Article

Multi-environment robotic transitions
through adaptive morphogenesis
https://doi.org/10.1038/s41586-022-05188-w
Received: 21 January 2022

Robert Baines1,4, Sree Kalyan Patiballa1,3,4, Joran Booth1, Luis Ramirez1, Thomas Sipple1,
Andonny Garcia1, Frank Fish2 & Rebecca Kramer-Bottiglio1 ✉Accepted: 3 August 2022
Published online: 12 October 2022
Check for updates

The current proliferation of mobile robots spans ecological monitoring, warehousemanagement and extreme environment exploration, to an individual consumer’s
home1–4. This expanding frontier of applications requires robots to transit multiple
environments, a substantial challenge that traditional robot design strategies havenot effectively addressed5,6. For example, biomimetic design—copying an animal’smorphology, propulsion mechanism and gait—constitutes one approach, but it loses
the benefits of engineered materials and mechanisms that can be exploited to surpass
animal performance7,8. Other approaches add a unique propulsive mechanism foreach environment to the same robot body, which can result in energy-inefficientdesigns9–11. Overall, predominant robot design strategies favour immutablestructures and behaviours, resulting in systems incapable of specializing acrossenvironments12,13. Here, to achieve specialized multi-environment locomotion
through terrestrial, aquatic and the in-between transition zones, we implemented‘adaptive morphogenesis’, a design strategy in which adaptive robot morphology andbehaviours are realized through unified structural and actuation systems. Taking
inspiration from terrestrial and aquatic turtles, we built a robot that fuses traditional
rigid components and soft materials to radically augment the shape of its limbs andshift its gaits for multi-environment locomotion. The interplay of gait, limb shape andthe environmental medium revealed vital parameters that govern the robot’s cost oftransport. The results attest that adaptive morphogenesis is a powerful method toenhance the efficiency of mobile robots encountering unstructured, changing
environments.

Animals that primarily inhabit one ecological niche tend to exhibit
specialized body plans and gait kinematics that increase their locomotive efficiency in that niche, at the expense of degraded performancein other environments8. Conversely, semi-aquatic and semi-terrestrial
animals display inherent morphological and gait compromises thatmake them only moderately efficient in both environments12. Environmental specialization also holds true for mobile robots, which
are typically confined to operate exclusively on land or in water. The
introduction of amphibious robots capable of navigating aquatic andterrestrial environments promises to advance diverse sectors such as
bio-monitoring, disaster response and security14,15, or serve as proxies
to study locomotion physics in animals16–19 (see ref. 13 for a review ofamphibious robots). Importantly, amphibious robots provide pertinent
platforms to evaluate design paradigms aimed at realizing efficient,multi-environment robots.
We considered that a single robot could specialize for locomotion
across multi-environments through ‘adaptive morphogenesis’: adaptive morphology and behaviours realized through unified structuraland actuation systems (see ‘A note on the term ‘adaptive morphogenesis’’ in Methods for further discussion on this term). Towards this end,

we merged specialized morphogenic features for aquatic and terrestrial
locomotion—the streamlined flipper shape and gaits of sea turtles andthe columnar leg shape and gaits of land-faring tortoises20,21—to create
an Amphibious Robotic Turtle (ART) (Fig. 1a). With a single turtle-likebody plan, ART employs adaptive morphogenesis through a combination of stimulus-responsive soft materials and traditional robotics
components. Limbs capable of morphing between functional hydrodynamic and load-bearing shapes using variable-stiffness composites22(Fig. 1b, and ‘Robot components and fabrication’ and ‘Kinematics,
control and gait programming’ in Methods), in tandem with a rangeof gaits, enable ART to swim submerged, swim at the water’s surface,
locomote over various substrates, and transition between land andwater. Herein we study the efficacy of adaptive morphogenesis by: (1)evaluating ART’s cost of transport (COT) against other animals androbots in both environments, and (2) combining favourable policies
from both environments to derive transitional policies between terrestrial and aquatic habitats.
ART’s body features a morphing limb able to adapt its stiffness andshape to its environment, fully integrated into a robotic structure for
efficiency gain testing. The body comprises four subsystems: chassis,

1
School of Engineering and Applied Science, Yale University, New Haven, CT, USA. 2Department of Biology, West Chester University, West Chester, PA, USA. 3Present address: Department of
Mechanical Engineering, The University of Alabama, Tuscaloosa, AL, USA. 4These authors contributed equally: Robert Baines, Sree Kalyan Patiballa. ✉e-mail: rebecca.kramer@yale.edu

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Article
a

b

c

z
y

Leg modex

T

Flipper mode

+

I
D
x
y

z

Fig. 1 | Turtle-inspired amphibious robot. a, ART replicates the limb shapes
and gaits of highly adapted turtle species, and is a platform capable ofspecialized locomotion modes for transition between aquatic and terrestrial
habitats. b, Side view of the morphing limb. Scale bar, 30 mm. c, Isometric andtop views of the robot computer-aided-design model. Scale bar, 0.16 m.
The inset shows the joint arrangement. The joints are typically clad in rubber
bellows, removed here for visualization. θ, ϕ and α are axes for forwards andbackwards, up and down, and angle-of-attack movements, respectively.

shell, shoulder joints and morphing limbs (Extended Data Fig. 1a and‘Robot components and fabrication’ in Methods). The chassis holds
the electronics, and the shell provides streamlining, ballast space forbuoyancy tuning, payload storage and protection. The shoulder joints
each have three motors in a kinematic configuration to achieve a rangeof gaits (Fig. 1c, Extended Data Fig. 1b and ‘Kinematics, control and gait
programming’ in Methods). A morphing limb consisting of an antagonistic pneumatic actuator pair with strain-limiting layers adhered tothermoset polymers is connected to each shoulder joint. Heating thethermosets through embedded heaters to soften them and inflating
the pneumatic actuators enables changes in limb cross-sectional area
(4 times) and stiffness (storage modulus; 450 times). These changes
permit ART’s limbs to morph adaptively between a cylindrical geometry
conducive to walking and a flat flipper geometry conducive to swimming (Supplementary Videos 4 and 5).
As ART must function in three distinct zones—water, land and thein-between transition—we calculated its COT to determine favourable

limb morphology and gait pairs for each zone. COT is a dimensionlessmetric that allows locomotor efficiency comparisons across different robots and organisms, and is defined as: COT = Pin/mgv where m is
the robot’s mass, g is the acceleration due to gravity, v is the speed in
the forwards direction and Pin is the power drawn from the motors(‘Calculation of COT’ in Methods).
In aquatic tests (‘Swimming tests’ in Methods), ART’s buoyancy was
adjusted for surface and submerged swimming (Fig. 2a and Supplementary Video 1). With the limbs morphed to the flipper mode, we studied
paddling, as per observation of freshwater turtles and semi-aquatic
mammals, and a flapping motion inspired by sea turtles and fully
aquatic mammals. The paddling gait is a stroke directed ventrally
rearwards relative to the robot’s body, followed by a feathering recovery stroke moving forwards and dorsally. The flapping gait features avertical movement profile of sequential upstrokes and downstrokes.
We noticed the flapping gait’s strong dependence on the angle-ofattack offset θ , a constant angle deviation from ART’s horizontal (0°)

284 | Nature | Vol 610 | 13 October 2022

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b

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COT, flapping gait

7
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Fz (N)

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Gait cycle (%)

