Chapter 3

Amphibious Robotic Propulsive
Mechanisms: Current Technologies
and Open Challenges
Robert Baines, Frank Fish, and Rebecca Kramer-Bottiglio

3.1 Introduction
Much research effort has been dedicated to underwater robots, as evidenced bynumerous papers and the contents of this book [1]. An even larger body of literature
concerns terrestrial robots. But what about amphibious robots that can operate bothin water and on land? From the literature, we glean that amphibious robots are
fantastic vehicles for studying autonomous navigation strategies in unstructured,complex environments [2]. Furthermore, they have proven useful as physical models
for gaining deeper insight into the gait patterns and mechanics of animal locomotion[3–5], analyzing the health of ecosystems [6, 7], and understanding physicalprinciples underlying propulsion in various media [8, 9]. Beyond the academic
space, advances in amphibious robotics are projected to be a significant boon toindustries such as reconnaissance, surveying, offshore mine detection, and water
quality monitoring, where seamless transitioning between locomotion modes iscritical to success [10–13].
In spite of their versatility, relatively few amphibious robots have been reported
in the literature. Significant challenges remain for designing, building, and implementing amphibious systems outside of the laboratory setting. Central to realizing
an amphibious robot is designing propulsive mechanisms for effective water- andland-based locomotion. In doing so, the engineer must strive to balance conflicting
features. As we shall investigate in this chapter, both in natural and physical systems,

R. Baines · R. Kramer-Bottiglio ()Department of Mechanical Engineering and Materials Science, Yale University,
New Haven, CT, USAe-mail: rebecca.kramer@yale.edu
F. FishDepartment of Biology, West Chester University, West Chester, PA, USAe-mail: ffish@wcupa.edu© Springer Nature Switzerland AG 2021
D. A. Paley, N. M. Wereley (eds.), Bioinspired Sensing, Actuation, and Control in
Underwater Soft Robotic Systems, https://doi.org/10.1007/978-3-030-50476-2_3

41

42

R. Baines et al.

functional shapes conducive to load bearing and terrestrial maneuverability often
detract from hydrodynamic efficiency and water compatibility.
The transition between water and land, called the littoral zone, also presents
challenges. The littoral zone is characterized as a turbulent environment due towave action, intermixing of heterogeneous substrates, suction forces, and abrasiveflows imposed by fluidized sediment. Rocks, shoals, uneven slopes, dense algal
beds, and reefs are all obstacles that an amphibious robot might encounter andhave to negotiate in a transition zone [14, 15]. The dynamic onslaught of physicalphenomena and obstacles in the littoral zone constitute a multi-faceted problem forwhich there are no obvious robot design solutions.
To provide biological inspiration in the design of amphibious propulsors, thischapter first analyzes animals’ body plans and their locomotor adaptations in
Sect. 3.2. Animal morphology and physiology is, in fact, chiefly influenced byevolutionary pressures for effective movement in an environment [16]. For the sakeof brevity, we hone in on key examples from semi-aquatic, semi-terrestrial, andhighly specialized species that typify the range of propulsive modes exhibited byanimals.
With biological context, we transition to a survey of existing amphibious robotic
platforms in Sect. 3.3. Designs striving to address the slew of environmental
challenges amphibious robots face can be broadly classified into systems that
locomote using separate or united propulsive mechanisms. We define separate tomean that distinct subsystems move a robot on land and though water, whereas
movement with a united mechanism is achieved in both media via the same
subsystem. While separating propulsive mechanisms is a more traditional approachand may allow robots to locomote with specialized modes of transit in eachenvironment (i.e., using wheels to move on land and jets to move through water),
uniting propulsive mechanisms has gained popularity as a means of reducing systemcomplexity and exploring propulsive architectures inspired by amphibious animals(i.e., using snake-like undulations to move in water and on land) [17]. Beyond
separate and united propulsive mechanisms, we further sort robots into (1) wheeled,(2) legged, (3) undulatory, or (4) soft categories, based on their body plans andprimary means of propulsion. Section 3.3 further expounds on what distinguishes
these classifications from each other.
After a synthesis of existing work, Sect. 3.4 identifies promising avenues for
future research on amphibious robotics. Lastly, Sect. 3.5 presents a case study: ourresearch on a variable stiffness morphing limb, a design that seeks to unite various
propulsive functionalities into a single cohesive mechanism.

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

43

3.2 Biological Perspectives on Amphibious Locomotion
3.2.1 Movement through Different Media
There are physical differences between water and air that determine the different
mechanisms of animal locomotor modes in either environment. Density and viscosity are the most important physical properties [18]; water is 800 times denser
than air and 55 times more viscous. The ratio of inertial to viscous effects is
also of paramount importance to aquatic locomotion [19], and can be expressed
quantitatively via the Reynolds number:
Re =

ρU L
,
μ

(3.1)

where ρ is the fluid density, U speed, L characteristic length of the body in the fluid,and μ dynamic viscosity. We will touch on the ramifications of scale with regard tospecific propulsive mechanisms later. Regardless of scale, swimming animals tend
toward a density close to that of water to support their body weight via buoyancy.
They use the high density and viscosity of the medium to generate hydrodynamic
forces for propulsion. Swimming is accomplished by propulsors that can be broadlyclassified as undulatory, lift-based oscillatory, drag-based oscillatory, or jetting [20–22].
On land, an animal moves through air, so gravitational forces predominate andthe weight of an animal has to be supported by rigid or hydrostatic skeletons.
Animals apply frictional forces from contact of a body or limbs on the solid
ground for propulsion. Broadly speaking, terrestrial locomotion is enabled by
propulsors that induce undulatory motions, limbed locomotion, a combination ofboth undulating and limbed locomotion, or rolling [23–26].
Many animals are capable of moving between water and land [22]. The reasons
why animals adapted for multi-modal locomotion between water and land stem fromsurvival adaptations, including catching prey, escaping from predators, mating, andsearching for food [27]. For vertebrate animals, the shift from finned swimming tolegged terrestrial locomotion in the transition from fish to amphibians is considered
one of the watershed events in evolution. Aside from amphibians, mammals,
reptiles, and birds have amphibious species exhibiting varying degrees of terrestrial
and aquatic locomotor adaptations. Amphibious behaviors are also exhibited byinvertebrate lineages, most notably mollusks and arthropods. All amphibious
animals, regardless of classification, must strike a balance between being both semiaquatic and semi-terrestrial, and utilize united or separate propulsive mechanisms
for locomotion in either media.

44

R. Baines et al.

3.2.2 Amphibious Animals with United Propulsive
Mechanisms
Numerous amphibious animals exist in nature that utilize the same propulsive
mechanism in both mediums [28]. Amphibians, notably frogs, hop and swim using
a similar movement pattern: maximum extension of hind limbs, followed by asweeping recovery phase [29]. Mammalian limbs can relatively easily engage indrag-based propulsion in water. Drag-based swimming and quadrupedal walking
locomotion modes are embodied by mammals such as muskrats, elephants, andopossums [30]. When swimming in a drag-based regime, propulsive drag force
is produced only through half of the stroke cycle by the rearward movement of
the appendage, since forward motion is a non-thrust generating recovery phase.
Consequently, limbed amphibious mammals demonstrate high locomotor costs dueto their inability to specialize for water or land [22].
Amphibious reptiles, like freshwater turtles, also utilize united propulsive
mechanisms—swinging of limbs—for drag-based swimming and quadrupedal
walking. Amphibious snakes, on the other hand, leverage bodily undulations tomove in the water and on land. Evolutionary adaptations that enhance aquatic
locomotion at the expense of terrestrial locomotion, such as diminished ventral
plates and a flattened tail, can be observed between some species of snakes. [31].
Mollusks like the octopus represent a rather unique case in that they use unsupported
limbed locomotion to crawl along the ocean bottom and on land [32].
Propulsive mechanisms for amphibious animals that walk both on the surface ofwater and on land are very much governed by size. Small animals with hydrophobic
surfaces, such as water striders, can exploit surface tension to support the body [33].
As the size of an animal increases, surface tension becomes insufficient to support its
weight. The basilisk lizard can run atop water by simultaneously generating surfacelevel drag and expanding an air cavity underwater [34]. As the size of a basilisk
lizard increases, the kinematics of the foot stroke change to keep it atop the surface[35]. For even larger organisms, like aquatic birds, movement atop water requires
the addition of broad wings impacting the surface [36].

3.2.3 Amphibious Animals with Separate Propulsive
Mechanisms
A less common model in nature than united propulsive mechanisms is to utilize
separate propulsive mechanisms for either medium. Among mammals, otters engage
in quadrupedal walking and undulatory swimming [37]. Reptiles of the order
Crocodilia, including alligators and crocodiles, use tail undulations in the water but
rely on quadrupedal gaits on land. Similarly, newts and salamanders undulate theirbodies in a standing wave while using their limbs to walk [28]. Some at high speeds
will undulate on land with their legs tucked in to their sides.

