
1416–1420 (2007).
18. Li, M., Guo, S., Hirata, H. & Ishihara, H. Design and performance evaluationof an amphibious spherical robot. Robot. Auton. Syst. 64, 21–34 (2015).
19. Myeong, W. C., Jung, K. Y., Jung, S. W., Jung, Y. & Myung, H. Developmentof a drone-type wall-sticking and climbing robot. In 2015 12th International
Conference on Ubiquitous Robots and Ambient Intelligence (URAI)
386–389 (IEEE, 2015).
20. Bachmann, R. J., Boria, F. J., Vaidyanathan, R., Ifju, P. G. & Quinn, R. D. A
biologically inspired micro-vehicle capable of aerial and terrestrial
locomotion. Mech. Mach. Theory 44, 513–526 (2009).
21. Roderick, W. R., Cutkosky, M. R. & Lentink, D. Touchdown to take-off: at theinterface of flight and surface locomotion. Interface Focus 7, 20160094 (2017).
22. Korayem, M. H., Tourajizadeh, H. & Bamdad, M. Dynamic load carrying
capacity of flexible cable suspended robot: robust feedback linearization
control approach. J. Intell. Robot. Syst. 60, 341–363 (2010).
23. Li, J., Ma, H., Yang, C. & Fu, M. Discrete-time adaptive control of robot
manipulator with payload uncertainties. In 2015 IEEE International
Conference on Cyber Technology in Automation, Control, and Intelligent
Systems (CYBER) 1971–1976 (IEEE, 2015).
24. Bongard, J., Zykov, V. & Lipson, H. Resilient machines through continuous
self-modeling. Science 314, 1118–1121 (2006).
25. Cully, A., Clune, J., Tarapore, D. & Mouret, J.-B. Robots that can adapt likeanimals. Nature 521, 503–507 (2015).
26. Chatzilygeroudis, K., Vassiliades, V. & Mouret, J.-B. Reset-free trial-and-error
learning for robot damage recovery. Robot. Auton. Syst. 100, 236–250 (2018).
27. Rosendo, A., von Atzigen, M. & Iida, F. The trade-off between morphology
and control in the co-optimized design of robots. PLoS ONE 12,
e0186107 (2017).
28. Garrad, M., Rossiter, J. & Hauser, H. Shaping behavior with adaptive
morphology. IEEE Robot. Autom. Lett. 3, 2056–2062 (2018).
29. Hauser, H. Resilient machines through adaptive morphology. Nat. Mach.
Intell. 1, 338–339 (2019).
30. Yim, S. & Sitti, M. Shape-programmable soft capsule robots forsemi-implantable drug delivery. IEEE Trans. Robot. 28, 1198–1202 (2012).
31. Shah, D. S., Yuen, M. C.-S., Tilton, L. G., Yang, E. J. & Kramer-Bottiglio, R.
Morphing robots using robotic skins that sculpt clay. IEEE Robot. Autom.
Lett. 4, 2204–2211 (2019).
32. Lee, D.-Y., Kim, S.-R., Kim, J.-S., Park, J.-J. & Cho, K.-J. Origami wheeltransformer: a variable-diameter wheel drive robot using an origami
structure. Soft Robot. 4, 163–180 (2017).
33. Kriegman, S. et al. Automated shapeshifting for function recovery indamaged robots. In Proc. Robotics: Science and Systems (2019).
34. Hiller, J. & Lipson, H. Dynamic simulation of soft multimaterial 3D-printed
objects. Soft Robot. 1, 88–101 (2014).
35. Jakobi, N., Husbands, P. & Harvey, I. Noise and the reality gap: the use ofsimulation in evolutionary robotics. In European Conference on Artificial Life
(eds. Morán, F. et al.) 704–720 (Springer, 1995).
36. Lipson, H. & Pollack, J. B. Automatic design and manufacture of robotic
lifeforms. Nature 406, 974 (2000).
37. Koos, S., Mouret, J.-B. & Doncieux, S. The transferability approach: crossing
the reality gap in evolutionary robotics. IEEE Trans. Evol. Comput. 17,
122–145 (2013).