Fig. 2 | Swimming. a, The robot is capable of surface and submerged swimmingby adjusting its buoyancy. b, Angle-of-attack offset versus COT for the
sea-turtle-inspired flapping gait. Three distinct regions are highlighted: in theleft (red) region, the COT of flapping was higher than that of paddling; in the
middle (yellow) region, the COT drops within a span of 10°, pinpointing atransition where the robot is generating predominately productive thrust; inthe right (blue) region, COT approaches its best value. The points are theaverage of five trials; error bars indicate one standard deviation from the mean.
c,d, Snapshots of important steps over one gait cycle (top) and x (middle) andz (bottom) forces for the paddling (c) and flapping (d) gaits. The solid lines arean average of five stroke cycles and shaded regions show one standard
deviation from the mean.

posture applied to the angle-of-attack motor for the duration of thestoke (Fig. 1c). A parametric study across a range of offsets pinpointed
the lowest COT of 3 at θ = 40° (Fig. 2b). Three regions were also revealed:(1) a region where flapping is less efficient than paddling owing to thegeneration of substantial counterproductive thrust on the downstroke;(2) a region where the COT drops (computational fluid dynamics simulations indicate that this drop coincides with a shift in the angle ofattack towards more productive thrust throughout the gait cycle byreducing drag between the upstrokes and downstrokes); and (3) a region
where the COT begins to plateau, suggesting that the optimal θ for the
gait is nearby (see ‘Swimming tests’ in Methods for more information
on determining these regions).
Forward (Fx) and lift (Fz) directional forces attained by fixing ART toa multi-axis load cell elucidated the difference in the COT between
paddling and the best flapping gait (Fig. 2c,d). The graph of Fx indicatescounterproductive thrust is generated on the recovery portion of thepaddling gait, causing ART to markedly decelerate or to move rearwards(Fig. 2c and Supplementary Video 1). Only 27% of the paddling stroke
constituted productive thrust. During the downstroke of the flapping
gait, ART also decelerated, but maintained productive Fx thrust for 95%
of the stroke (Fig. 2d). The peak in Fz of 3.4 N during free paddling caused
pitching (Supplementary Video 1). Deviation from the x direction
increased ART’s projected area A against oncoming flow, raising drag1
proportionally by FD = 2 ρV 2CD A, where V is the forward velocity, CD is
the coefficient of drag and ρ is the the density of water. In contrast, thelower peak Fz of 2.5 N during flapping maintained a more level bodyand nearly constant A along the flow direction.
In summary, owing to productive thrust being maintained over moreof the stroke cycle and a higher sustained velocity from a reduced dragcoefficient, ART’s COT decreased in the favourable-angle flapping
regime. The results suggest that either gait could be useful in a specificcontext. If high acceleration in shallow water is desired, paddling may be
a viable option, but if steady, efficient swimming is favoured, flappingis the best choice. The results are consistent with the gaits of actual
turtles. Paddling by freshwater turtles enhances manoeuvrability 23,
whereas a flapping-style gait by sea turtles increases swimming efficiency24. ART exploits engineered mechanisms to accomplish both
gaits while retaining the hydrodynamically favourable flipper morphology, reinforcing how adaptive morphogenesis can enable specialized
robotic locomotion within an environment.
Terrestrial locomotion strategies were assessed on porcelain tile, concrete and granite—representative substrates for outdoor urban environments (‘Terrestrial tests’ in Methods and Supplementary Video 2).
We implemented a statically stable creeping gait inspired by the uprightwalking of terrestrial tortoises and other quadrupedal animals forlow-speed locomotion. When creeping (a lateral sequence walk), ART
only has one limb off the ground at a time while incrementally pivoting
its body to move forwards (Fig. 3a,b).
Three-dimensional (3D) motion capture of the distal tip of ART’s
back-left limb while creeping on different substrates shows a consistent
Nature | Vol 610 | 13 October 2022 | 285

Articlec

Porcelain800–1,200 –1,000x (mm)–400–1,000–500
z (mm)800
Step FR–1,000–500
x (mm)

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Encoder positions (º)

–400

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Substrate roughness vibrations

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Concrete
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right

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Step BR0y (mm)

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Step BL Step FL–1,300400

z (mm)b–1,200y (mm)

a

75

15
10

0
Leg splay
–100

0

15

30

45

60

75

100

Gait cycle (%)

10

15

20

Stability metric,

Fig. 3 | Walking. a, ART can handily traverse several terrestrial substrates withan upright creeping gait inspired by land-faring tortoises. b, Top: important
steps over one gait cycle. Bottom: commanded encoder positions for the ϕ andθ motors. BL refers to the back left leg, BR the back right, FL the front left, andFR the front right. c, Three-dimensional motion capture of the distal tip ofART’s back-left limb over five steps. The insets are representative projectionsin the x–y plane during a portion of the gait where the limb is pivoting and being
used in ART’s support polygon. d, Motion capture z-axis projection. The inset
zooms to the representative pivot and stand phase used to calculate S .
e, The COT as a function of S . Error bars indicate one standard deviation fromthe mean over five trials.

swept trajectory and stride length, verifying the efficacy of the gait
(Fig. 3c and ‘Terrestrial tests’ in Methods). Motion capture data also
help explain the COT differences across substrates. In particular, thez-axis data projection (z*) contains (1) sharp increases when ART swings
its leg for a step phase (common across all substrates), and (2) vibration signatures corresponding to interactions with the terrain, suchas instabilities arising from intermittent ground contacts when in apivot or stance phase (‘Terrestrial tests’ in Methods and Fig. 3d). Driftof the z-axis data over the gait cycle indicates gradual splay or tuckingof the legs as ART walks.
We calculated the z-axis data’s deviation from an ideal, completely
stable trajectory (z) during which ART’s limb would be fully in contact

1 to N . A positive correlation between COT and S underscores theimportance of maintaining slip-free contact with the substrate (Fig. 3e).
Substrate-dependent slippage can be attributed to friction and topographical features. For instance, the evaluated granite was coarse andexhibited a range of surface normals, which explains why its S was 64%
higher than that of the relatively smooth porcelain.
Despite variable topographical characteristics, ART effectively
traversed all evaluated substrates using a terrestrial-specialized limb
geometry, illustrating the functional versatility provided through adaptive morphogenesis. ART’s terrestrial locomotion abilities enable it tonavigate outdoor environments with comparable facility to its swimming (Supplementary Video 2), prompting the question of what limb
morphology–gait pairing will allow transitioning between land and water.
The land-to-water transition features fluidized sediment that exerts
drag forces and impacts stability. Locomotor efficiency on granularN2with the ground, as: S = ∑i =1 (zi − zi*) /N (‘Terrestrial tests’ in Methods).
Here, S is the ‘stability metric’, denoting the extent of z-axis deviationfrom the ideal trajectory, and i indexes points in the trajectory from286 | Nature | Vol 610 | 13 October 2022

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b

Crawl

Downstroke

Recovery

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c
20

0
0.2

Porcelain
Sand
Intertidal
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COT

Limb
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COT

Shell

50

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Front
right

–50
0

20

40

Commanded

60

80

100

Gait cycle (%)
Fig. 4 | Crawling on transition substrates. a, Crawling distributes ART’s
weight, allowing it to traverse substrates commonly found in the transition
between water and land, including sand and intertidal substrate (a mixture ofsand, water and pebbles). b, Top: important steps over one gait cycle. Bottom:
commanded encoder positions for the ϕ and θ motors. c, The COT plotted as afunction of µ between the PLA shell (top) or elastomer limb (bottom) and thetwo transition substrates as well as the porcelain control surface. Horizontal
error bars indicate one standard deviation from the mean over seven trials.
Vertical error bars indicate one standard deviation from the mean over
five trials.