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

45

3.2.4 Specialization for Water or Land
Generally, semi-aquatic or semi-terrestrial animals—like those mentioned up to thispoint—are less energy efficient and slower (in terms of body lengths per second)
than animals that are specialized for one environment [22]. Yet in engineering, anamphibious robot is not limited by the same physiological factors that limit animals.
Animals must move by oscillations of appendages or body undulations poweredby muscles, must respire with gills or lungs for oxygen to fuel cells constituting
their muscles, are composed of biomaterials such as bone, cartilage, and chitinthat have lower strengths compared to metals used in engineered systems, andhave a large portion of the body devoted to reproductive functions. An amphibious
robot can take advantage of specialized, rapid, and efficient aquatic and terrestrial
propulsive mechanisms, or those that are dangerous for animals [5]. It is thus worth
enumerating some of the more optimal propulsive mechanisms and body plans forwater and land exhibited by highly derived (specialized for certain environments asa result of evolution) species.
Inhabiting an exclusively aquatic environment, tuna and dolphins have streamlined, hydrodynamic bodies and rely on oscillation of their caudal fins to generate
thrust as a vector component of lift. Other fast and efficient aquatic animals withlateral fins and flippers can produce thrust by undulatory (bluegill, sunfish, stingray)swimming, as well as oscillatory wing-like movements (sea lion, sea turtle). Though
not sustainable over long periods, jetting can enable rapid accelerations and isseen in jellyfish, squid, and octopus. Larger aquatic animals, like those mentioned
above, are considered to be nekton, that is, capable of swimming long distances
independent of water currents. Nektonic animals swim at high Reynolds number(Re > 103 up to 108 ) [38]. At high ranges of Re, swimming is performed byaccelerating a mass of water for propulsion. Viscous forces are small, whereas
inertial forces are large [38]. Yet the overwhelming number of animals that exist in
the oceans are small, like plankton, and use ocean currents pushing on their bodies
as a propulsive mechanism to move long distances. Most planktonic animals (e.g.,
copepods) lie within an intermediate range of Re (1 < Re < 103 ), where viscousand inertial forces are both important [39]. At even smaller scales, bacteria cilia andflagella operate between 10−5 and 10−6 Re, where viscous effects dominate [40].
Terrestrial vertebrates are generally not streamlined. They have a defined neck,no blubber to contour the body shape, and if they have limbs, the limbs are generally
cylindrical with an approximately circular cross section. As size (and therebymass) of a terrestrial organism increases, gravity becomes a more dominant force,
unlike in water where weight is supported by buoyancy. Among limbed terrestrial
animals, peak limb stresses can increase with increasing body size, so posture of
the skeletal elements of the legs tends toward a more columnar (upright) stance[41, 42]. Such a change in posture maintains a safety factor independent of size, but
at the expense of accelerative capability and maneuverability. Horses and cheetahs
are exemplar animals with skeletal components disposed to upright walking andhigh-speed linear galloping. Highly derived terrestrial animals, like the horse and46

R. Baines et al.

cheetah, exploit spring-like interactions of their body with the ground to enhancethrust produced with each stride [43]. The storage and release of elastic energy
as a propulsive mode actually increases in efficiency at higher speeds in someanimals [44]. In addition to limbed propulsion aided by elastic potential energy
storage, it is instructive to mention another (perhaps more unusual) specialized
terrestrial propulsive mechanism that harnesses gravity: rolling. Passive rolling isdemonstrated by arachnids, while species of caterpillar actively build up angularmomentum during rapid escape maneuvers [26]. Top speeds of rolling animals canbe an astounding tens of body lengths per second.

3.2.5 Biological Inspiration for Design of Amphibious Robotic
Propulsive Mechanisms
Both environmental medium and scale influence an organism’s propulsive mechanism adaptations. The intermediate status of amphibious animals compromises
their locomotive performance in either environment, but the mechanics of theseintermediate species can potentially serve as a template to develop a new generationof amphibious robots. Furthermore, amphibious robots can be designed to incorporate locomotor mechanics that are specialized for either environment or any scale,
expanding upon what nature has been capable of producing through evolution.
It is thus the charge of the robotic designer to synthesize various propulsive
mechanisms and corresponding body plans found in nature—even to look beyond
these natural examples to synthetic solutions—to innovate and produce an effective
amphibious robotic system. Such a methodology to realizing future amphibious
robots is depicted in Fig. 3.1. The next sections review current work in amphibious
robotics. An exposé of novel designs, biologically inspired or of purely synthetic
origin, as well as the advantages and disadvantages of these designs, supplies
additional foreknowledge to synthesize next-generation amphibious robots.

3.3 Classification of Amphibious Robots
A strict template for classification does not necessarily encompass any given robot’s
propulsive mechanisms. While robots with united propulsive mechanisms may bemuch easier to classify, robots with separate propulsive mechanisms defy any strict
classification. For the sake of review, we sort amphibious robots into wheeled,legged, and undulating based on the most salient aspect of their morphologies.
Wheeled, legged, and undulating amphibious robots utilize significantly different
mechanisms to move in water and on land. Wheeled systems include rounded
entities concentric to axles that, when engaged in rolling, provide leverage basedon the radius. Wheels can be driven passively (by gravity) or actively (by motors).

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

47

Fig. 3.1 Combining knowledge of the propulsive mechanisms of amphibious animals, the specialized mechanisms exhibited by highly derived species, and existing amphibious robot designs
is key to developing the next generation of amphibious robots. Note that the relative positioning ofgroups is based on the authors’ qualitative assessment of performance

In water, movement of treads through the fluid medium can serve as discretizedpaddles for drag-based thrust. On land, wheels rest on the ground at all times andrely on friction contact force on the substrate at a point and repetitive revolutions togenerate a thrust vector.
Legs are a more generic morphology. They can be articulated, multi-degreeof-freedom, or single degree-of-freedom links of various shapes and kinematicconfigurations. In water, legs engage in oscillations or power strokes to generate
thrust. On land, legged systems utilize discrete footholds to move. The body is
supported off the ground with either upright or sprawled legs. Having a lower centerof mass, sprawled posture is generally more stable than the full upright orientation oflegs. A robot’s legs must leave the ground in periodic increments to achieve bodily
displacement.
Undulating robots come in elongated forms, often consisting of a series ofmodules connected together. In water, undulatory swimmers display a gradient of
propulsive modes for thrust production—from undulatory waves encompassing thetotal length of the body (anguilliform), through progressively expanded posterior
regions of the body (carangiform), culminating in thrust production confined to the

48

R. Baines et al.
Wheeled/tracked

LeggedUndulating

Soft

Water

Land

Fig. 3.2 Amphibious robots sorted into four distinct categories based on their primary propulsive
mechanisms and structural features: wheeled/tracked (note, wheels are half-submerged in waterin the depicted image), legged, undulating, and soft. Here, we illustrate how each category mightunite the same propulsive mechanism, or transform its limbs or body plan to accommodate waterand landcaudal fin (thunniform). On land, undulating robots move in a fashion characterizedby multiple surface contact points. Waves passing posteriorly down the body push
on solid substrate for forward movement.
Soft amphibious robots may locomote in a way that is consistent with theprevious three delineated categories, but are distinguished by their composition ofcontinuously deformable materials, typically having a Young’s modulus on the orderof, or less than, one MPa. Consequently, soft robots do not commonly use traditional
rigid motors. Reliance on soft actuators [45] is thus another factor that separates
them from the other three categories.
Figure 3.2 depicts how each category might unite the same propulsive mechanism, albeit with morphological transformations present in the legged and soft
categories. Each category is associated with a unique set of advantages anddisadvantages that motivate discussion on what constitutes an effective amphibious
robot design. The following subsections address each of the classes of robots inthe listed order. For each, we open with a discussion of its respective advantages.
We then highlight seminal amphibious robots belonging to that class. Our intention
is to not to detail every amphibious robot reported in literature, but to summarize
key innovations as embodied by the seminal designs. Aspects we focus on whenappraising an amphibious robot are its capacity to bear payloads (i.e., sensors,
camera, equipment; this criteria is of course dependent on size), ease of control,
efficiency, maneuverability, and speeds in water and on land. Aside from absolutespeeds in water and on land, which we have plotted against each other for anumber of designs and comparably sized animals in Fig. 3.3, the other metrics are
not consistently reported for amphibious robots throughout literature. We instead
provide a qualitative assessment of these metrics. Each section closes with asynopsis of a particular class’ drawbacks, and therefore opportunities for future
research.

Fig. 3.3 A comparison of absolute sustained speeds between representative amphibious robots from each of the delineated categories, as well as semi-aquatic,
semi-terrestrial, and aquatic animals. Note that many of the increases in robots’ speed have naturally come hand-in-hand with improved research hardware,such as higher torque motors and lower footprint microcontrollers. We try and account for this factor by featuring a variety of older and newer publishedwork from each category. Citations for (a–l) are [4, 6, 9, 46–54]. We include comparably sized animals operating in a similar Reynolds regime (thus excluding
whales, bacteria, etc.) for comparison to the robots. The animals are from (m–p): muskrat, river otter, yellow-lipped sea krait, and bottlenose dolphin. Citations
for speeds (m–p): [37, 55–59]

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .
49

50

R. Baines et al.

3.3.1 Wheeled and Tracked Amphibious Robots
Wheels represent a unique propulsive mechanism for amphibious robots since,
compared to legs and undulations, wheel-like forms are less readily used in nature[26]. On land, wheels pose an energetic benefit because when traveling at aconstant speed, the kinetic energy remains constant [40]. Compare this energy
profile to most other natural propulsive mechanisms that necessitate trajectories ofcyclic acceleration and deceleration that may incur a sizable energy cost. It is not
surprising then, that a common—and perhaps the simplest—propulsive mechanism
for amphibious robots is wheels or tracks.
A ubiquitous amphibious robot design, similar to many amphibious vehicles,
uses wheels to move on land and on top of water. Such robots are far along in thedevelopment pipeline and are commercially available [60]. Though rotating wheels
to move in water and on land unite the same propulsive mechanism, simplifying
control, it comes at the expense of speed in water. Speed is limited because wheels
increase drag due to the heightened relative velocity from the rotation of the wheel,
which can induce flow separation [61].
Yamada et al. built what appears to be a quintessential wheeled amphibious
robot, but with a clever twist for improved aquatic locomotion. Their four-wheeled
platform, R-Crank, incorporates a ribbed crank link between its front and backwheels on each of its sides. The crank link generates thrust for surface-based aquatic
locomotion as the tires spin [62].
While the previously mentioned robots include wheels as a part of their hardware,other robots are, by no stretch of definition, wheels. A design perk of wheel-bodied
robots over robots with wheels is that the need for a bulky chassis is eliminated,
reducing weight, and potentially conferring hydrodynamic benefits. Consider thatthe drag force on a body is
F D = CD A