38. Bartlett, N. W. et al. A 3D-printed, functionally graded soft robot powered by
combustion. Science 349, 161–165 (2015).
39. Rusu, A. A. et al. Sim-to-real robot learning from pixels with progressive
nets. In Conference on Robot Learning 262–270 (PMLR, 2017).
40. Chebotar, Y. et al. Closing the sim-to-real loop: adapting simulation
randomization with real world experience. In 2019 International Conferenceon Robotics and Automation (ICRA) 8973–8979 (2019).
41. Peng, X. B., Andrychowicz, M., Zaremba, W. & Abbeel, P. Sim-to-real transferof robotic control with dynamics randomization. In 2018 IEEE International
Conference on Robotics and Automation (ICRA) 1–8 (IEEE, 2018).
42. Hwangbo, J. et al. Learning agile and dynamic motor skills for legged robots.
Sci. Robot. 4, eaau5872 (2019).
43. Hiller, J. & Lipson, H. Automatic design and manufacture of soft robots.
IEEE Trans. Robot. 28, 457–466 (2012).
44. Mitchell, M., Holland, J. H. & Forrest, S. in Advances in Neural Information
Processing Systems 6 (eds Cowan, J. D. et al.) 51–58 (Morgan-Kaufmann,
1994).
45. Booth, J. W. et al. OmniSkins: robotic skins that turn inanimate objects into
multifunctional robots. Sci. Robot. 3, eaat1853 (2018).
46. Felton, S. M., Tolley, M. T., Onal, C. D., Rus, D. & Wood, R. J. Robot
self-assembly by folding: a printed inchworm robot. In 2013 IEEE
International Conference on Robotics and Automation 277–282 (IEEE, 2013).
47. Lee, D., Kim, S., Park, Y. & Wood, R. J. Design of centimeter-scale inchworm
robots with bidirectional claws. In 2011 IEEE International Conference on
Robotics and Automation 3197–3204 (IEEE, 2011).
48. Fukushima, N., Nagata, Y., Kobayashi, S. & Ono, I. Proposal of
distance-weighted exponential natural evolution strategies. In 2011 IEEE
Congress of Evolutionary Computation (CEC) 164–171 (IEEE, 2011).
49. Booth, J. W., Case, J. C., White, E. L., Shah, D. S. & Kramer-Bottiglio,
R. An addressable pneumatic regulator for distributed control of soft
robots. In 2018 IEEE International Conference on Soft Robotics (RoboSoft)
25–30 (IEEE, 2018).
50. Kim, S. Y. et al. Reconfigurable soft body trajectories using unidirectionallystretchable composite laminae. Nat. Commun. 10, 3464 (2019).
51. Howard, D. et al. Evolving embodied intelligence from materials to machines.
Nat. Mach. Intell. 1, 12–19 (2019).
52. Soter, G., Conn, A., Hauser, H. & Rossiter, J. Bodily aware soft robots:
integration of proprioceptive and exteroceptive sensors. In 2018 IEEE
International Conference on Robotics and Automation (ICRA) 2448–2453(IEEE, 2018).
53. Umedachi, T., Kano, T., Ishiguro, A. & Trimmer, B. A. Gait control in a soft
robot by sensing interactions with the environment using self-deformation.
Open Sci. 3, 160766 (2016).
54. Corucci, F., Cheney, N., Giorgio-Serchi, F., Bongard, J. & Laschi, C. Evolving
soft locomotion in aquatic and terrestrial environments: effects of material
properties and environmental transitions. Soft Robot. 5, 475–495 (2018).
55. Baines, R., Freeman, S., Fish, F. & Kramer, R. Variable stiffness morphinglimb for amphibious legged robots inspired by chelonian environmental
adaptations. Bioinspir. Biomim. 15, 025002 (2020).

Acknowledgements

This work was supported by NSF EFRI award 1830870. D.S.S. was supported by a NASASpace Technology Research Fellowship (80NSSC17K0164). J.P.P. was supported by the
Vermont Space Grant Consortium under NASA Cooperative Agreement NNX15AP86H.

Author contributions

J.B., R.K.-B., S.K., D.S.S. and J.P.P. conceived the project and planned the experiments.
J.P.P. coded the simulation and ran the evolutionary algorithm experiments. D.S.S. and
L.G.T. manufactured the robot and performed the hardware experiments. D.S.S., J.P.P.,
L.G.T., S.K., J.B. and R.K.-B. drafted and edited the manuscript. All authors contributed
to, and agree with, the content of the final version of the manuscript.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary information is available for this paper at https://doi.org/10.1038/
s42256-020-00263-1.
Correspondence and requests for materials should be addressed to R.K.-B.
Peer review information Nature Machine Intelligence thanks the anonymous reviewers
for their contribution to the peer review of this work.
Reprints and permissions information is available at www.nature.com/reprints.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.
© The Author(s), under exclusive licence to Springer Nature Limited 2020

Nature Machine Intelligence | VOL 3 | January 2021 | 51–59 | www.nature.com/natmachintell

59

Last updated by author(s): Oct 7, 2020

Reporting Summary
Nature Research wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency
in reporting. For further information on Nature Research policies, see Authors & Referees and the Editorial Policy Checklist.