media is governed by a critical yield stress dependent on substrate
penetration depth25,26, percent water content27, and granule size anddispersity28. We therefore assessed locomotion strategies over representative transition terrains: dry sand and intertidal substrate—a mixture of sand, pebbles and water (‘Transition-substrate tests’ in Methods).
As expected, upright locomotion was unsuited to the transition
substrates. In attempts to creep on sand, ART exceeded the yield stressand slipped, burrowing its limbs into the sand instead of generating
forward thrust during the pivot (Supplementary Video 3). Similarly,
attempts at creeping on intertidal substrate entailed slippage on thepebbles, deviating ART from its forwards trajectory. A crawling gait,akin to movements of beaching sea turtles, was selected as a meansof locomotion over transition substrates. When crawling, ART lies on
its belly while using both fore and aft limbs in tandem to simultaneously lift slightly upwards and push rearwards for forwards progression (Fig. 4a,b and ‘Transition-substrate tests’ in Methods). Crawling
distributes the weight of the robot, mitigating catastrophic slip andpreventing ensnarement during locomotion. By crawling, ART was able
to successfully traverse both transition terrains, with 140% greater COT(averaged over all cases) than when creeping on land.
Friction tests (see ‘Transition-substrate tests’ in Methods for information) were conducted between the substrates and ART’s constituent
materials to understand the elevated COT of crawling compared withcreeping. The results show a positive correlation between the COT andthe static coefficient of friction (µ) for the shell and a negative correlation between the COT and µ for the limb material (Fig. 4c), suggestingthat the dominant mechanics governing the COT are sliding of ART’s
carapace along the substrate. The grip of limbs on the substrate aswell as the agglomeration of granular media at the front of the robot
probably also impact the COT.
Overall, gait adaptations shifting from an upright creep to a splayed
crawl permitted ART to traverse transition substrates. Although thekinematics of crawling differ substantially from those of walking, ART

still uses the leg shape when crawling as it provides stiffness to push therobot upwards and forwards. This preternatural mélange of morphology and gait highlight how adaptive morphogenesis enables unprecedented ability to specialize for multiple environments.
ART’s successful locomotion strategies in water, on land (Fig. 5a,b)and on transition substrate were combined to create a policy for
terrestrial-to-aquatic transition (Fig. 5c). The transition site consistsof an ocean inlet with hard-packed, pebbly soil flowing into a wet sandy
region before becoming shallows rife with rocks and plants (‘Field
tests’ in Methods). ART used its leg mode and creeping to traverse thehard-packed soil section. As ART approached the water and the substrate
became more saturated, it started crawling, ensuring stability andpreventing concentrated point loads of the upright gait from penetrating deep into the substrate. ART did not travel far into open water andlifted its limbs up out of the water before morphing (‘Morphing tests’in Methods). When only partially submerged in the shallows, ART reliedon paddling for swimming. ART documented its environment in-transit,
causing little disruption to its surroundings (Supplementary Video 6).
ART’s minimum COT performances are compared with those of ahost of terrestrial and aquatic animals and robots (Fig. 5d and ‘COT
Comparison Chart’ in Methods). ART had a minimum COT of 3 and 10
for aquatic and terrestrial locomotion, respectively. Owing to specializing for multiple environments, ART performs within the vicinity of,
and in some cases outperforms, state-of-the art unimodal aquatic or
terrestrial robots. For example, ART outperforms terrestrial legged
robots, such as the Massachusetts Institute of Technology learning
biped, by three times29, and performs similarly to unimodal tetheredquadrupeds such as Cheetah Cub and Titan V-III. ART outperforms
many exclusively aquatic robots, including a dielectric elastomer actuator robotic jellyfish by ten times, and a single-motor-actuated fish by
two times30. Crucially, ART can transition in unstructured environments while retaining comparable or better performance to unimodal
robots—a feat that no robot has demonstrated so far, to our knowledge.
Nature | Vol 610 | 13 October 2022 | 287

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b

c

d

103
TetheredLand Water

102

Robotic jellyfish

Fish
Reptiles
Birds
Mammals
RobotsMultimodal EELWORM

Multimodal LEO
Earthworm robot
Mice

Minimum COT (P/mgv)

Tunabot
Robotic fish

HAMR
101

La

nd

HAMR

Lizards

Snake

100

MIT learning
biped
Yale ART (crawling)
Yale ART (walking)Titan V-III
Delft pneumatic biped

Cheetah Cub

Finbot Mink
Rat Crab-like robot
Honda ASIMO
DuckYale ART (swimming)
TurtleDog

Rhex running
ANYmalWater skink

Wa

Sea
turtlester

Rhex

MIT Cheetah III
FishesSea snake
10–1
10–4

10–2

Sea lions

Cornell Robot Madeleine
biped

100

W Prize
102

104

Body mass (kg)Fig. 5 | Transition policy and COT contextualization. a–c, Composite images
with superimposed snapshots of the robot while swimming (a), walking (b) andtransitioning (c). d, ART situates itself among other animals and robots well,outperforming some state-of-the-art unimodal terrestrial and aquatic robots.
The robot mass increases for submerged swimming owing to incorporation ofballast. See ‘Robot components and fabrication’ in Methods for the referencesused for the plot. ASIMO refers to 'Advanced Step in Innovative MObility'; HAMR
refers to 'Harvard Ambulatory MicroRobot'; LEO refers to 'LEgs ONboARD
drOne' of the California Institute of Technology; MIT refers to Massachusetts
Institute of Technology; and W Prize refers to a target point for legged robotic
efficiency.

For unstructured, dynamic environments, such as the terrestrialto-aquatic transition, a robot design philosophy that treats morphology
and behaviour as mutable yields efficiency gains. ART combines bioinspired aquatic, terrestrial and transitional locomotion modes
through traditional robotic components, and functional shapes
through variable-stiffness composites to reduce morphological andbehavioural compromises. Doing so has spurred several questions, suchas when and where should transitions take place, can environmental
perturbations in transition be harnessed to enhance efficiency, andhow close to optimal are the gaits studied herein. Beyond providing aplatform to answer future questions such as these, we anticipate thatthe concept of uniting stimulus-responsive materials with traditional
robotics components will catalyse the next generation of adaptive
robotic systems.

288 | Nature | Vol 610 | 13 October 2022

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information,
acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-022-05188-w.