ρV 2
,
2

(3.2)

where CD is the drag coefficient, ρ is the density of the fluid, V is the flow velocity
relative to the body, and A is the reference area. Note removing a chassis will
substantially decrease A. Also, the CD of a wheel, typically shaped like a sphereor disk can be much lower than typically angular, rectangular chassis.
One wheel-bodied system, Groundbot, was developed by Rotundus AB in
Sweden as a multi-terrain surveillance robot. Spherical, treaded, made of rubber, andfully resembling a tire, Groundbot can roll and steer itself using an offset internal
weight actuated by motors. It boasts up to 3 m/s (5 bl/s) sustained speeds on levelground. It employs the same rolling mechanism to traverse water as it does for land,
floating atop the surface and generating thrust with its specifically engineered treads
that essentially serve as a series of paddles [63].
Another robot with a wheel-like body is the triphibious MUWA. MUWA consistsof a ring of polystyrene foam surrounding a multicopter. The polystyrene ring gives

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

51

MUWA enough buoyancy to float atop water, but also provides geometry conducive
to rolling. When rolling on land, MUWA controls its trajectory by adjusting thepitch of its rotating propellers [64].
Transition areas rife with loose or fluidized sediment threaten to ensnare wheels.
Rolling resistance of wheels increases in proportion with soil compliance [65]; in
fact, one study found that rolling resistance on concrete can be 10–15 times less thanthat of sand [66]. Terramechanics research models physical interactions with thesubstrate and provides an estimate of the extent to which sinking into the substrate
impedes motion [67]. Concentrated weight is a primary cause of local soil fracture,causing ensnarement. Tracks distribute the weight of a robot over a larger area tomitigate sinking and improve locomotion across muddy terrain, but may sacrificesome speed and maneuverability.
Tracked amphibious robots have been built that are intended to sink below thesurface to crawl on lake beds [11]. Sinking to the bottom is not always practical,
though. Motivated by the need to monitor an estuary system composed of multiple
rapid transitions from shallow water to soggy land, one robot was designed withbuoyant tracks so it can engage in surface swimming while retaining the ability tonavigate muddy sections [6]. This surface-swimming robot has the fastest speed onwater reported in Fig. 3.3.
The aforementioned wheeled or tracked designs have not demonstrated ability toswim in 3D. For certain applications, amphibious robots need to be able to engage
in 3D swimming so that they can transition between the surface and underwaterand explore the water column in between. In order to enable 3D swimming while
retaining the merits of wheels on land, one group introduced a class of robot withhybrid wheels/propellers and separate fins [53]. The hybrid wheels/propellers havespokes emanating radially from the termination of their axle, effectively providing
the hydrodynamic thrust of propellers and generating sustained speed of up to
0.36 m/s (0.375 bl/s) in water (Fig. 3.3j). The fins on the robot are used to steer
when swimming. Owing to its wheeled design, this robot also exhibits the top speed
on land out of all designs in Fig. 3.3, at 1 m/s (1.04 bl/s). Transitions from aquatic toterrestrial locomotion are accomplished by orienting the wheels/propellers so theirrevolution will provide forward thrust in water or serve as a wheel on the land.
Another hybrid wheel/propeller mechanism that allows for 3D swimming,
dubbed the eccentric paddle, consists of a shaft embedded in a wheel on whichpaddles are radially distributed. The paddles move in and out of the wheel toadjust the extent of their interaction with the environment. Equipped with eccentricpaddles, the robot demonstrates an unusual capability: a quasi-walking mode oflocomotion by cyclically protruding the paddles from the wheel [68–70]. Offering
the speed of wheels as well as aquatic mobility, hybrid approaches, like combined
wheels/propellers and separate fins or the eccentric paddle, nonetheless rely oncomplex agglomerations of mechanisms that are difficult to control. Such intricate
hybrid mechanisms with many moving components may also be susceptible todebris in the littoral zone compromising their function.
Overall, although they offer efficiency and high top speeds on flat land and therequisite structural integrity to support large payloads, a major drawback of wheeled

52

R. Baines et al.

and tracked robots is their lack of ground clearance and consequently diminishedability to traverse uneven terrain [71, 72]. Heavy systems with wheels, specifically,
have a propensity to become trapped in shallow, fluidized sediment [73]. Moreover,wheels do not scale well to small sizes because they become sensitive to substratecompliance and uneven terrain impacting forward motion [40]. A promising design
strategy, creating a wheel-bodied robot or a hybridized paddle-wheel mechanism,
can reduce mass, enable 3D swimming, and address minor challenges posed byuneven terrain [53, 70]. Yet, hybrid mechanisms can be plagued by their host of
moving parts, especially in the littoral zone rife with obstacles. If creating hybridmechanisms, designers should err on the side of simplicity to provide resilienceagainst environmental detritus. Lastly, robots with wheels or tracks can leave
destructive trails behind them—a heavy wake or dislodged soil. While observing
fragile ecosystems or trying to maintain stealth, disturbances to the environment
can undermine mission success. More work on wheeled systems that minimize
environmental impact thus represents an open area of research. When navigationof uneven terrain or stealth are prerequisites to a successful mission, other typesof amphibious robots might be better options than current designs with wheels or
tracks.

3.3.2 Legged Amphibious Robots
Legged amphibious robots tend to be more complex in design and control architecture than wheeled robots due to the multiple controlled degrees of freedom
associated with each leg. Primary advantages of legged robots include theircapability to traverse obstacles wheels or tracks cannot, and need for only discrete
footholds to locomote, as opposed to a continuous supporting surface. On especially
soft ground, legged robots deform terrain less than wheeled or tracked systems andthereby can diminish the energy required for traversal [74]. Due to their multiple
degrees of freedom, legged robots can also change direction without slippage.
Like wheeled robots, legged robots can sustain concentrated payloads undulating
robots cannot, since their motion is not dependent on dynamic oscillations ofinterconnected bodily modules.
Spurred by calls to develop systems to locate and destroy mines in the surf zone,
one of the first examples of a legged amphibious robot—let alone one of the firstamphibious robots—was published in 1996. The report detailed a hexapod robot,
Ariel, inspired by the crab that walks at a shallow depth along the seabed [12].
Since Ariel, similar work has been published focusing on the creation of lobsterinspired robots with the same purpose [75]. A major concern for benthic walking
robots is the large hydrostatic pressures associated with great depths—not only forwater-proofing but also for feasibility of walking. Large moments would be createdabout the leg joints at depths, and it is unlikely compact actuators could overcome
such moments.

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

53

In contrast to robots that crawl along the seabed are surface walkers: amphibious
robots inspired by insects and reptiles (mentioned in Sect. 3.2) that are able to walkon the surface of water by exploiting the physical properties of their feet, and/or
their small body mass. Park et al. presented a platform inspired by the basilisk
lizard. The crux of their design revolves around a light-weight robot body and acompliant foot pad, which transfers elastic energy to propulsive momentum [76–78].
Yet such a robot cannot bear payloads that would compromise its light weight andwould therefore be limited to minimal integrated circuits. Another surface-walkerinspired robot is bulkier and able to bear payloads, compensating for its increased
weight via Styrofoam spherical feet that provide buoyant forces [79]. A cockroachinspired microrobot fabricated by Chen et al. uses partially submerged foot pads topaddle on the surface of the water, exploiting surface tension. Unlike the previous
two mentioned platforms, it is able to dive from the surface to the bottom by emittinghigh voltage from its padded feet to temporarily break surface tension. It can thenwalk on underwater surfaces as it does on land [80]. Nevertheless, the robot is unable
to replicate the speed and dexterity of an actual water strider due to constraints on
the force density of such small actuators. In addition to those mentioned, there havebeen a variety of other surface-walking robots [81].
Though bottom and surface walking may be sufficient in some scenarios,
3D swimming offers greater surveying capability. To this end, a new chapter inamphibious legged robotics started with AQUA [82, 83]. AQUA, based on Boston
Dynamics’ R-hex platform [84], utilizes six independently controlled paddles on
single degree-of-freedom (DOF) joints as control surfaces during swimming. It also
has interchangeable, curved cockroach-style legs for walking that act as springs,
efficiently storing and releasing potential energy with each stride. AQUA represents
the first robot of its kind—legged, able to proficiently move on land and traverse
obstacles, but also able to engage in 3D swimming to fair depths. There are many
subsequent amphibious robots that drew design inspiration from AQUA’s body plan
and leg design.
One series of robots inspired by AQUA are hexapods equipped with Whegs™
(a portmanteau for wheel-legs). Whegs™ integrate swimming and walking mechanisms, combining the simplistic control of a wheel with the articulated cadence andability to traverse some obstacles that legs typically can [85]. Whegs™ are similar
to the cockroach-style legs initially equipped to AQUA, but are built with three
protruding paddles equally distributed radially about the center shaft, as opposed
to AQUA’s single paddle. Whegs™ have been implemented on amphibious robotic
platforms as a combined propeller/wheel with great success [86–88]. Despite theircritical appeal, it should be noted that the drag-based propulsion supplied byWhegs™ is inefficient relative to lift-based locomotion [30]. Also, like propellers,
Whegs™ induce turbulent vortices that may pose too much of an environmental
disturbance for some applications. Lastly, the geometry of Whegs™ does not allow
backwards locomotion on land (the paddles contact the ground at a point, acting as
a rigid rod and stunting motion), which detracts from their terrestrial mobility.
Bearing strong resemblance to Whegs™ -style robots but with modifications toaddress the fact that Whegs™ are not able to back-drive, Ninja Legs incorporate a