Statistics

nature research | reporting summary

Corresponding author(s): Rebecca Kramer-Bottiglio

For all statistical analyses, confirm that the following items are present in the figure legend, table legend, main text, or Methods section.
n/a Confirmed
The exact sample size (n) for each experimental group/condition, given as a discrete number and unit of measurement
A statement on whether measurements were taken from distinct samples or whether the same sample was measured repeatedly
The statistical test(s) used AND whether they are one- or two-sided
Only common tests should be described solely by name; describe more complex techniques in the Methods section.

A description of all covariates tested
A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons
A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient)AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals)
For null hypothesis testing, the test statistic (e.g. F, t, r) with confidence intervals, effect sizes, degrees of freedom and P value noted
Give P values as exact values whenever suitable.

For Bayesian analysis, information on the choice of priors and Markov chain Monte Carlo settings
For hierarchical and complex designs, identification of the appropriate level for tests and full reporting of outcomes
Estimates of effect sizes (e.g. Cohen's d, Pearson's r), indicating how they were calculated
Our web collection on statistics for biologists contains articles on many of the points above.

Software and code
Policy information about availability of computer code
Data collection

For the soft robot simulations, we utilized custom scripts that used the open source physics simulator Voxelyze and publicly-available
Julia packages: Cxx, Libdl, Makie, LinearAlgebra, StatsBase, Colors, Random. Our code has been published for public access at https://doi.org/10.5281/zenodo.4067077

Data analysis

Data analysis of the physical robot was performed using standard functions in MATLAB 2019b, and simulated robots were analyzed using
publicly-available Julia package HypothesisTests, and using gnuplot [www.gnuplot.info].

For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published literature, software must be made available to editors/reviewers.
We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Research guidelines for submitting code & software for further information.

Data
Policy information about availability of data
All manuscripts must include a data availability statement. This statement should provide the following information, where applicable:

The data that support the findings of this study are available from the corresponding author upon reasonable request

October 2018

- Accession codes, unique identifiers, or web links for publicly available datasets- A list of figures that have associated raw data
- A description of any restrictions on data availability1Please select the one below that is the best fit for your research. If you are not sure, read the appropriate sections before making your selection.
Life sciences

Behavioural & social sciences

Ecological, evolutionary & environmental sciences

For a reference copy of the document with all sections, see nature.com/documents/nr-reporting-summary-flat.pdf

Life sciences study design
All studies must disclose on these points even when the disclosure is negative.
Sample size

Describe how sample size was determined, detailing any statistical methods used to predetermine sample size OR if no sample-size calculation
was performed, describe how sample sizes were chosen and provide a rationale for why these sample sizes are sufficient.

Data exclusions

Describe any data exclusions. If no data were excluded from the analyses, state so OR if data were excluded, describe the exclusions and therationale behind them, indicating whether exclusion criteria were pre-established.

Replication

Describe the measures taken to verify the reproducibility of the experimental findings. If all attempts at replication were successful, confirm thisOR if there are any findings that were not replicated or cannot be reproduced, note this and describe why.

Randomization

Describe how samples/organisms/participants were allocated into experimental groups. If allocation was not random, describe how covariates
were controlled OR if this is not relevant to your study, explain why.

Blinding

Describe whether the investigators were blinded to group allocation during data collection and/or analysis. If blinding was not possible,
describe why OR explain why blinding was not relevant to your study.

nature research | reporting summary

Field-specific reporting

Behavioural & social sciences study design
All studies must disclose on these points even when the disclosure is negative.
Study description

Briefly describe the study type including whether data are quantitative, qualitative, or mixed-methods (e.g. qualitative cross-sectional,
quantitative experimental, mixed-methods case study).

Research sample

State the research sample (e.g. Harvard university undergraduates, villagers in rural India) and provide relevant demographic information(e.g. age, sex) and indicate whether the sample is representative. Provide a rationale for the study sample chosen. For studies involving
existing datasets, please describe the dataset and source.