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Nature | Vol 610 | 13 October 2022 | 289

Article
Methods
A note on the term ‘adaptive morphogenesis’
We introduce the design paradigm of ‘adaptive morphogenesis’ todescribe adaptive robot morphology and behaviours realized throughunified structural and actuation systems. Our specific illustration of thisdesign paradigm leverages a combination of soft stimulus-responsive
materials and traditional robotics components to achieve on-demandchanges in a quadrupedal robot’s limb shape and gaits. In the term adaptive morphogenesis, ‘morphogenesis’ alludes to the emergence of form,
and thereby function (that is, in our case, the disparate tortoise leg or
turtle flipper morphology) as a result of environmental pressures31.
‘Adaptive’ refers to morphogenic features that are not fixed as they are
in animals through genetic encoding; they are mutable at a condensed
timescale and responsive to environmental context.
Some previous use of ‘adaptive morphogenesis’ in the biologicalliterature merits mention. Specifically, in literature concerning bacteria,
terms such as adaptive morphogenesis, morphological plasticity andphenotypic plasticity describe hypotheses of how bacteria change
shape and size based on environmental influences32,33. The biologicaluse of adaptive morphogenesis, despite being a lens through which to
explain cellular-level phenomenon, relates to the same notions that we
implement intentionally with our design paradigm.
Robot components and fabrication
With ballast for submerged swimming, ART’s total mass is 9 kg and its
density is slightly less than that of water. It spans 0.32 m from front toback, 0.96 m from limb tip to limb tip (with limbs raised up horizontallyon either side) and 0.358 m width-wise (with limbs lowered to their full
extent, measured about the top half of the shell). The robot comprises
four distinct subsystems: polyvinyl chloride (PVC) chassis, shell, shoulder joints and limbs. The inside of the chassis and shoulder joints arehermetically sealed together as a single volume. Extended Data Fig. 1ashows an exploded computer-aided-design view of the robot detailingthe various components.
Chassis. ART’s modular PVC chassis is composed of seven components:
central tube, front and back T-sections (the front one is labelled as front
viewport, where are camera may be installed), and four caps mounted
on the ends of the T-sections (labelled shoulder joint to chassis mount).
These caps have holes drilled in them to mount shoulder modules andallow cabling to pass through to the central tube where controllers arehoused. Each of the PVC modules are press-fit together. Hot wax wasapplied around their mating interfaces for further waterproofing.
The robot is tethered to an external pressure supply (Porter Cable,
Pancake Compressor A15414), power supply and computer for collecting data. The tether consists of silicone tubing (McMaster Carr, 3184K8)
for the pneumatic lines, a 12-V, 10-A power supply cable a.c. adaptor for
motor power (ROBOTIS), an extended universal serial bus cable for thedata line and 22-gauge insulated copper wire (Amazon, TYUMEN Extension Wire) for the heaters. The tether emanates through a hole in the
T-section at the tail end of the robot. We potted the hole around the cables
with marine-grade epoxy (Amazon, Loctite 1919324 Marine Epoxy).
Shell. The robot’s shell was fabricated in eight parts—four parts eachfor the top and bottom halves. Each shell part was 3D-printed with 100%
infill polylactic acid (PLA) (Prusa i3 MK3). On the top and the bottomof the interior of the shell, we designed an offset groove to fit snugly
around the curvature of the central tube of the PVC chassis. Two shellmounting holes, symmetrically on either side of the shell are included
so that a pin can fix the shell into position. Slots for ballast are included
on the bottom part of the shell.
Shoulder joint. A shoulder joint consists of three motors connectedby aluminium brackets (ROBOTIS) in a configuration that allows theend effector to sweep through turtle-inspired aquatic and terrestrial
gaits (Extended Data Fig. 1b). Having three motors in the shoulder
allows controlled movements of forwards and backwards, up anddown, and angle of attack, defined in Fig. 1c and Extended Data Fig. 1b
as θ, ϕ and α, respectively. The motors that control these angles are, inorder, Dynamixel MX-64, Dynamixel MX-106 and Dynamixel MX-64.
The stall torque for the MX-64 series is 6 Nm, and for the MX-106 series,
8.4 Nm at constant operating 12 V. Each shoulder joint is surrounded by
a 2-mm-thick stretchable rubber bellows that provides waterproofing
for the motors and chassis while still allowing three degrees-of-freedom(DoF) movements. A port installed on the top of the chassis allows us toevacuate air from the bellows, decreasing their volume and effectively
further tuning the robot’s buoyancy. A 3D-printed offset shaft at the output of the angle-of-attack motor has the bellows sandwiched between
its top (shoulder–limb interface) and bottom pieces. The other end of
the bellows is wrapped around the diameter of one of the T-sections
and clamped down with a ring clamp. The shoulder–limb interface
terminating from the bellows provides a spot to mount limb modules.
Morphing limb. One limb module consists of a morphing limb attached
to a 3D-printed interface, the limb–shoulder connector, that mateswith the shoulder–limb interface. A limb is made in the fashion of ref. 22(Extended Data Fig. 3). To summarize, elastomeric actuators of two
different types, A and B, are cast in Dragon Skin 10 Slow (SmoothOn).
Type A is longer and consists of two patterned chambers inducing
axial curling and distal tip bending. Type B is shorter and only hasinternal chambers for axial curling. The two actuators are bonded to astrain-limiting layer of cross-ply fabric, given pneumatic tubing inlets,
and a unidirectional lamina is then adhered to their surfaces to further
direct deformation34. Next, thin and flexible foil copper-clad Kapton
sheets (DigiKey) with the same contours as the actuators types A and
B are ablated in a laser cut to form two serpentine heaters (LPKF lasers
and electronics). These copper heaters are cast in a 10:4 by mass mixtureof EPON 828 resin (Momentive Performance Materials) and Jeffamine
D400 amine (Hunstaman International), degassed and cured at 60 °C
for 12 h. The thermally activated variable-stiffness composites are thenbonded to their respective actuators atop the fabric strain-limiting
layer. Lastly, part A and part B sub-assemblies are sewn together along
their edges. An aluminium rod is sewn to their newly shared leadingedge, and the protruding end of the variable-stiffness composite isslid into the 3D-printed interface where epoxy is poured and to securethem in place. The limb module is then ready to mount to the shaft on
the shoulder module.
Benefits conferred by the use of soft, stimulus-responsive materials
in the morphing limb are as follows. First, the synthesized variablestiffness polymer enables radical changes (450 times) in stiffness.
This attribute permits low effort, in a bending-energy sense, to switch
between flipper and leg shapes when the limb exceeds its glass transition temperature (Tg), as well as resilience in the final configurationon cooling.
Second, move-and-hold operations effectively eliminate the need tocontinuously supply pressure or some other actuation input (that is,
voltage with an electrostatic clutch) to maintain a limb configuration
during operation, enhancing safety and long-term energetic efficiency,
and circumventing potential failure modes. Moreover, passively holding a morphed shape removes any control effort that would otherwise
be needed to maintain a setpoint with alternative mechanisms.
Third, the chemistry of the limb materials allow for complex shapechange. Being soft and continuously deformable past its Tg, the limb isable to assume compound curvatures across its length, generating boththe cylindrical shell whose geometric stiffness facilities load bearing,as well as the curved limb tip that aids in traction and balance. Shapes
are generated with disordered polymer networks that constitute acontinuous, cohesive medium, whereas with conventional robotic
components, such a task might require many interleaved components.