54

R. Baines et al.

thin circular wire enclosure around flippers. The enclosure protects the compliant
flippers and simultaneously serves as an offset wheel for hybrid rolling/walking[89]. In a similar vein as Ninja Legs, one robot named RoboTerp unites flippers andlegs into a single hybrid propulsion mechanism. The structure of one limb consistsof a flap passively hinged to a grate. The grate serves as a rigid load-bearing leg
to support the robot’s weight on land. While swimming, during the robot’s powerstroke, the flap flattens against the grate thereby increasing paddle surface area andproducing forward thrust. On the upstroke, the flap freely swings back, reducing
drag [90].
RoboTerp’s passive paddle mechanism is not conducive to high aquatic mobility.
This reinforces the observation that walking legs, in addition to producing less thrustcompared to more hydrodynamic, high aspect ratio surfaces, are far from optimal
forms for maneuvering in the water. Indeed, the original AQUA platform had
separate flipper and leg modules for water and land, respectively, optimized independently of one another. However, the need for human intervention to manually
exchange limb designs undermines a system’s ability to autonomously transition
between environments.
One group introduced AmphiHex-I (Fig. 3.3d) and in doing so initiated a
new amphibious legged robot design paradigm. AmphiHex-I [48, 91, 92] featuresa transformable leg-flipper propulsion mechanism. The leg-flipper consists ofinterlocking rigid segments connected via a cable. When the cable is pulled, theinterlocking segments are compressed to create a curled cockroach-style leg. Whenreleased from tension, the limb becomes a compliant flipper. Although the robot’s
speeds of 0.16 m/s (0.18 bl/s) underwater and 0.2 m/s (0.23 bl/s) on land rank lower
middle-tier in Fig. 3.3, the AmphiHex-I design philosophy seems promising in termsof efficiency. Namely, as opposed to relying on separate propulsive mechanismsthat may impede each other’s performance, or a united propulsive mechanismthat sacrifices specialization for average performance, transforming a propulsive
mechanism’s shape offers the ability to greatly hone locomotive performance inboth environments.
After AmphiHex-I came AmphiHex-II (Fig. 3.3e). This robot introduced an
entirely different mechanism than AmphiHex-I: manually adjustable variable stiffness legs. Its semi-circular legs are rigid, fan-shaped frames, and protect flexible
flippers within. By adjusting a pin joint along the leg’s length and the robot’s
chassis, one can set the leg to five different stiffnesses. Experiments with the robot
underscore that modulating the stiffness improves locomotive performance based on
fluid content in a soil-like terrain. It was found that higher stiffness limbs allow the
robot to locomote fastest in sandy substrates and soft soils. An intermediate stiffness
was found to be more efficient for locomotion in fluidized (25%) soil reminiscent of
the littoral zone. Lastly, for swimming, the researchers found the highest stiffness
elicited maximum achievable, sustained velocity [9].
Though legs give a robot the ability to skillfully traverse a wide swath of terrain,
legged robots are generally slower and less energy efficient on flat land, especiallywhen compared to wheeled robots [5]. Moreover, control of legged robots is much
more complex than that of wheeled robots. Particularly in the aquatic environment,

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

55controlling legs as hydrodynamic surfaces for efficient propulsion represents anopen area of research. Whegs™ -style legs simplify the control problem by replacing
articulated joints with just 1-DOF. However, Whegs™ , as well as a majority of
the legged amphibious robot designs mentioned, employ drag-based paddling tomove through water. As mentioned, paddling is not an efficient mode of swimming,
because thrust is only generated in half of the stroke [30]. Thus, alternative modesof aquatic locomotion must be explored and mechanisms developed to achieve thosemodes. One example of an alternative locomotion mode, incorporating separate jet
nozzles on the bottom of a robot’s legs [49, 93], seems like a promising strategy
but requires highly complex modeling of jet orientation to optimize locomotion(moreover, this specific robot is extremely slow, as seen by its relative position in
Fig. 3.3f). If land speed, hydrodynamics, or control complexity are precursors for a
successful mission, legged amphibious robots may not fare well.

3.3.3 Undulating Amphibious Robots
The third class of amphibious robots is undulating robots, often those with aserpentine body. Key advantages of undulating robots are their high maneuverability
in water, small turning radii on land, and multiple DOF that lend themselves tonovel locomotion strategies and negotiation of restricted spaces. Arguably one of
the most significant jumps in amphibious robotics coincides with the advent of thesnake-inspired robot, AmphiBot. Unlike other land-based snake robots of the time,
AmphiBot is capable of swimming and crawling, all with the same mechanism:
undulation [17, 94]. AmphiBot’s body is composed of interconnected, independently actuated modules. Selective actuation of each of the modules via a central
pattern generator allows AmphiBot to undulate to move smoothly through waterwith a speed of 0.2 m/s (0.26 bl/s). However, it has wheels to overcome friction andattain higher speeds on land. In terms of relative speed to other robots, AmphiBot
falls into the middle of the pack (Fig. 3.3g). Subsequent to AmphiBot, there havebeen a fair number of snake-like robots capable of amphibious locomotion. Thesefollow-ups make slight variations to hardware in efforts to generate more productive
thrust with each oscillation, such as including radially distributed wheels around thebody, and placing continuous ridges along the body [95–97].
One group sought to integrate undulatory caudal fin swimming, propellergenerated thrust, and flipper-like control surfaces for locomotion in water withwheels for locomotion on land: the results were Amphirobots-I and II [98, 99].
Amphirobots are composed of a multi-link serial chain whose units possess passive
wheels and has axles that can swivel both laterally and dorsoventrally, unlike previous amphibious undulating robots. This clever mechanism enables both dolphinand fish-style swimming up to 0.45 m/s (0.64 bl/s) as well as serpentine crawlingon land of 0.6 m/s (0.86 bl/s), positioning Amphirobot-II near the top of thosesurveyed in both categories (Fig. 3.3h). Caudal oscillation in the fashion of somefish happens to yield one of the lowest costs of transport among swimming modes as

56

R. Baines et al.

mass increases [22]. Yet, Amphirobot’s agglomeration of components increases the
projected area in Eq. (3.2), proportionally increasing drag, countering to some extent
the merits of the efficient propulsive mode. Additionally, as mentioned, having
multiple separate propulsive mechanisms obfuscates control, which the authors
concede reduces the efficacy of their system [98].
The most recent amphibious undulating robot at the time of this writing
originated at Pliant Energy Systems, an energy firm based out of Brooklyn, NY.
Their robot, Velox, consists of a static, rigid body lined with two sets of dynamically
undulating, elongate fins [100]. These fins are based on Pliant’s blade-less energyharvesting turbines that passively harness fluid flow. A geared transmission systeminternal to the robot pulls parts of the flexible fins up in a wave. The resulting
coordinated undulation endows the robot with high mobility over a variety of terrain.
Videos of the robot traversing snow, flat ground, and swimming freely in three
dimensions testify to its effective united propulsive mechanism design [101].
Despite its superiority in water, undulating propulsion over land has several
drawbacks. First, ongoing challenges with snake-like robots are to get themto traverse uneven terrain, and developing appropriate contact models for suchtraversal [102]. Second, undulation relies on high surface area contact between arobot’s body and the underlying substrate. Friction or smoothness of a substrate
therefore governs cost of transport much more than a legged robot experiencing
less surface contact. Although friction issues have been partly addressed via theincorporation of passive wheels onto multi-segment robots, wheels are bulky
protrusions to a robot’s body plan that may further reduce ability to clear obstacles.
From a hydrodynamic perspective, wheels can incur undesired drag forces. Thus itstands as an open challenge to devise undulating robots that modulate their substrate
friction coefficient without negatively impacting other aspects of locomotion. Third,
serpentine undulating robots do not generally have the capacity to bear large,
centralized payloads due to size limitations of the modules composing their bodies.
More work on centralized chassis-based undulating systems, like Pliant Energy
Systems Velox, represents a promising future direction in this regard. In brief, if
desiring a simplistic platform for transporting larger payloads or navigating unevenground, current undulating robot designs may fall short.

3.3.4 Soft Amphibious Robots
The fourth and final class of amphibious robot, ones made primarily of soft
materials, constitute a subset of the already small body of literature pertaining
to amphibious robots. It is well-established that robots can benefit from newresearch in soft, responsive materials [45, 103]. The properties of soft materials—
compliance, continuous deformation, stretchability, incompressibility, conferenceof hydrodynamic benefits [104, 105], and resilience to damage and harsh conditions[106]—make them apt candidates for incorporation into amphibious robotics.

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

57

To the best of our knowledge, the first explicitly declared soft amphibious
robot was developed by Faudzi et al. Inspired by the salamander, the robot has anelongated body with short legs. The body and legs consist of McKibben pneumatic
actuators. Though quite slow, selective contraction of McKibbens on various partsof its body enables the robot to traverse solid ground, sand, and patches of shallow
water [47]. To enable underwater crawling of an amphibious soft robot, Tang et al.
integrated two switchable adhesion actuators on distal ends of a bending actuator.
Their robot can execute inchworm-style gaits while adhered to both submerged anddry substrates [46].
The salamander-inspired robot and the underwater inchworm-like crawler, being
composed of entirely soft actuators, likely cannot bear significant payloads. Anotheramphibious crawling robot that demonstrated payload capacity and separated its
soft actuators from its body is the un-tethered sea urchin-inspired robot developed
by Paschal et al. [107]. The sea urchin bot consists of a rigid body, rigid spines,
and soft bending actuators (analogs to tubercle feet on a real sea urchin). A uniqueaspect of the sea urchin robot is that it uses actuation of rigid spines in tandem withbending actuators to engage in bio-mimetic, in-place turning motions. The robot isalso able to drag itself on land or under the surface of water. In spite of its highmobility, the robot is confined to ferrous surfaces because it relies on embedded
magnets in the tips of its bending actuators for anchor points while dragging [107].
In another instance of utilizing separate soft actuators on a rigid robot body, soft
pneumatic bending actuators were equipped as legs to an amphibious dog-inspired
robot. The soft actuators were not implemented in a traditional sense, as with theprevious two examples. Instead, they are pre-inflated and routed with cables. By
pulling on the pre-inflated actuator with the cable, it straightens. Upon release of
the tension in the cable, the actuator’s stored energy snaps it back into the bent
configuration. The researchers leveraged this mechanism to show the dog-inspired
robot trotting on land and dog-paddling in water [4]. Though they provide sufficient
force to propel the robot to land speeds of 0.18 m/s (0.34 bl/s)—a rate much fasterthan other soft amphibious robots—the pre-inflated actuators necessitate additional
motors to pull the attached cables.
The same material properties that make soft amphibious robots flexible andresilient impede their locomotive performance. Soft amphibious robots substantiallylag behind their rigid counterparts in terms of their reported maximum sustained
speeds, as indicated by Fig. 3.3a–c. Lack of speed can be attributed to the dissipative
effects of soft materials and the low force density of soft actuators relative to motors
used on rigid amphibious robots. An open design challenge is thus to enhance
speed of soft robots, both in water and on land, while retaining their desirable
rheological properties. A wealth of soft actuation schemes that still have yet to be
applied to amphibious soft robots, including shape-memory materials, chemicallyinduced volumetric expansion, dielectric elastomers, and combustion [108–110],
might facilitate higher speeds. A second drawback is soft robots’ lack of payloadbearing capabilities. Even if they could be designed to move faster, entirely soft
structures would buckle under external loads. Fortunately, recent work regarding
granular and layer jamming and variable stiffness polymers offers novel ways to58