Sampling strategy

Describe the sampling procedure (e.g. random, snowball, stratified, convenience). Describe the statistical methods that were used topredetermine sample size OR if no sample-size calculation was performed, describe how sample sizes were chosen and provide a rationale
for why these sample sizes are sufficient. For qualitative data, please indicate whether data saturation was considered, and what criteria
were used to decide that no further sampling was needed.

Data collection

Provide details about the data collection procedure, including the instruments or devices used to record the data (e.g. pen and paper,computer, eye tracker, video or audio equipment) whether anyone was present besides the participant(s) and the researcher, and whether
the researcher was blind to experimental condition and/or the study hypothesis during data collection.

TimingIndicate the start and stop dates of data collection. If there is a gap between collection periods, state the dates for each sample cohort.

Data exclusions

If no data were excluded from the analyses, state so OR if data were excluded, provide the exact number of exclusions and the rationale
behind them, indicating whether exclusion criteria were pre-established.

Non-participation

State how many participants dropped out/declined participation and the reason(s) given OR provide response rate OR state that noparticipants dropped out/declined participation.

Randomization

If participants were not allocated into experimental groups, state so OR describe how participants were allocated to groups, and if
allocation was not random, describe how covariates were controlled.

All studies must disclose on these points even when the disclosure is negative.
Study description

Briefly describe the study. For quantitative data include treatment factors and interactions, design structure (e.g. factorial, nested,hierarchical), nature and number of experimental units and replicates.

Research sample

Describe the research sample (e.g. a group of tagged Passer domesticus, all Stenocereus thurberi within Organ Pipe Cactus National

October 2018

Ecological, evolutionary & environmental sciences study design

2Monument), and provide a rationale for the sample choice. When relevant, describe the organism taxa, source, sex, age range andany manipulations. State what population the sample is meant to represent when applicable. For studies involving existing datasets,
describe the data and its source.

Sampling strategy

Note the sampling procedure. Describe the statistical methods that were used to predetermine sample size OR if no sample-size
calculation was performed, describe how sample sizes were chosen and provide a rationale for why these sample sizes are sufficient.

Data collection

Describe the data collection procedure, including who recorded the data and how.

Timing and spatial scale Indicate the start and stop dates of data collection, noting the frequency and periodicity of sampling and providing a rationale forthese choices. If there is a gap between collection periods, state the dates for each sample cohort. Specify the spatial scale from which
the data are taken

Data exclusions

If no data were excluded from the analyses, state so OR if data were excluded, describe the exclusions and the rationale behind them,
indicating whether exclusion criteria were pre-established.

Reproducibility

Describe the measures taken to verify the reproducibility of experimental findings. For each experiment, note whether any attempts torepeat the experiment failed OR state that all attempts to repeat the experiment were successful.

Randomization

Describe how samples/organisms/participants were allocated into groups. If allocation was not random, describe how covariates were
controlled. If this is not relevant to your study, explain why.

Blinding

Describe the extent of blinding used during data acquisition and analysis. If blinding was not possible, describe why OR explain why
blinding was not relevant to your study.

Did the study involve field work?

Yes

nature research | reporting summary

Research sample

No

Field work, collection and transport
Field conditions

Describe the study conditions for field work, providing relevant parameters (e.g. temperature, rainfall).

Location

State the location of the sampling or experiment, providing relevant parameters (e.g. latitude and longitude, elevation, water
depth).

Access and import/export

Describe the efforts you have made to access habitats and to collect and import/export your samples in a responsible manner andin compliance with local, national and international laws, noting any permits that were obtained (give the name of the issuingauthority, the date of issue, and any identifying information).

DisturbanceDescribe any disturbance caused by the study and how it was minimized.

Reporting for specific materials, systems and methods
We require information from authors about some types of materials, experimental systems and methods used in many studies. Here, indicate whether each material,
system or method listed is relevant to your study. If you are not sure if a list item applies to your research, read the appropriate section before selecting a response.

Materials & experimental systems

Methods

n/a Involved in the study

n/a Involved in the study

Antibodies

ChIP-seq

Eukaryotic cell lines

Flow cytometry

Palaeontology

MRI-based neuroimaging

Animals and other organisms
Human research participants
Clinical data

Antibodies
Describe all antibodies used in the study; as applicable, provide supplier name, catalog number, clone name, and lot number.

Validation

Describe the validation of each primary antibody for the species and application, noting any validation statements on the
manufacturer’s website, relevant citations, antibody profiles in online databases, or data provided in the manuscript.