Finally, the limb is disposed to emerging facile manufacturing techniques and is made from readily commercially available, inexpensive
materials. Morphing speed is a primary bottleneck for the proposed
limb. Although it is possible to rapidly heat the limb past its Tg andactuate it, cooling to the final shape depends on the environmental
temperature and the nature of the heat transfer boundary conditions.
However, we are not particularly concerned with minimizing morphingtimes in the present work. Morphing lasts at maximum on the order ofminutes, which is more than sufficient for effective transition between
environments.
Treating the limb as a column under compression gives a simple
mathematical explanation for its greater load-bearing capacity in the leg
mode. Consider both the cross-sectional area (a) change and change inshape from approximately circular (leg) to hollow rectangular (flipper).
The area moments of inertia for these cross-sections are:Ileg =

π 4 4(r − r )4 2 1
3Iflipper =(1)3b2h2 − b 1h1
12(2)

For the leg cross-section, a = π (r2 2 − r12); for the flipper, a = b2h2 − b 1h1.
Here, ri are the inner or outer radii of the circular cross-section, and bi
and hi are inner or outer widths and lengths of the rectangularcross-section. In our formulation, i = 1 refers to the smaller dimension.
We consider the Euler critical buckling load of the limb, given by:

Pcr =

π 2EI
(kL)

(3)

2

where E is elastic modulus of the variable-stiffness material (this dominates the compression response compared with the silicone elastomer), I is the cross-sectional area moment of inertia, k is a length factor(assumed as 1 in a case for virtual pin boundaries on either side) and L isthe unsupported length of the limb. Although k and E remain the same
between leg and flipper mode, I changes from Ileg to Iflipper. The morphing
operation is isoperimetric and constant thickness with respect to thelimb’s cross-section. Thus, the ratio between the two area moments ofinertia, expressed in terms of the same set of parameters b2, h2 and t,
assuming equivalent perimeters and thicknesses (h1 = h2 − 2t; r1 = r2 − t),gives:

Ileg /Iflipper =

π
4

(


2 (b 2 + h 2 )
2π

4

) −(

2 (b 2 + h 2 )−t2π

b 2 h23 − (b 2 − 2t ) (h 2 − 2t ) 3

4

) 

(4)

12

This ratio is always greater than 1 for fixed b2, h2 and t. A higher Pcr forthe leg mode of the morphing limb makes it well suited to terrestrial
locomotion, where gravitational loads must be supported. It is also
noted how L slightly decreases in leg mode owing to the curling of thefoot pad. This decrease in L further increases Pcr.
Operational power requirements. ART’s power requirements varydepending on its environmental context, if it is moving and, if so, withwhat gait, as well as if it is undergoing morphing. Whereas morphing
requires 50-W peak, maintaining upright posture requires a substantiallylower 3-W peak. The computer used to control ART (64-bit Windows 10
on a Dell XPS 13 9343 with 2.4 GHz Intel core i7) was monitored using
the Intel Power Gadget application. We noted a power draw of 5–7 W
during operation. Compressed air at 30 kPa is sufficient for inflating
the actuators while morphing; although compressor systems vary intheir efficiency, the one we used mandates a peak 735 W at start-up.
However, in practice, air is compressed beforehand, brought to the testsite and attached to the robot. Thus we do not count this compressor
power in the total live operational cost. During morphing, the robot
does not move its motors, so power draw from motors is on the orderof 1–3 W. We can assert that the maximum power requirement for running ART is the sum of heating (50 W), computer (7 W) and idle motors(3 W) contributions, in addition to a 5-W safety factor, which yields
65 W in total.

Kinematics, control and gait programming
The robot’s forward kinematics were derived to (1) define a workspace,(2) visualize candidate gaits in a MATLAB simulation before implementing them on the physical robot, and (3) mirror the trajectory of
one shoulder to the opposite side to render symmetric gaits. A Monte
Carlo MATLAB simulation sweeping through joint angles boundedby the robot’s hardware limits was conducted to visualize the workspace (Extended Data Fig. 2). The robot’s modified Denavit–Hartenberg
parameters are tabulated in Extended Data Table 1.
The robot runs on several Robot Operating System (ROS) nodes
coded in Python that control motor-specific functionality. Each ofrobots’ motors operates on an independent closed-loop position controller. Specifically, a proportional position controller with a gain of
32 was used.
To program swimming and crawling gaits, we rely on kinesthetic
teaching: manually moving the robots’ limbs while recording a rosbag
to acquire the motors’ trajectories. We sampled trajectories at a rate of
60 Hz and then post-processed the data by applying a moving averagefilter with a 20 sample window over the trajectory. The discrete set of
motor position data, after it is processed, can be played back as a seriesof waypoints. The effect of the filter is to smooth the hand-programmed
gaits. We used kinematic mirroring to take the hand-taught trajectoryof one shoulder and transfer it symmetrically to the other shoulders,if applicable.
It is noted that, in contrast to actual turtles, ART’s crawling gait
uses all four limbs to propel itself forwards. Also, while crawling, ART
employed its leg mode rather than the flipper because the flipper was
too compliant to partially lift its body off the substrate.
We did not use kinesthetic teaching to program the creep gait, owing
in large part to the asymmetry of the gait and need for coordination ofmultiple joints to produce forward locomotion while remaining statically stable. Thus, we programmed the creeping gait as a superpositionof linear waypoints between encoder values, and then applied a runningaverage filter over the waypoints to elicit smoother movements.
Calculation of COT
To calculate ART’s average COT for both aquatic and terrestrial gaits,
we used the relation considering the average electrical input power Pin
to the robot:
COT =Pin (t)mg v bot(5)

For our robot, the mass m = 9 kg and gravity g = 9.81 m s−1. The robot’s
average velocity over five trials, v bot , was calculated from highdefinition video at 30 fps and with a spatial resolution of 1 px mm−1. The
camera for recording video was positioned perpendicular to the robot’s
forward movement direction, approximately 4 m away, to capture
the entire field of the robot’s movement. The three types of motor oneach of the shoulder joints contribute to the power input, via:Pin (t) =4

3∑i=1 ∑n=1 In, i (t) V(6)where In,i is the average amperage measured from the nth motor on theith shoulder (in amperes) during the gait, and V is voltage supplied to
the robot at a constant 12 V. Five trials of each gait were performed.

Article
COT discussion. As evidenced by equation (5), the COT is a nondimensional metric that is calculated by dividing average power input
to a system by the product of mass, the local gravitational acceleration
and average velocity. It describes the energetic cost to move a unit massa unit distance. Alternatively, the total energy expenditure (Etotal) canbe divided by the product of the mass, the local gravitational constantand the total distance travelled (d):COT =Etotalmgd(7)

It is important to note that sometimes the COT is reported without
dividing by g, resulting in a COT with units of J kg−1 m−1, which further
simplifies to s2 m−1. In other works on animals, the energy expenditureis expressed as VO2, which is the volume of oxygen consumed duringrespiratory metabolism and the COT is reported as a having units similar
to VO2 kg−1 × km, although VO2 can be converted to joules by taking its
equivalent caloric value. In this paper, all COT values reported fromprevious work were converted into the unitless form defined as per
equation (7). In addition, previous works take different approaches
when measuring P(t) or Etotal, based on what is most practical to measure, and owing to this disparity some reported COT values cannot becompared.
When comparing COT values, it is important to consider whichpower or energy value is measured and what assumptions influencethat measurement. Since at least the 1970s, metabolic COT and COT
values derived from the energy input into the system, in our case theelectrical COT, have been the standard metrics used for comparing
biological and artificial systems.
When calculating COT for living organisms, respiratory metabolism is commonly used as a proxy for energy expenditure where thecaloric value of VO2 is assumed to be the same as the system energy
input. Several techniques are used for measuring oxygen uptake. In
some experiments, animals have intravenous probes inserted into
their arteries and sometimes veins.
In others, the entire volume of fluid entering and exiting an experimental chamber is tested in separate chambers to determine the gas
composition. In more recent experiments, masks are fitted to theanimals and the composition of the gas flows in and out are analysed.
In contrast, robotic systems often report two different types of COT.
Some calculate COT using the total energy or power input to the system
to propel the robot along a trajectory, such as the electrical power
input (P = IV) or the potential chemical energy of the fuel consumed ( J).
Some robotic systems only measure the mechanical power at the endof the powertrain (often calculated via P = τω, where τ is the torqueand ω is the angular velocity). The two types of COT differ by the inefficiencies between the input and output of the robot powertrains, andpotentially other inefficiencies. For example, in a wheeled robot, theelectrical power supplied to the motors from an external power sourceis larger than the mechanical power exerted by the wheels, differingby the efficiency of the powertrain. A COT calculated using electric
power expended during movement will necessarily be higher than a
COT calculated using the mechanical power exerted by the wheels. The
same holds true for other energy inputs, such as chemical or pneumatic
power supplies and their respective downstream actuators.
ART’s average forward velocity and COT for different substrates
and gaits are tabulated in Extended Data Table 2. For a biologicalcomparison, sea turtles exhibit typical cruising speeds of 0.5–0.6 m s−1(ref. 35). Galapagos tortoises have been found to walk at 0.16 m s−1 (ref. 21),
although this value has a large range depending on conditions. The COTof hatchling and juvenile sea turtles (Chelonia mydas) ranges between
0.3 and 2 (refs. 20,36) when swimming, whereas that of the semi-aquatic
Macquarie turtle (Emydura macquarii) ranges between 0.2 and 0.6 (ref. 37)
when walking. The discrepancy in speeds and COT between actual