R. Baines et al.

endow a compliant robot with rapid stiffness-changing capacity [111–115] andmight prove useful if applied to amphibious soft robots.

3.4 Overarching Challenges
As evidenced in the literature, the exact design specifications for an amphibious robot traditionally depend on the task it is intended to complete. In some
applications, like shoreline monitoring, capability to traverse muddy terrain andsurface-level immersion in water with a small camera will suffice to complete all
mission objectives. Other applications, however, like routine inspections of offshore
rigs, may mandate climbing uneven terrain and deeper dives with specialized sensor
suite payloads.
The various presented propulsive mechanism architectures—wheeled, legged,
undulating, and soft—bring their own unique sets of advantages and disadvantages
to the design table. As research strives to realize increasingly autonomous systems
that are not specifically designed for a task, but rather are multi-functional entities,
the following question stands: how does an engineer synthesize current amphibious
robot propulsive mechanism designs to create new, highly effective ones? To help
guide answers to this question, let us observe facts about the current state of robotic
technology and review areas for improvement in each category.
Amphibious robots of all categories are outclassed by animals in terms ofabsolute speed, as shown in Fig. 3.3. Even the state-of-the-art robots that operate
exclusively terrestrially or underwater fall short of animals in terms of max sustained
speed (both in body lengths per second and absolute speed), operational duration
capacity, acceleration, turning ratio, ability to maneuver in compact spaces, costof transport, and stealth [116, 117]. Though metrics other than speed are not wellreported in the literature for amphibious robots, one can infer that amphibious robots
suffer from the same shortcomings (maybe more so) as their exclusively terrestrial
or aquatic counterparts. With these observations in mind, improvements in the force
density and compactness of actuators would be a significant leap for the field.
Wheeled amphibious robots could become much more effective if they areaugmented to accommodate uneven terrain, swim in 3D, mitigate flow separationfrom wheel surfaces in water, and reduce environmental impact. Many of these
improvements could be made by creating hybrid mechanisms that augment wheelmorphology.
Legged platforms would benefit from simpler control policies (and correspondingly, actuation systems), as their lack of deployment in field missions to-date is
attributed to complex control [118]. Existing force models for legged locomotion
on granular media rely on assumptions of size and uniformity of particulates[119] that diminish their accuracy in the highly unstructured littoral zone. Thus,
more detailed experiments should be conducted focusing on legged locomotion in
fluidized sediment to converge on robust physical models that can inform actuation
policies. Second, legged systems can be improved by hydrodynamic form factors,

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

59

or more generally, ways to augment morphology between functional terrestrial andaquatic streamlined shapes.
Undulating robots could be modified for enhanced ground traversal. In contrast to limbless animals that can navigate almost any surface [120], undulating
robots struggle with uneven surfaces or low friction coefficients [102]. Snakelocomotion strategies of undulation, including concertina motion (used to movethrough restricted spaces like tunnels), sidewinding (limited to sandy terrain), andrectilinear movement (uses bottom scales to move without undulations of the body;useful for moving along tree branches), have been applied to robotics, but arefar from mirroring the fluidity and efficiency of natural systems [102]. Simplified
controllers that can replicate the diversity of complex undulating gaits would thus
expand the utility of undulating amphibious robots. As with legged platforms, afundamental understanding of undulating propulsion over fluidized sediment needs
comprehensive experimental analysis and could help inform locomotion policies forlittoral zones. Lastly, the lack of large centralized payload capability seems to be an
inherent shortcoming of undulating. One solution could be towing a payload behind
the robot. Another could be creating systems with a centralized chassis like Pliant
Energy’s Velox [100].
A consistent disadvantage among most wheeled, legged, and undulating robots
presented in the preceding sections is that they are composed of immutablestructures with high stiffness, precluding the capability to substantially adapt
a propulsive mechanism or body structure for more effective locomotion in aparticular environment. Zhong et al. took a step in this direction and showed how atransformable robot limb geometry could be used to enhance performance in waterand on land [121]. Zhong et al. also showed that modulating stiffness of a robot’s
limbs can benefit its locomotion across fluidized sediment [9]. The results of studies
such as these, in tandem with studies of terrestrial and aquatic animal locomotor
adaptions [22, 30, 116], motivate two pillars to strive for with future amphibious
robot designs: (1) endow shape change and (2) devise mechanisms that can switch
between soft and rigid states. Soft amphibious robots are well-suited to adapting
their shape and stiffness to the environment and therefore represent an untappedreservoir of potential for addressing the multi-faceted challenge of transitions
between aquatic and terrestrial locomotion. However, they are not a panacea;
as mentioned, soft robots have the prominent disadvantages of low speeds andreduced ability to bear payloads. A promising research avenue is thus developing
systems that marry the advantages of soft and rigid materials into a cohesive robotic
platform.

60

R. Baines et al.

3.5 Case Study: Example Propulsive Mechanism for Efficient
Amphibious Locomotion
Our group is currently building an amphibious turtle/tortoise-inspired robot withvariable stiffness limbs that change between the shape of a flipper and a leg[115, 122]. We drew inspiration from the specialized flipper propulsor of thegreen sea turtle and the legs of the Galapagos tortoise (Fig. 3.4a). Aside from the
propulsors, we noted that sea turtles and tortoises demonstrate similar body plans.
In addition to being quadrupedal, they have protective shells occupying a large
portion of their bodies. A hybrid robotic platform based on the turtle/tortoise bodyplan should permit highly efficient movement in both water and on land, moderate
speeds and maneuverability in water, as well as stability to negotiate obstacles in thelittoral zone. Furthermore, a rigid central shell lends itself to storing control system
hardware and a heavy payload.
The limb of the robot is pictured alone in Fig. 3.4b and in the context ofa rendered quadruped robot in Fig. 3.4c. The limb consists of an antagonistic
pneumatic actuator pair whose strain limiting layers are thermoset polymers thatare rigid below 60 ◦ C. Heating up the thermoset polymer past its glass transition
temperature softens it, and it is subsequently deformed into a round geometry using
the pneumatic actuators. The actuators are held at the inflated state until the material
cools, at which point it retains the leg shape. Heating up the material again induces
relaxation and it morphs back to the flipper shape.
Placing the morphing limb in a flow tank, we varied its angle of attack andmonitored lift and drag forces (inset of Fig. 3.4d shows components). Figure 3.4d
illustrates how the airfoil geometry of the flipper markedly increased its glide ratio(ratio of lift to drag forces on an object) in water compared to the leg. Like a
traditional airfoil, the peak of the flipper state’s glide ratio occurred around an
8◦ angle of attack. The leg state, on the other hand, resembles a thick hydrofoil,
delaying onset of stall to 30◦ and exhibiting much lower glide ratio [123].
We subjected the limb to compression tests in either its flipper or leg phase (Fig.
3.4e). The leg’s circular cross section (and correspondingly increased moment ofinertia) enhanced its capability to bear compressive loads relative to the flipper.
Consider that the critical buckling load for a beam (leg) under compression isPcr =π 2 EI
,
(kL)2

(3.3)

where E is the elastic modulus of the variable stiffness material, I is the crosssectional area moment of inertia, k is the length factor (1 for pin boundaries oneither side), and L is the unsupported length of the limb. Based on the fact that
Icircle =π 4r2 − r144(3.4)

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

61

Fig. 3.4 (a) Sea turtles and tortoises demonstrate specialized propulsors for aquatic and terrestrial
environments, respectively (images adapted from [115]). (b) Turtle-inspired limb: morphing
between streamlined and load-bearing geometries allows it to perform well in water and serve
as a strong leg for land. Scale bar: 40 mm. Inset scale bar: 30 mm (images adapted from [122]). (c)Rendering of morphing limbs equipped to quadruped amphibious robot. (d) Flow-tank test results
at 0.6 m/s water speed. Ratio of lift to drag on the flipper and leg. (e) Compress-to-failure test for
the flipper and leg

62

R. Baines et al.

Irectangle =bh3 − b1 h31
,
12

(3.5)

having as close to a circular cross section as possible enhances the limb’s critical
Euler buckling load [122].
Moreover, modulating the material’s stiffness by heating it past Tg gives us theability to tune the limb’s mechanical response to external forces [115]. This ability
may prove useful if bumping into obstacles, or further tuning propulsor performancefor a given media [9]. By leveraging on-demand shape and stiffness changes andmodulating the gait of the quadruped robot it is attached to, we hypothesize thelimb will enable a legged amphibious robot to traverse land and water with highspeed, efficiency, maneuverability, and payload capacity.
Beyond our case study, there are myriad soft, responsive, and rigid materials
that could be incorporated into a single robot design to facilitate shape change
and variable stiffness. Studies should seek to leverage shape change not just of asingle propulsor, but of the entire robot body, to improve amphibious locomotion.
For instance, changing its body from a fish to a legged quadruped form might
grant a robot high speeds in water and on land (Fig. 3.2–soft). We also see workon varying stiffness in amphibious locomotion as a promising domain for future
research. Combining variable stiffness materials with wheels, for instance, may
enable a robot to selectively distribute its weight over a higher area to easily traverse
patches of fluidized sediment; variable stiffness in combination with undulation
may allow a robot to passively harness flow of the water to generate productive
thrust; toggling between stiff states during the power stroke and compliant states
during the retraction stroke can enhance swimming of legged robots; and so on.
Lastly, new complementary control strategies must be developed in parallel withhardware that changes shape and stiffness. Controllers must account for an internal
representation of the shape and stiffness states of a robot at all times to adapt tounderwater currents, terrain grade, and viscosity of substrate, among other factors.
For instance, central pattern generators commonly employed to control amphibious
robots could be altered with terms that scale amplitude and phase offset as a robotchanges shape or stiffness.

