robotics.sciencemag.org/cgi/content/full/5/42/eaaz1012/DC1

Supplementary Materials for

Bioinspired underwater legged robot for seabed exploration with low

environmental disturbance

G. Picardi, M. Chellapurath, S. Iacoponi, S. Stefanni, C. Laschi, M. Calisti*

*Corresponding author. Email: marcello.calisti@santannapisa.it

Published 13 May 2020, Sci. Robot. 5, eaaz1012 (2020)

DOI: 10.1126/scirobotics.aaz1012

The PDF file includes:

Text Fig. S1. Exploded view of SILVER2 with all subsystems. Fig. S2. CAD rendering of three-DOF segmented leg. Fig. S3. Electronic subsystem. Fig. S4. Exploded view of the camera canister. Fig. S5. The original U-SLIP and the articulated version. Fig. S6. Comparison between SILVER2 and U-SLIP simulation over a single step. Fig. S7. Control of hopping locomotion. Fig. S8. Parametric analysis of U-SLIP performance with respect to touchdown angle and spring stiffness. Fig. S9. Control of omnidirectional walking locomotion. Fig. S10 Reconstructed long-exposure images. Table S1. Parameters of U-SLIP model and values used in simulations. Table S2. Free parameters of omnidirectional walking gait. Table S3. Data of the tests presented. Legends for movies S1 to S5

Other Supplementary Material for this manuscript includes the following: (available at robotics.sciencemag.org/cgi/content/full/5/42/eaaz1012/DC1)

Movie S1 (.mp4 format). Hopping locomotion. Movie S2 (.mp4 format). Hopping locomotion. Movie S3 (.mp4 format). Walking locomotion. Movie S4 (.mp4 format). Sea life. Movie S5 (.mp4 format). Approaching procedure.

TEXT

Hardware details

Fig. S1. Exploded view of SILVER2 with all subsystems.

Chassis

The chassis of the robot acts as a structural entity to hold the components of the robot and protect the robot

from any external impact. It consists of two parallel vertical polycarbonate plates connected together by two

aluminum bars and a Delrin™ plate that provide structural integrity and space for attaching different

components of the robot. The components were arranged to provide easy access to the canister while being

as compact as possible. The legs were connected to the bottom of the vertical plates. Electronic and power,

camera and sampling subsystems were attached to the horizontal structural elements fig. S1. The two

canisters containing components of electronic and power subsystem were attached to the horizontal plate.

The camera subsystem was attached to the horizontal aluminum bar in the frontal side. The sampling system

was also attached to bottom of the same bar. The fasteners used were made of stainless steel to have better

corrosion resistance. The aluminum alloy used was Al 6061.

Propulsion subsystem

Fig. S2. CAD rendering of 3DOFs segmented leg. The coxa motor allows rotations around z-axis and defines the coxa

plane, where the two links of the leg lie. Femur and tibia motors define the position of the leg in the coxa plane. Overall

the configuration of leg Li can be described by the angles of the motors with the following notation qi = [ci fi ti]. Each

leg coordinate frame {Li} is centred on the coxa motor axis, at the same height of the femur motor axis. The x-axis is

parallel to the x-axis of the body frame, the z-axis points upward and y-axis completes a right-handed coordinate frame.

SILVER2 propulsion subsystem is made of two sets of 3 legs per side. Legs 3, 4, 5 are mirrored with respect

to legs 1, 2, 6. Each leg is composed of two links and has 3 rotational DOFs (fig. S2). Each joint is actuated

with a XM430-W350-R Dynamixel servomotor enclosed in a custom design waterproof canister. Motors are

attached to the inner part of the canister and connected to a stainless-steel shaft which extrudes from one of

the canister cap. A dynamic sealing on the shaft ensures watertight enclosure. For each leg, the three

canisters are connected with underwater cables carrying the serial communication channel and leakage

sensors signals. The first motor of each leg Li, namely coxa motor, is connected to the polycarbonate vertical

plate and defines the vertical plane on which Li lies, namely the coxa plane. The second and third motors,

namely femur and tibia motor, control the position of Li on the coxa plane. The leg geometry allows for a

wide workspace, so that the geometric limitation for the leg configurations are almost always related to

interferences with the body, the ground or the other legs. Following the tibia motor (third motor), the shaft is

not directly connected to the last leg section but to a specifically tuned torsion elastic component. The elastic

component allows for the tibia junction to act as a torsional Serial Elastic Actuator (SEA). The torsional

elasticity is obtained by mounting two compressive springs in contraposition into a circular slot. At the end

of the leg, the foot structure encloses a piezoelectric disk, lodged in a 3d printed case and embedded in

watertight silicone. The foot is free to rotate shortly around a hinge, pressing against the center of the

piezoelectric disc when in contact with the ground. The hinge is placed far from the central axis to allow for

the contact pressure to be transmitted even when the foot gets in contact with the ground with a stiff angle.