turtles and ART is partly attributable to the lower energy density, efficiency, elastic energy storage and power output of transmission-based
servomotors compared with animal muscle38. Gaits were programmed
by observing animals’ gaits and are consequently not optimized. Further
tuning gait parameters to minimize extraneous movements might
improve speed and COT.

Swimming tests
Swimming tests were conducted in a large outdoor pool (l × w × d =15 m × 8 m × 5 m). Operational Reynold’s numbers for the robot, defined
as

Re =

Ul
γ

(8)

where U is the velocity of the fluid, l is the length of the robot and γ isthe kinematic viscosity, ranging between 6.4 × 103 and 2.6 × 104 for all
aquatic gaits tested. This Re falls within a similar range as leatherback
hatchlings with l = 0.08 m at Re = 7.2 × 103 for slow sustained swimmingand Re = 2.7 × 104 for vigorous swimming39. Compare this with grownleatherback sea turtles with l = 1 m, operating at Re = 5 × 105 (ref. 40).
Free swimming tests for calculating the COT were conducted along
the length of a pool, while recording the velocity of the robot with ahigh-definition camera. Two gaits, paddling and flapping, were studied.
We varied the offset angle (Fig. 2b) of the flapping gaits from 10° to
40° in increments of 5°. Before 10°, the robot exhibited no forwards
displacement.
The regions of Fig. 2b were determined as follows, after collecting
COT data from flapping across a span of angles. The first (red) region
was determined by partitioning where COT of flapping was higher thanthat of paddling. The second (yellow) region was at first empiricallydemarcated because it exhibited a steep drop in COT; subsequent computational fluid dynamics simulations (‘Computational fluid dynamics
simulation of flipper’) demonstrated that this region corresponds to a
critical shift in angle of attack that reduces drag throughout the stroke.
The third (blue) region was delineated because it witnesses a decreasein slope of the trend line as the COT approaches its best value.
To assess the force profile of paddling and flapping gaits, a customdesigned test rig (Extended Data Fig. 4b) was constructed on which
to mount the robot and measure forces using a multi-axis transducer(ATI Industrial Gamma F/T sensor). The test rig was affixed to the sideof a pool and the robot was attached 0.635 m submerged and 2 m offset
from the pool walls and bottom to mitigate boundary effects. The robot
being fixed prevents analysis of the dynamics of a full propulsion cycle,
and therefore we cannot make any conclusions about the steady stateor transient quality of flow about the robot. We can, however, still gain
insight into the magnitude and direction of forces exerted during eachtype of gait. While a gait was executed, we sampled x- and z-direction
forces (Extended Data Fig. 4) at a rate of 1,000 Hz using a data acquisition unit (National Instruments USB-6212). Five trials of each gaitwere performed. Extended Data Fig. 5 shows one set of representative
commanded and actual angular displacements, speeds and motor
amperages corresponding to the force profiles of the paddling andflapping gaits shown in Fig. 2c,d.

Computational fluid dynamics simulation of flipper
We conducted a numerical analysis in ANSYS Fluent to examine the lift
(normal to flow direction) and drag (parallel to flow direction) forceson the limb during the downstrokes and upstrokes of the flapping
gait, at a condition with a flow rate of 0.3 m s−1. A speed of 0.3 m s−1 isapproximately the robot’s peak speed at the upstroke; at this moment,
the flipper’s angle of attack will have the strongest influence over dragforces than any other time in the stroke, owing to the increased relative
velocity between robot and fluid.

Steady-state simulations, parametrically varying the angle ofattack as 0° ≤ Φ ≤ 60° in increments of 5°, were conducted with an.IGS model of the flipper, placed in the centre of a virtual flow domain.
The flow domain was modelled as a 2-m-long cylindrical volume with
inlet and outlets of area 3.141 m2. Meshing for the flipper and flow
domain employed adaptively sized tetrahedral elements, rendering acomputational domain of approximately 1,000,000 cells. The boundary condition was set to mass flow rate in equal to mass flow rate outof the entrance and exit to the cylindrical volume. For the calculation,
we selected the Fluent computational fluid dynamics (CFD) solver withthe method as SIMPLEC. A solution was initialized at v = 0 m s−1 in the
direction of flow. To determine convergence, we monitored forces oflift and drag, as well as the flow-direction velocity, with convergenceoccurring if these metrics dipped below 0.001 residual value.
CFD results. Before we discuss the CFD results, we first define Φ as theangle of attack of the flipper relative to the flow direction (Extended Data
Fig. 6, inset). Recall that α measures the angular displacement of theterminal motor in the shoulder joint, in the kinematic chain’s frame ofreference (Extended Data Fig. 1). Therefore, Φ and α do not necessarily
coincide. Lastly, as defined in the main text, θ is a scalar offset appliedto α for the duration of the stroke.
The results of the simulation reveal a typical hydrofoil response forthe flipper (Extended Data Fig. 6). A peak in lift force occurs aroundΦ = 15°, quickly followed by a region of stall. Drag forces are monotonically increasing with Φ in a nearly linear fashion. In the yellow regionof Fig. 2b, the steeper drop in COT corresponds to a favourable angleof-attack offset, θ .
By analysing the flapping gait’s kinematics and the results of simulation, we can predict what factors cause this drop in the COT. During theflapping gait’s upstroke, the flipper is used essentially as a paddle topush back the water. Increasing θ makes Φ higher with respect to theflow direction (the robot is pushing back, so net flow about the flipper occurs in the defined positive direction of Extended Data Fig. 4),
thereby allowing the robot to produce more effective thrust on the
upstroke. At the end of the upstroke and before the beginning of thedownstroke, the flipper slows down while the robot glides forwards.
During this part of the gait cycle, increases to θ move the flipper tocloser to Φ = 0° with respect to the flow direction (which is now opposite to the defined forward direction of Extended Data Fig. 4), reducing
drag. Furthermore, angles between 0° < Φ < 15° cause the generation ofsome lift force; its vector component in the forwards direction can help
maintain speed through to the next portion of the gait, the downstroke.
During the downstroke, the robot moves its flipper slightly rearwards.
In this scenario, it is again favourable to have a higher Φ against theforwards direction to produce more thrust, whereas angles between
0° < Φ < 15° may generate a vector component of lift in the forwards
direction.
In summary, a favourable θ puts the flipper at higher Φ during quasipaddling sections of the gait cycle, and orients it between 0° and thepeak angle before stall in gliding after an upstroke or downstroke. This
is why we see the COT decreasing with increasing θ. However, this will
not be a monotonically decreasing trend for even higher values of θ.
Eventually θ will exceed a value where it is generating net counterproductive thrust, as it did before 10°. In our case, hardware constraintsof the bellows twisting too much capped the tenable angle-of-attack
offset at θ = 40°, and thus we did not test past this value.