October 2018

Antibodies used3

Policy information about cell lines
Cell line source(s)State the source of each cell line used.

Authentication

Describe the authentication procedures for each cell line used OR declare that none of the cell lines used were authenticated.

Mycoplasma contamination

Confirm that all cell lines tested negative for mycoplasma contamination OR describe the results of the testing formycoplasma contamination OR declare that the cell lines were not tested for mycoplasma contamination.

Commonly misidentified lines

Name any commonly misidentified cell lines used in the study and provide a rationale for their use.

(See ICLAC register)

Palaeontology
Specimen provenance

Provide provenance information for specimens and describe permits that were obtained for the work (including the name of theissuing authority, the date of issue, and any identifying information).

Specimen deposition

Indicate where the specimens have been deposited to permit free access by other researchers.

Dating methods

If new dates are provided, describe how they were obtained (e.g. collection, storage, sample pretreatment and measurement),
where they were obtained (i.e. lab name), the calibration program and the protocol for quality assurance OR state that no newdates are provided.

nature research | reporting summary

Eukaryotic cell lines

Tick this box to confirm that the raw and calibrated dates are available in the paper or in Supplementary Information.

Animals and other organisms
Policy information about studies involving animals; ARRIVE guidelines recommended for reporting animal researchLaboratory animals

For laboratory animals, report species, strain, sex and age OR state that the study did not involve laboratory animals.

Wild animals

Provide details on animals observed in or captured in the field; report species, sex and age where possible. Describe how animals
were caught and transported and what happened to captive animals after the study (if killed, explain why and describe method; if
released, say where and when) OR state that the study did not involve wild animals.

Field-collected samples

For laboratory work with field-collected samples, describe all relevant parameters such as housing, maintenance, temperature,
photoperiod and end-of-experiment protocol OR state that the study did not involve samples collected from the field.

Ethics oversight

Identify the organization(s) that approved or provided guidance on the study protocol, OR state that no ethical approval or
guidance was required and explain why not.

Note that full information on the approval of the study protocol must also be provided in the manuscript.

Human research participants
Policy information about studies involving human research participants
Population characteristics

Describe the covariate-relevant population characteristics of the human research participants (e.g. age, gender, genotypic
information, past and current diagnosis and treatment categories). If you filled out the behavioural & social sciences study design
questions and have nothing to add here, write "See above."

Recruitment

Describe how participants were recruited. Outline any potential self-selection bias or other biases that may be present and how
these are likely to impact results.

Ethics oversight

Identify the organization(s) that approved the study protocol.

Note that full information on the approval of the study protocol must also be provided in the manuscript.

Clinical data
All manuscripts should comply with the ICMJE guidelines for publication of clinical research and a completed CONSORT checklist must be included with all submissions.

Clinical trial registration

Provide the trial registration number from ClinicalTrials.gov or an equivalent agency.

Study protocol

Note where the full trial protocol can be accessed OR if not available, explain why.

Data collection

Describe the settings and locales of data collection, noting the time periods of recruitment and data collection.

October 2018

Policy information about clinical studies

4Describe how you pre-defined primary and secondary outcome measures and how you assessed these measures.

ChIP-seq
Data deposition
Confirm that both raw and final processed data have been deposited in a public database such as GEO.
Confirm that you have deposited or provided access to graph files (e.g. BED files) for the called peaks.
May remain private before publication.

For "Initial submission" or "Revised version" documents, provide reviewer access links. For your "Final submission" document,
provide a link to the deposited data.

Files in database submission

Provide a list of all files available in the database submission.

Genome browser session

Provide a link to an anonymized genome browser session for "Initial submission" and "Revised version" documents only, toenable peer review. Write "no longer applicable" for "Final submission" documents.

Data access links(e.g. UCSC)

nature research | reporting summary

Outcomes

Methodology
Replicates

Describe the experimental replicates, specifying number, type and replicate agreement.

Sequencing depth

Describe the sequencing depth for each experiment, providing the total number of reads, uniquely mapped reads, length ofreads and whether they were paired- or single-end.

Antibodies

Describe the antibodies used for the ChIP-seq experiments; as applicable, provide supplier name, catalog number, clone
name, and lot number.

Peak calling parameters

Specify the command line program and parameters used for read mapping and peak calling, including the ChIP, control andindex files used.

Data quality

Describe the methods used to ensure data quality in full detail, including how many peaks are at FDR 5% and above 5-foldenrichment.