3.6 Conclusion
A brief discussion of biological propulsors provided insight into solutions thatanimals use to transition between aquatic and terrestrial locomotion. Amphibious
animals strive to balance performance in various media, which results in mediocre
performance. Contrastingly, highly derived species are well-adapted to a specificenvironment, often at the expense of locomotion in the other. The diversity ofaquatic and terrestrial locomotor strategies and body plans invites researchers to
combine mechanisms in clever ways to converge on some measure of optimal performance (Fig. 3.1). Our discussion on biology segued into a survey of amphibious

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

63robots, which we classify into those that utilize separate or united propulsive mechanisms. Further, we break down amphibious robots into (1) wheeled, (2) legged,(3) undulating, and (4) soft categories. We sort them by analyzing salient aspectsof their body plans and locomotion strategies. The advantages and disadvantagesof specific robot propulsive mechanism designs from each category highlight areas
where future research effort is needed. In particular, it seems that soft, stiffnesschanging materials offer significant opportunities to enhance mechanical resilience,hydrodynamic efficiency, and shape-morphing capability of amphibious robots. Our
preliminary results toward a turtle/tortoise-inspired quadruped robot with variable
stiffness morphing limbs provide a case study of this design philosophy. We believe
there is promising future research oriented around amphibious robots that follow asimilar design paradigm, one in which shape-morphing, variable-stiffness materials
serve to balance the locomotive merits of rigid and soft robots in water and on land.

References
1. F. Fish, Advantages of aquatic animals as models for bio-inspired drones over present AUV
technology. Bioinspir. Biomim. 15, 025001 (2020)
2. A.J. Ijspeert, A. Crespi, D. Ryczko, J.-M. Cabelguen, From swimming to walking with asalamander robot driven by a spinal cord model. Science 315(5817), 1416–1420 (2007)
3. J.A. Nyakatura, K. Melo, T. Horvat, K. Karakasiliotis, V.R. Allen, A. Andikfar, E. Andrada,
P. Arnold, J. Lauströer, J.R. Hutchinson, M.S. Fischer, A.J. Ijspeert, Reverse-engineering the
locomotion of a stem amniote. Nature 565(7739), 351–355 (2019)
4. Y. Li, F. Fish, Y. Chen, T. Ren, J. Zhou, Bio-inspired robotic dog paddling: kinematic andhydro-dynamic analysis. Bioinspir. Biomim. 14(6), 066008 (2019)
5. A.J. Ijspeert, Biorobotics: using robots to emulate and investigate agile locomotion. Science
346, 196–203 (2014)
6. L. Cui, P. Cheong, R. Adams, T. Johnson, AmBot: a bio-inspired amphibious robot formonitoring the swan-canning estuary system. J. Mech. Des. 136(11), 115001 (2014)
7. S. Dhull, D. Canelon, A. Kottas, J. Dancs, A. Carlson, N. Papanikolopoulos, Aquapod: a small
amphibious robot with sampling capabilities, in 2012 IEEE/RSJ International Conference onIntelligent Robots and Systems (2012), pp. 100–105
8. K. Tadakuma, R. Tadakuma, M. Aigo, M. Shimojo, M. Higashimori, M. Kaneko, OmniPaddle amphibious spherical rotary paddle mechanism, in 2011 IEEE International Conference on Robotics and Automation (2011), pp. 5056–5062
9. B. Zhong, S. Zhang, M. Xu, Y. Zhou, T. Fang, W. Li, On a CPG-based hexapod robot:
amphiHex-II with variable stiffness legs. IEEE/ASME Trans. Mechatron. 23(2), 542–551(2018)
10. H. Zhang (ed.), Climbing and Walking Robots: Towards New Applications (I-Tech Education
and Publisher, Vienna 2007), oCLC: 254375799
11. T.R. Consi, B.R. Ardaugh, T.R. Erdmann, M. Matsen, M. Peterson, J. Ringstad, A. Vechart,
C. Verink, An amphibious robot for surf zone science and environmental monitoring, in
OCEANS 2005 MTS/IEEE (2005), p. 7
12. H. Greiner, A. Shectman, C. Won, R. Elsley, P. Beith, Autonomous legged underwater
vehicles for near land warfare, in Proceedings of Symposium on Autonomous Underwater
Vehicle Technology (1996), pp. 41–48
13. M. Dunbabin, L. Marques, Robots for environmental monitoring: significant advancements
and applications. IEEE Rob. Autom. Mag. 19(1), 24–39 (2012)

64

R. Baines et al.

14. R.H. Harkins, T. Dunbar, A.S. Boxerbaum, R.J. Bachmann, R.D. Quinn, R. Vaidyanathan,
S.C. Burgess, Confluence of active and passive control mechanisms enabling autonomy
and terrain adaptability for robots in variable environments, in Advances in Electrical andElectronics Engineering—IAENG Special Edition of the World Congress on Engineering andComputer Science 2008 (2008), pp. 138–149
15. J. Ayers, J. Witting, C. Wilbur, P. Zavracky, N. McGruer, D. Massa, Biomimetic robots
for shallow water mine countermeasures, in Autonomous Vehicles Mine Countermeasures
Symposium (2000), p. 16
16. M.H. Dickinson, How animals move: an integrative view. Science 288(5463), 100–106 (2000)
17. A. Crespi, A. Badertscher, A. Guignard, A. Ijspeert, AmphiBot I: an amphibious snake-likerobot. Robot. Auton. Syst. 50(4), 163–175 (2005)
18. A.A. Biewener, S.N. Patek, Animal Locomotion (Oxford University, Oxford, 2018)19. C. Li, T. Zhang, D.I. Goldman, Locomotion: energy cost of swimming, flying, and running.
Science 177(4045), 222–228 (1972)
20. P. Webb, Hydrodynamics and energetics of fish propulsion. Bull. Fish. Res. Board Can. 190,
1–158 (1975)
21. P. Webb, R. Blake, Swimming, in Functional Vertebrate Morphology, ed. by M. Hildebrand,
D.M. Bramble, K.F. Liem, D.B. Wake (Harvard University Press, Cambridge, 1985), pp. 110–128
22. F.E. Fish, Biomechanics and energetics in aquatic and semiaquatic mammals: platypus towhale. Physiol. Biochem. Zool. 73(6), 683–698 (2000)
23. C. Gans, Biomechanics: An Approach to Vertebrate Biology (Lippincott, Philadelphia, 1974)
24. M. Hildebrand, The adaptive significance of tetrapod gait selection. Am. Zool. 20, 255–267(1980)
25. R.J. Full, Mechanics and energetic of terrestrial locomotion: bipeds to polypeds, in Energy
Transformations in Cells and Organisms, ed. by W. Wieser, E. Gnaiger (Thieme, Stuttgart,1989), pp. 175–182
26. H.-T. Lin, G.G. Leisk, B. Trimmer, GoQBot: a caterpillar-inspired soft-bodied rolling robot.
Bioinspir. Biomim. 6(2), 026007 (2011)
27. K. Low, T. Hu, S. Mohammed, J. Tangorra, M. Kovac, Perspectives on biologically inspired
hybrid and multi-modal locomotion. Bioinspir. Biomim. 10, 020301 (2015)
28. R. Lock, S. Burgess, R. Vaidyanathan, Multi-modal locomotion: from animal to application.
Bioinspir. Biomim. 9, 011001 (2014)29. S.E. Peters, L.T. Kamel, D.P. Bashor, Hopping and swimming in the leopard frog, Ranapipiens: I. Step cycles and kinematics. J. Morphol. 230(1), 1–16 (1996)
30. F.E. Fish, Transitions from drag-based to lift-based propulsion in mammalian swimming. Am.
Zool. 36(6), 628–641 (1996)
31. L.A. Isaac, P.T. Gregory, Aquatic versus terrestrial locomotion: comparative performance of
two ecologically contrasting species of European natricine snakes. J. Zool. 273(1), 56–62(2007)
32. M. Calisti, A. Arienti, F. Renda, G. Levy, B. Hochner, B. Mazzolai, P. Dario, C. Laschi,
Design and development of a soft robot with crawling and grasping capabilities, in Proceedings of the 2012 IEEE International Conference on Robotics and Automation (2012), pp.
4950–4955
33. D.L. Hu, B. Cean, J.W.M. Bush, The hydrodynamics of water strider locomotion. Nature 424,
663–666 (2003)
34. J.W. Glasheen, T.A. Mcmahon, A hydrodynamic model of the locomotion in the Basilisk
Lizard. Nature 380, 340–342 (1996)
35. S.T. Hsieh, Three-dimensional hindlimb kinematics of water running in the plumed Basilisk
Lizard (Basiliscus plumifrons). J. Exp. Biol. 206, 4363–4377 (2003)
36. W.T. Gough, S.C. Farina, F.E. Fish, Aquatic burst locomotion by hydroplaning and runningin common eiders (Somateria mollissima). J. Exp. Biol. 218, 1632–1638 (2015)
37. T. Williams, M. Ben-David, S. Noren, M. Rutishauser, K. McDonald, W. Heyward, Runningenergetics of the North American river otter: do short legs necessarily reduce efficiency