Terrestrial tests
Terrestrial tests took place on flat porcelain tile inside the lab, and concrete or granite in an outside environment. COT and Pin were calculated
in the same fashion as with aquatic gaits, as per equations (5) and (6).
We used Ascension trakSTAR (Ascension Technology Corporation (anNDI company)) motion tracking markers to monitor the 6-DoF of ART’slimb trajectory on the different substrates.

For calculating the stability metric, S , we used the disparity between
the actual z-axis trajectory and an ideal trajectory of the robot with
enforced perfect ground contact. The ideal trajectory as the robot pivots or resides in a stance phase is a constant line of zero slope. In otherwords, an ideal trajectory entails no slip, intermittent ground contacts,or splay/tucking in of the legs, all of which may decrease force generated
for forwards locomotion. Projected z-axis data used in the calculationof 𝒮 started after the robot completed a ‘step BL’ phase (Fig. 3b,d).
Data were normalized to start at a value of 0. An average value for S was
calculated over five trials.
Terrestrial locomotion analysis. The robot’s stride frequency andlength while creeping depended on the substrate it was traversing.
For the porcelain control substrate, the stride frequency was
0.145 strides per second averaged over the entire data collection period.
Three-dimensional motion capture data collected of creeping on different substrates revealed consistency in terms of stride length and swept
trajectory. In the cases of porcelain, concrete and granite, the stride
length was 0.182 m ± 0.015 m, 0.217 m ± 0.022 m and 0.206 m ± 0.027 m,
respectively.
Extended Data Fig. 7 shows the commanded and actual positions
for the creep gait over porcelain, for each of the four shoulder joints.
Extended Data Fig. 8a gives plots for the front-right shoulder joint overporcelain. Extended Data Fig. 9 shows the same for the crawl gait, but
only focuses on one shoulder joint owing to symmetry.
Of particular relevance to limbed locomotion offset from the ground—in our case, the creep gait—is the Froude number, a quantity that helpsclassify animals across different sizes into groups that locomote similarly. It is the ratio of the centripetal force around the centre of motion—
the foot—and the weight of the entity walking:

FR =

U2
gh

(9)

where U is the forwards velocity of the robot, g is the acceleration
owing to gravity and h is the height of the robot’s hip joint from theground (0.3 m). The average Froude number for the creeping gait acrosssubstrates was 2.9 × 10−4. It is interesting to note that this number
is lower than the range characteristic of terrestrial vertebrates andtortoises21. ART’s legs are longer than actual turtles’ legs, and this caused
some stability issues when trying to creep on the granular substrates.
Moreover, unlike most quadrupedal robots, ART uses 2-DoF for eachleg when walking. Although somewhat restrictive in terms of uprightmovement, this design choice was intentional for preserving thecritically important angle-of-attack DoF in the swimming kinematicconfiguration, and simultaneously minimizing the hardware required
for locomotion across multiple environments.

Transition-substrate tests
For transition-substrate tests, we filled a sandbox with the substrate toa depth of 101.6 mm, for 0.34 m3 volume of substrate. The sand used
was Pavestone patio/paver sand with a granule diameter distributed
between 0.08 mm and 2.4 mm, average 0.4 mm. All dry substrates
were at 22 °C. We also made an intertidal substrate consisting of pebbles (Vigoro decorative stone: all-purpose stone; diameter distributed
between 20 mm and 100 mm, average 50 mm), sand and water mixed
together. First, 15% water by volume was mixed with the sand. Then we
added 15% by volume pebbles to the sand/water mixture.
A complex interaction between several factors including flipper
thrust generated by pushing through the fluid-like medium, body lift,base drag, ground yielding and texture of the ground governs turtles’
locomotion over granular media17. We considered that friction wasa main contributor to the robot’s performance over the different
substrates when crawling. To test this hypothesis, we conducted friction
tests between the three substrates and PLA, elastomer and the rubber

Article
bellows to quantify the coefficient of static friction between each.
A rectangular specimen of the material with a fixed surface area was
attached to a low-friction string, routed through a pulley, and mounted to
the load-head of a materials testing machine (Instron). Atop this material
specimen, we applied distributed weight. Applying 150 mm min−1, thespecimen with weight atop was dragged along either porcelain (control),sand or the intertidal substrate. Force and displacement data wererecorded. For a given material–substrate pairing, we conducted sevenindependent tests. The static coefficient of friction was calculated as:µ = Fm /W(10)

where Fm is the force at the initial specimen movement and W is theweight of the rectangular material specimen plus the additional distributed mass atop. As the robot varies its weight exertion on the substratedepending on the exact moment in the stroke cycle, we tested a range
of weights from 50 g to 1 kg. We noticed a dependence of the coefficient of friction on the weight used. The average of µ for all weights
was reported for a given substrate–material pairing. Extended Data
Fig. 10 gives representative test data averaged over seven cycles forthe 500-g mass used in the calculation of µ.
A positive correlation between µ (between primary contact interfaces, PLA or elastomer, and substrates) and the COT for crawling
validates that µ is a reasonable predictor of performance for the crawling mode of locomotion. Although it is likely that the bellows madesome contribution to the forces during locomotion, we expect thatthe robot’s primary contact interfaces have a much more dominant
contribution. Consider that the majority of the bellows’ surface areathat is touching substrate does so lightly, and this surface area consists
predominately of creases and folds, not a flush interface. A smaller
normal force arises from the bellows, which will yield a lower friction
force. In contrast, the PLA shell and elastomer limb bear more of therobot’s weight, have greater surface areas that are more directly in ashear with the substrate and are more rigid, so we expect these primaryinterfaces to be the source of most of the forces. The µ values forall substrate–interface combinations is tabulated in Extended Data
Table 3.
Transition-substrate gait considerations. In preliminary experiments, we found that a four-limb crawl was more effective in generating
forwards thrust and speed than using two limbs. Thus, for the present
paper, ART implements a four-limbed crawl for transition-substrate
locomotion. Actual sea turtles do not have the functional shapes ormusculature to perform such a gait, and predominately generate thrustwith their fore flippers when beaching. ART’s marked departure fromits biological inspiration in this respect underscores its advantages as asynthetic system capable of ‘unnatural’ yet highly effective locomotion
modes. As creep is characterized by totally different mechanics, wenote the importance of substrate yield stress and penetration depth,
and how these factors are influenced by fluidization and disperse
grain sizes.