SoftwareDescribe the software used to collect and analyze the ChIP-seq data. For custom code that has been deposited into acommunity repository, provide accession details.

Flow Cytometry
Plots
Confirm that:
The axis labels state the marker and fluorochrome used (e.g. CD4-FITC).
The axis scales are clearly visible. Include numbers along axes only for bottom left plot of group (a 'group' is an analysis of identical markers).
All plots are contour plots with outliers or pseudocolor plots.
A numerical value for number of cells or percentage (with statistics) is provided.

Methodology
Describe the sample preparation, detailing the biological source of the cells and any tissue processing steps used.

Instrument

Identify the instrument used for data collection, specifying make and model number.

SoftwareDescribe the software used to collect and analyze the flow cytometry data. For custom code that has been deposited into acommunity repository, provide accession details.

Cell population abundance

Describe the abundance of the relevant cell populations within post-sort fractions, providing details on the purity of the samples
and how it was determined.

Gating strategy

Describe the gating strategy used for all relevant experiments, specifying the preliminary FSC/SSC gates of the starting cell
population, indicating where boundaries between "positive" and "negative" staining cell populations are defined.

Tick this box to confirm that a figure exemplifying the gating strategy is provided in the Supplementary Information.

October 2018

Sample preparation

5

Experimental design
Design type

Indicate task or resting state; event-related or block design.

Design specifications

Specify the number of blocks, trials or experimental units per session and/or subject, and specify the length of each trialor block (if trials are blocked) and interval between trials.

Behavioral performance measures

State number and/or type of variables recorded (e.g. correct button press, response time) and what statistics were used
to establish that the subjects were performing the task as expected (e.g. mean, range, and/or standard deviation acrosssubjects).

Acquisition
Imaging type(s)Specify: functional, structural, diffusion, perfusion.

Field strength

Specify in Tesla

Sequence & imaging parameters

Specify the pulse sequence type (gradient echo, spin echo, etc.), imaging type (EPI, spiral, etc.), field of view, matrix size,
slice thickness, orientation and TE/TR/flip angle.

Area of acquisition

State whether a whole brain scan was used OR define the area of acquisition, describing how the region was determined.

Diffusion MRI

Used

nature research | reporting summary

Magnetic resonance imaging

Not used

Preprocessing
Preprocessing software

Provide detail on software version and revision number and on specific parameters (model/functions, brain extraction,
segmentation, smoothing kernel size, etc.).

Normalization

If data were normalized/standardized, describe the approach(es): specify linear or non-linear and define image types
used for transformation OR indicate that data were not normalized and explain rationale for lack of normalization.

Normalization template

Describe the template used for normalization/transformation, specifying subject space or group standardized space (e.g.
original Talairach, MNI305, ICBM152) OR indicate that the data were not normalized.

Noise and artifact removal

Describe your procedure(s) for artifact and structured noise removal, specifying motion parameters, tissue signals andphysiological signals (heart rate, respiration).

Volume censoring

Define your software and/or method and criteria for volume censoring, and state the extent of such censoring.

Statistical modeling & inference
Model type and settingsSpecify type (mass univariate, multivariate, RSA, predictive, etc.) and describe essential details of the model at the firstand second levels (e.g. fixed, random or mixed effects; drift or auto-correlation).

Effect(s) tested

Define precise effect in terms of the task or stimulus conditions instead of psychological concepts and indicate whether
ANOVA or factorial designs were used.

Specify type of analysis:
Statistic type for inference(See Eklund et al. 2016)

Correction

Whole brain

ROI-based

BothSpecify voxel-wise or cluster-wise and report all relevant parameters for cluster-wise methods.
Describe the type of correction and how it is obtained for multiple comparisons (e.g. FWE, FDR, permutation or Monte
Carlo).

Models & analysis
n/a Involved in the study
Functional and/or effective connectivity

Multivariate modeling or predictive analysis

Functional and/or effective connectivity

Report the measures of dependence used and the model details (e.g. Pearson correlation, partial
correlation, mutual information).

Graph analysis

Report the dependent variable and connectivity measure, specifying weighted graph or binarized graph,subject- or group-level, and the global and/or node summaries used (e.g. clustering coefficient, efficiency,etc.).

October 2018

Graph analysis

6Specify independent variables, features extraction and dimension reduction, model, training and evaluation
metrics.

nature research | reporting summary

Multivariate modeling and predictive analysis

October 20187