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

65

on land? in Comparative Biochemistry and Physiology Part A: Molecular and Integrative
Physiology, vol. 133 (2002), pp. 203–212
38. S. Vogel, Life in Moving Fluids (Princeton University, Princeton, 1994)
39. C.E. Jordan, A model of rapid-start swimming at intermediate Reynolds number: undulatory
locomotion in the chaetognath Sagitta elegans. J. Exp. Biol. 169, 119–137 (1992)
40. M. LaBarbera, Why the wheels won’t go. Am. Nat. 121(3), 395–408 (1983)
41. A. Biewener, Scaling body support in mammals: limb posture and muscle mechanics. Science
245, 45–48 (1989)
42. A.A. Biewener, Biomechanical consequences of scaling. J. Exp. Biol. 208(9), 1665–1676(2005)
43. A. McNeil, Elastic Mechanisms in Animal Movement (Cambridge University, Cambridge,
1998)
44. T. Dawson, C. Taylor, Energetic cost of locomotion in kangaroos. Nature 246(5431), 313–314(1973)
45. D. Rus, M.T. Tolley, Design, fabrication and control of soft robots. Nature 521(7553), 467–
475 (2015)46. Y. Tang, Q. Zhang, G. Lin, J. Yin, Switchable adhesion actuator for amphibious climbing soft
robot. Soft Robot. 5(5), 592–600 (2018)
47. A.A.M. Faudzi, M.R.M. Razif, G. Endo, H. Nabae, K. Suzumori, Soft-amphibious robot using
thin and soft McKibben actuator, in Proceedings of the 2017 IEEE International Conference
on Advanced Intelligent Mechatronics (2017), pp. 981–986
48. X. Liang, M. Xu, L. Xu, P. Liu, X. Ren, Z. Kong, J. Yang, S. Zhang, The AmphiHex: anovel amphibious robot with transformable leg-flipper composite propulsion mechanism,in Proceedings of the 2012 IEEE/RSJ International Conference on Intelligent Robots andSystems (2012), pp. 3667–3672
49. L. Shi, S. Guo, S. Mao, C. Yue, M. Li, K. Asaka, Development of an amphibious turtleinspired spherical mother robot. J. Bionic Eng. 10(4), 446–455 (2013)
50. A.J. Ijspeert, A. Crespi, Online trajectory generation in an amphibious snake robot using alamprey-like central pattern generator model, in Proceedings of the 2007 IEEE International
Conference on Robotics and Automation (2007), pp. 262–268
51. W. Wang, J. Yu, R. Ding, M. Tan, Bio-inspired design and realization of a novel multimodeamphibious robot, in Proceedings of the 2009 IEEE International Conference on Automationand Logistics (2009), pp. 140–145
52. A. Crespi, K. Karakasiliotis, A. Guignard, A.J. Ijspeert, Salamandra robotica II: an amphibious robot to study salamander-like swimming and walking gaits. IEEE Trans. Robot. 29(2),pp. 308–320 (2013)
53. J. Yu, Y. Tang, X. Zhang, C. Liu, Design of a wheel-propeller-leg integrated amphibious robot,
in Proceedings of the 2010 11th International Conference on Control Automation Robotics
Vision (2010), pp. 1815–1819
54. Y. Yi, Z. Geng, Z. Jianqing, C. Siyuan, F. Mengyin, Design, modeling and control of a novel
amphibious robot with dual-swing-legs propulsion mechanism, in Proceedings of the 2015
IEEE/RSJ International Conference on Intelligent Robots and Systems (2015), pp. 559–566
55. F. Fish, Aerobic energetics of surface swimming in the muskrat Ondatra Zibethicus. Phys.
Zool. 55, 180–189 (1982)
56. T. Lode, Comparative measurements of terrestrial and aquatic locomotion in Mustela lutreolaand M. putorius. Int. J. Mamm. Biol. 64, 110–115 (1999)
57. T.M. Williams, Swimming by sea otters: adaptations for low energetic cost locomotion. J.
Comp. Physiol. 164(6), 815–824 (1989)
58. R. Shine, S. Shetty, Moving in two worlds: aquatic and terrestrial locomotion in sea snakes(Laticauda Colubrina, Laticaudidae): sea snake locomotion. J. Evol. Biol. 14(2), 338–346(2001)
59. T.M. Williams, W.A. Friedl, J.E. Haun, The physiology of bottlenose dolphins (Tursiops
truncatus): heart rate, metabolic rate and plasma lactate concentration during exercise. J. Exp.
Biol. 179, 31–46 (1993)

66

R. Baines et al.

60. Amphibious 4WD WiFi Robotics SuperDroid. https://www.superdroidrobots.com/shop/item.
aspx/ig42-sb4-ea-amphibious-4wd-wifi-robot/2121/
61. J. Katz, Race Car Aerodynamics (Bentley Publishers, Cambridge, 1995)
62. S. Yamada, S. Hirose, G. Endo, K. Suzumori, H. Nabae, R-Crank: amphibious all terrain
mobile robot, in Proceedings of the 2016 IEEE/RSJ International Conference on Intelligent
Robots and Systems (2016), pp. 1067–1072
63. V. Kaznov, M. Seeman, Outdoor navigation with a spherical amphibious robot, in Proceedingsof the 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (2010), pp.
5113–5118
64. K. Kawasaki, M. Zhao, K. Okada, M. Inaba, MUWA: multi-field universal wheel for airland vehicle with quad variable-pitch propellers, in Proceedings of the 2013 IEEE/RSJ
International Conference on Intelligent Robots and Systems (2013), pp. 1880–1885
65. M.G. Bekker, Theory of Land Locomotion (University of Michigan Press, Michigan, 1956)
66. J.Y. Wong, Theory of Ground Vehicles (Wiley, New York, 1978)
67. G. Meirion-Griffith, M. Spenko, An empirical study of the terramechanics of small unmanned
ground vehicles, in Proceedings of the IEEE Aerospace Conference (2010), pp. 1–6
68. Y. Sun, S. Ma, ePaddle mechanism: towards the development of a versatile amphibious
locomotion mechanism, in International Conference on Intelligent Robots and Systems(2011), pp. 5035–5040
69. Y. Sun, S. Ma, Y. Yang, H. Pu, Towards stable and efficient legged race-walking of an ePaddlebased robot. Mechatronics 23(1), 108–120 (2013)
70. Y. Shen, Y. Sun, H. Pu, S. Ma, Experimental verification of the oscillating paddling gait for an
ePaddle-EGM amphibious locomotion mechanism. IEEE Rob. Autom. Lett. 2(4), 2322–2327(2017)
71. N.B. Ignell, N. Rasmusson, J. Matsson, An overview of legged and wheeled robotic
locomotion, in Mini-Conference on Interesting Results in Computer Science and Engineering,
vol. 21 (2012)
72. C. Bernstein, M. Connolly, M. Gavrilash, D. Kucik, S. Threatt, Demonstration of surf-zone
crawlers: results from AUV Fest 01, in Surf Zone Crawler Group, Naval Surface Warfare
Center, Panama City, FL (2001)
73. M.A. Klein, A.S. Boxerbaum, R.D. Quinn, R. Harkins, R. Vaidyanathan, Seadog: a rugged
mobile robot for surf-zone applications, in IEEE RAS and EMBS International Conference on
Biomedical Robotics and Biomechatronics (2012), pp. 1335–1340
74. M.F. Silva, J.T. Machado, A literature review on the optimization of legged robots. J. Vib.
Control 18(12), 1753–1767 (2012)
75. J. Ayers, J. Witting, C. Olcott, N. McGruer, D. Massa, Lobster robots, in Proceedings of the2000 International Symposium on Aqua Biomechanisms (2000)
76. S. Floyd, T. Keegan, J. Palmisano, M. Sitti, A novel water running robot inspired by basilisk
lizards, in Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots
and Systems (2006), pp. 5430–5436
77. H.S. Park, M. Sitti, Compliant footpad design analysis for a bio-inspired quadruped amphibious robot, in Proceedings of the 2009 IEEE/RSJ International Conference on Intelligent
Robots and Systems (2009), pp. 645–651
78. H.S. Park, S. Floyd, M. Sitti, Roll and pitch motion analysis of a biologically inspired
quadruped water runner robot. Int. J. Robot. Res. 29(10), 1281–1297 (2010)
79. H. Kim, D. Lee, K. Jeong, T. Seo, Water and ground-running robotic platform by repeatedmotion of six spherical footpads. IEEE/ASME Trans. Mechatron. 21(1), 175–183 (2015)
80. Y. Chen, N. Doshi, B. Goldberg, H. Wang, R.J. Wood, Controllable water surface tounderwater transition through electrowetting in a hybrid terrestrial-aquatic microrobot. Nat.
Commun. 9(1), 2495 (2018)81. B. Kwak, J. Bae, Locomotion of arthropods in aquatic environment and their applications inrobotics. Bioinspir. Biomim. 13(4), 041002 (2018)
82. G. Dudek, M. Jenkin, C. Prahacs, A. Hogue, J. Sattar, P. Giguere, A. German, H. Liu,
S. Saunderson, A. Ripsman, S. Simhon, L. Torres, E. Milios, P. Zhang, I. Rekletis, A visually