Morphing tests
The variable-stiffness composite is waterproof to facilitate morphingin wet environments. We sought to quantify how the different freeconvection conditions of being submerged in water or in air would
influence the softening of the variable-stiffness material through Joule
heating. We conducted morphing tests in water and in air, both at 22 °C(Supplementary Videos 3 and 4). The water test was conducted in a large
bin filled with tap water that was allowed to reach room temperatureof 22 °C. With the limb morphed into the leg mode, the test entailed
subjecting each heater to 50 W, supplied from an external power supply,
while recording high-definition video to monitor deformation of thelimb. The limb took around 100 s to morph in water and 50 s to morph
in air.

Field tests
We took the robot to East Rock Park, in New Haven, CT, for field testingin a natural intertidal transition environment. The shoreline featured
hard-packed dirt with various-sized pebbles and sticks. Closer to thewater, fluidized sand and mud were pervasive. The water was partiallysaline, exhibited weak currents and had a peak depth of 1 m. The robot
was powered from a Honda 2,500-W invertor generator. In previous
tests, a tether consisting of data and power lines was employed. For fieldtesting, we extended the pneumatic and heater lines into the tether.
Our first time testing ART occurred in autumn, with an air temperature of 5 °C and a water temperature of 9 °C. Locomotion and shapepolicies were chosen by an operator on-site based on data from land,transition-substrate and aquatic tests. We attempted to morph thelimbs while they were submerged to no avail, probably owing to the highheat transfer owing to forced convection of the cold water. We decided
it would be energetically expedient to conduct morphing out of thewater during field tests and to wait until a warmer season. The second
test occurred in spring, with an air temperature of 23 °C and a watertemperature of 15 °C. This time, we were able to achieve morphing by
programming ART’s limbs to lift up.
Challenges that became apparent during the transition included
difficulty transitioning from water to land—the robot needed to beachitself entirely, then perform a push-up, which the motors were notstrong enough to do. Alternatively, the robot could try and orient its
legs in the shallows, but currents and debris underfoot destabilized
the robot such that it could not stay balanced. Transition from waterto land thus remains an area for future work.
COT comparison chart
In Fig. 5b, the COTs for insects, reptiles, birds, mammals and other robots
were either directly reported, or obtained and replotted from refs. 29,37,41–53
using graph digitizing software (GetData v2.25).

Data availability
All data needed to evaluate the conclusions in the paper are present in
the paper and/or the Supplementary Information.
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Acknowledgements We thank V. Wilczynski, Deputy Dean of Yale School of Engineering,for use of his pool. This project was sponsored by the Office of Naval Research under award
N00014-21-1-2417. Any opinions, findings, and conclusions or recommendations expressed inthis material are those of the authors and do not necessarily reflect the views of the Office ofNaval Research. R.B. was supported by an NSF Graduate Research Fellowship (DGE-1752134).
Author contributions R.B., S.K.P., J.B., T.S. and A.G. designed and built the robot. R.B., S.K.P.
and L.R. conducted swimming, terrestrial and transition experiments. R.B., S.K.P., L.R. and
F.F. programmed gaits. R.B. conducted CFD simulations and friction tests. R.K.-B. conceived ofthe project and oversaw the research. All authors contributed to writing the manuscript.
Competing interests The authors declare no competing interests.
Additional information
Supplementary information The online version contains supplementary material available
at https://doi.org/10.1038/s41586-022-05188-w.
Correspondence and requests for materials should be addressed to Rebecca Kramer-Bottiglio.
Peer review information Nature thanks Navinda Kottege and Cecilia Laschi for theircontribution to the peer review of this work. Peer reviewer reports are available.
Reprints and permissions information is available at http://www.nature.com/reprints.

Article

Extended Data Fig. 1 | System description. a, Exploded computer-aided-design
view, detailing components of robot. Note that the shoulder joints are typicallyshrouded in rubber bellows, and thus not visible. For clarity, we only depict thebellows on the back right joint in transparent grey. b, 3-DoF kinematic mechanism
used to achieve bio-inspired gaits. Symbols θ, ϕ and α are the rotation axes for theswing forward/backward, up/down, and angle of attack motors, respectively.

Extended Data Fig. 2 | Robot workspace. Workspace visualized in the robot’s
kinematic simulation. The explored gaits are superimposed atop the cyan
workspace in a darker colour. Top two are swimming gaits; bottom two are

terrestrial and transition gaits. Chassis beneath the shell is rendered for context.
Links are line segments coloured red, green, and blue. The black arrow points inthe forward travel direction.

Article

Extended Data Fig. 3 | Fabrication of Morphing Limb. Fabrication can be
broken down into two main tracks: elastomeric actuators (top), and Jouleheating variable-stiffness material (bottom). We fabricate components foreach of the limbs’ two halves, A and B. Actuators and variable-stiffness material

components for A and B come together in the final step, in which they are
hinged together via a sewed joint. The limb cross-section is displayed in theinset. Figure and caption adapted from ref. 22.

Extended Data Fig. 4 | Test rig for evaluating force profiles of gaits. Coordinate system defines positive direction of forces measured via the multi-axis load cell.
Adjustable fixtures allowed us to tune the robot’s offset from the pool sides and bottom, as well as its submerged depth.

Article

Extended Data Fig. 5 | Representative data for front-right shoulder during
paddling and flapping gaits. Top row gives a robot schematic with superimposed
trajectory. Second row gives commanded and actual encoder positions, where

the solid line is the actual achieved position. Third row plots the angularvelocity. Fourth row is the amperage. Line colour and legend symbols match
those of Fig. 1b.

Extended Data Fig. 6 | CFD results. Simulation results of lift and drag forces on the flipper mode of the morphing limb, at 0.3 m/s. Inset depicts definition ofΦ with respect to the flow direction.

Article

Extended Data Fig. 7 | Representative data from all shoulder joints forcreeping gait on the porcelain substrate. Top row presents snapshots of therobot at key parts of the gait. Graphs underneath give commanded and actual

encoder positions, where the solid line is the actual achieved position. Linecolour and legend symbols match those of Fig. 1b.

Extended Data Fig. 8 | Additional creep data. a, Left to right: commanded
and actual encoder positions, angular velocity, and amperage for front-rightshoulder joint. The solid line is the actual achieved position. Line colour andlegend symbols match those of Fig. 1b. b, Representative data from motion
capture of back-left distal tip of limb during creep gait. Spikes in Z correspondto the limb swinging out, whereas the other portions are the pivot or where thelimb serves only to balance the robot. Notice the amplitude and frequency ofvibrations occurring at these times, which give an indication of surface
normals and roughness. At these sections, we calculated the stability metric tograsp the effect of substrates on COT when creeping. Here, the series are notnormalized to all start at 0, for ease of viewing.

Article

Extended Data Fig. 9 | Representative data from front-right shoulder joint
for crawl gaits across the three substrates. Top row gives a robot schematicwith superimposed trajectory. Second row gives commanded and actual

encoder positions, where the solid line is the actual achieved position. Thirdrow plots the angular velocity. Fourth row is the amperage. Line colour andlegend symbols match those of Fig. 1b.

Extended Data Fig. 10 | Example data from friction tests. Force versus displacement for elastomer, PLA, or bellows with 500 g weight placed atop them, over thevarious substrates. Clouds indicate one standard deviation from the mean, over 7 trials, with the solid line as the mean.

Article
Extended Data Table 1 | The robot’s modified Denavit–Hartenberg parameters54

Extended Data Table 2 | The robot’s velocities and COTs for all gaits

Article
Extended Data Table 3 | Experimentally determined friction coefficients between ART’s constituent materials and thevarious tested substrates