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

67

guided swimming robot, in Proceedings of the 2005 IEEE/RSJ International Conference onIntelligent Robots and Systems (2005), pp. 3604–3609
83. G. Dudek, P. Giguere, C. Prahacs, S. Saunderson, J. Sattar, L.-a. Torres-Mendez, M. Jenkin,
A. German, A. Hogue, A. Ripsman, J. Zacher, E. Milios, H. Liu, P. Zhang, M. Buehler,
C. Georgiades, AQUA: an amphibious autonomous robot. Computer 40(1), 46–53 (2007)
84. C. Prahacs, A. Saudners, M.K. Smith, D. McMordie, M. Buehler, Towards legged amphibious
mobile robotics, in Proceedings of the Canadian Engineering Education Association (2011)
85. R. Quinn, J. Offi, D. Kingsley, R. Ritzmann, Improved mobility through abstracted biologicalprinciples, in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots
and System, vol. 3 (2002), pp. 2652–2657
86. A. Boxerbaum, P. Werk, R. Quinn, R. Vaidyanathan, Design of an autonomous amphibious
robot for surf zone operation: part i mechanical design for multi-mode mobility, in Proceedings of the 2005 IEEE/ASME International Conference on Advanced Intelligent Mechatronics(2005), pp. 1459–1464
87. R. Harkins, J. Ward, R. Vaidyanathan, A. Boxerbaum, R. Quinn, Design of an autonomous
amphibious robot for surf zone operations: part II–hardware, control implementation andsimulation, in Proceedings of the 2005 IEEE/ASME International Conference on AdvancedIntelligent Mechatronics (2005), pp. 1465–1470
88. A.S. Boxerbaum, M.A. Klein, J.E. Kline, S.C. Burgess, R.D. Quinn, R. Harkins,
R. Vaidyanathan, Design, simulation, fabrication and testing of a bio-inspired amphibious
robot with multiple modes of mobility. J. Robot. Mechatron. 24(4), pp. 629–641 (2012)89. B.B. Dey, S. Manjanna, G. Dudek, Ninja legs: Amphibious one degree of freedom robotic
legs, in 2013 Proceedings of the IEEE/RSJ International Conference on Intelligent Robots
and Systems (2013), pp. 5622–5628
90. A.R. Vogel, K.N. Kaipa, G.M. Krummel, H.A. Bruck, S.K. Gupta, Design of a complianceassisted quadrupedal amphibious robot, in Proceedings of the 2014 IEEE International
Conference on Robotics and Automation (2014), pp. 2378–2383
91. S. Zhang, X. Liang, L. Xu, M. Xu, Initial development of a novel amphibious robot withtransformable fin-leg composite propulsion mechanisms. J. Bionic Eng. 10(4), 434–445(2013)
92. S. Zhang, Y. Zhou, M. Xu, X. Liang, J. Liu, J. Yang, AmphiHex-I: locomotory performancein amphibious environments with specially designed transformable flipper legs. IEEE/ASME
Trans. Mechatron. 21(3), 1720–1731 (2016)93. S. Guo, S. Mao, L. Shi, M. Li, C. Yue, Development of a spherical amphibious mother robot,
in Proceedings of the 2013 ICME International Conference on Complex Medical Engineering(2013), pp. 614–619
94. A. Crespi, A. Badertscher, A. Guignard, A.J. Ijspeert, Swimming and crawling with anamphibious snake robot, in Proceedings of the International Conference on Robotics andAutomation (2005), pp. 3024–3028
95. T. Matsuo, T. Yokoyama, D. Ueno, K. Ishii, Biomimetic motion control system based on a
CPG for an amphibious multi-link mobile robot. J. Bionic Eng. 5, 91–97 (2008)
96. S. Yu, S. Ma, B. Li, Y. Wang, An amphibious snake-like robot: design and motion experiments
on ground and in water, in Proceedings of the 2009 International Conference on Information
and Automation (2009), pp. 500–505
97. S. Yu, S. Ma, B. Li, Y. Wang, An amphibious snake-like robot with terrestrial and aquatic
gaits, in Proceedings of the 2011 IEEE International Conference on Robotics and Automation(2011), pp. 2960–2961
98. J. Yu, R. Ding, Q. Yang, M. Tan, W. Wang, J. Zhang, On a bio-inspired amphibious robot
capable of multimodal motion. IEEE/ASME Trans. Mechatron. 17(5), 847–856 (2012)
99. J. Yu, R. Ding, Q. Yang, M. Tan, J. Zhang, Amphibious pattern design of a robotic fish withwheel-propeller-fin mechanisms. J. Field Robot. 30(5), 702–716 (2013)100. Robotics Pliant Energy Systems. https://www.pliantenergy.com/
101. Robot traversing sea, sand and snow, in Pliant Energy Systems. https://www.youtube.com/
watch?v=2pVsaWwAOh0

68

R. Baines et al.

102. A.A. Transeth, K.Y. Pettersen, L. Påll, A survey on snake robot modeling and locomotion.
Robotica 27(7), 999–1015 (2009)
103. D. Trivedi, C.D. Rahn, W.M. Kier, I.D. Walker, Soft robotics: biological inspiration, state of
the art, and future research. Appl. Bionics Biomech. 5(3), 99–117 (2008)
104. F. Corucci, N. Cheney, F. Giorgio-Serchi, J. Bongard, C. Laschi, Evolving soft locomotion
in aquatic and terrestrial environments: effects of material properties and environmental
transitions. Soft Robot. 5(4), 475–495 (2018)
105. A.D. Marchese, C.D. Onal, D. Rus, Autonomous soft robotic fish capable of escapemaneuvers using fluidic elastomer actuators. Soft Robot. 1(1) 75–87 (2014)
106. R.F. Shepherd, F. Ilievski, W. Choi, S.A. Morin, A.A. Stokes, A.D. Mazzeo, X. Chen,
M. Wang, G.M. Whitesides, Multigait soft robot, in Proceedings of the National Academyof Sciences, vol. 108(51), pp. 20,400–20,403 (2011)107. T. Paschal, M.A. Bell, J. Sperry, S. Sieniewicz, R.J. Wood, J.C. Weaver, Design, fabrication,and characterization of an untethered amphibious sea urchin-inspired robot. IEEE Robot.
Autom. Lett. 4(4), 3348–3354 (2019)108. L. Hines, K. Petersen, G.Z. Lum, M. Sitti, Soft actuators for small-scale robotics. Adv. Mater.
29(13), 1603483 (2017)109. L.A. Hirano, L.S. Martins-Filho, R.O. Duarte, J.F. de Paiva, Development of an amphibious
robotic propulsor based on electroactive polymers, in Proceedings of the 2009 4th International Conference on Autonomous Robots and Agents (2009), pp. 284–289
110. N.W. Bartlett, M.T. Tolley, J.T.B. Overvelde, J.C. Weaver, B. Mosadegh, K. Bertoldi, G.M.
Whitesides, R.J. Wood, A 3d-printed, functionally graded soft robot powered by combustion.
Science 349(6244), 161–165 (2015)
111. J.L.C. Santiago, I.S. Godage, P. Gonthina, I.D. Walker, Soft robots and kangaroo tails:
modulating compliance in continuum structures through mechanical layer jamming. Soft
Robot. 3(2), 54–63 (2016)112. N.G. Cheng, M.B. Lobovsky, S.J. Keating, A.M. Setapen, K.I. Gero, A.E. Hosoi, K.D.
Iagnemma, Design and analysis of a robust, low-cost, highly articulated manipulator enabled
by jamming of granular media, in Proceedings of the 2012 IEEE International Conference on
Robotics and Automation (2012), pp. 4328–4333
113. A.R. Deshpande, Z.T.H. Tse, H. Ren, Origami-inspired bi-directional soft pneumatic actuatorwith integrated variable stiffness mechanism, in Proceedings of the 2017 18th International
Conference on Advanced Robotics (ICAR) (2017), pp. 417–421
114. I.D. Falco, M. Cianchetti, A. Menciassi, A soft multi-module manipulator with variable
stiffness for minimally invasive surgery. Bioinspir. Biomim. 12(5), 056008 (2017)115. R.L. Baines, J.W. Booth, F.E. Fish, R. Kramer-Bottiglio, Toward a bio-inspired variablestiffness morphing limb for amphibious robot locomotion, in Proceedings of the 2019 2ndIEEE International Conference on Soft Robotics (RoboSoft) (2019), pp. 704–710
116. F.E. Fish, Advantages of aquatic animals as models for bio-inspired drones over present AUV
technology. Bioinspir. Biomim. 15(2), 025001 (2020)
117. S. Seok, A. Wang, M.Y. Chuah, D. Otten, J. Lang, S. Kim, Design principles for highly
efficient quadrupeds and implementation on the MIT cheetah robot, in IEEE International
Conference on Robotics and Automation (2013), p. 3307–3312
118. A.J. Ijspeert, Amphibious and sprawling locomotion: From biology to robotics and back.
Annu. Rev. Control Robot. Auton. Syst. 3(1), 173–193 (2020)
119. C. Li, T. Zhang, D.I. Goldman, A terradynamics of legged locomotion on granular media.
Science 339(5452), 1408–1412 (2013)120. H. Marvi, C. Gong, N. Gravish, H. Astley, M. Travers, R. Hatton, J. Mendelson, H. Choset,
D. Hu, D. Goldman, Sidewinding with minimal slip: Snake and robot ascent of sandy slopes.
Science 346, 224–229 (2014)121. B. Zhong, Y. Zhou, X. Li, M. Xu, S. Zhang, Locomotion performance of the amphibious robot
on various terrains and underwater with flexible flipper legs. J. Bionic Eng. 13(4), 525–536(2016)

3 Amphibious Robotic Propulsive Mechanisms: Current Technologies and. . .

69122. R. Baines, S. Freeman, F. Fish, R. Kramer-Bottiglio, Variable stiffness morphing limb
for amphibious legged robots inspired by chelonian environmental adaptations. Bioinspir.
Biomim. 15(2), 025002 (2020)123. J. Bertin, R.M. Cummings, Aerodynamics for Engineers, 5th edn. (Pearson Prentice-Hall,
Upper Saddle River, 2009)