Design of the foot is modular, so that it is easy to replace the rotating part: as a matter of fact, to different

feet were used (a half spherical black one, and one presented in fig. S2), but no difference were observed.

Electronic and power subsystems

Fig. S3. Electronic subsystem. Connections with buoy, camera, power and propulsion subsystems.

The electronic and power subsystems are contained inside 2 wide aluminum canisters placed horizontally at

the center of body. The electric connection between the canisters and with camera and propulsion

subsystems is realized through a series of underwater cables. Each cable’s ends terminate with a watertight

penetrator sealed with resin. All the components and connections with buoy, power, camera, and propulsion

subsystems are shown in fig. S3. The first canister contains the power subsystem which is made of a lithium

battery of 12V 25000mA, voltage and current sensors, voltage regulator (not shown in Figure) and the power

switch. The battery is the only power source of Silver 2.0, which is independent from outer sources. The

second canister contains the electronic subsystem. The main control unit (MCU) is a 3.0 Raspberry pi b+.

Onboard sensors are pressure sensor penetrator (MS5837-30BA), Inertial measurement unit which includes a

3-axis magnetometer and embedded sensor fusion algorithm for estimation of orientation (BNO055), a

custom circuit board for the reading for the reading of the piezoelectric sensors , and a custom circuit board

to read 27 humidity sensors positioned across the waterproof canisters (motors, camera, electronic and

battery). The electronic subsystem is mounted on an easily extractable card cage.

Camera subsystem

Fig. S4. Exploded view of the camera canister. Exploded view of the watertight dome enclosing two HD cameras

mounted on a 2DOF Pan and tilt gimbal actuated with servomotors.

The camera subsystem is made of two components: the camera canister featuring a watertight dome

enclosing two HD cameras mounted on a 2DOFs (pan and tilt) gimbal (shown in fig. S4) and the four PWM

dimmable underwater torches. The torches are part of a standalone system (LUMEN-QUAD-R2) directly

connected to the electronics canister and are capable of generating up to 1500 lumen. The canister has a

hemispherical transparent dome enclosing two high-resolution Low-Light USB Camera, mounted on a

gimbal. The gimbal has two DOF, vertical (tilt) and horizontal (pan) rotation, actuated by two servomotors.

The two cameras area arranged to allow for stereoscopic video and 3D reconstruction. The gimbal system is

designed to have the rotation axis intersecting in the geometrical center of the dome and allow for a rotation

of 90 degrees in both direction and both rotations.

Sampling subsystem

The sampling device is a simple passive system consisting of 6 closed cylindrical aluminum tubes (diameter

10 mm). One end of each tube is screwed to a plate and the other was made truncated to penetrate easily into

sandy sediments. Each cylinder contains a small hole (diameter 4mm) closer to collect sand during sampling

actions. A sampling actions consists in lowering the posture to penetrate the sediment with the sampling

system, trapping sand into the small holes. When the body is raised, the sediment is collected inside the tube.

Samples were fetched from tube after each mission.

Communication subsystem and interface

The robot was tethered to the buoy on the surface using Ethernet cable (category 5, bandwidth: 100 MHz,

Data transfer rate: 100 Mbps). The antenna, Bullet M Omni (bandwidth: 2.4 GHz, Data transfer rate: 100

Mbps) was placed on a buoy in waterproof container together with battery and electronics and allow a

theoretical maximum range of 100m. The robot can be controlled wirelessly by a human operator from

land/boat through the antenna. A shorter steel cable connected the buoy to the robot to prevent the Ethernet

cable from stretching.

Software communication among the different components of the robot was performed by mean of Robot

Operating System (ROS), under a Lubuntu distribution mounted on the Raspberry board. The pilot-robot

interface exploited the software framework for generic user interface (GUI) embedded in ROS, the rqt

interface. Data collection was obtained by launching bag services.

Locomotion control

Legs are actuated by 18 XM430-W350-R Dynamixel servomotor. Position and velocity commands are pre-

computed by the MCU based on gait specific control parameters and sent to the robot via serial

communication. The frequency of the control loop is 100Hz.

Anchoring the U-SLIP model

Fig. S5. The original U-SLIP and the articulated version. U-SLIP model (a) and the articulated one (b), where the

articulated leg with the SEA anchors the behaviour of a linear spring from hip to foot.

In the presented approach, the selection of the appropriate stiffness of the SEA is crucial. The stiffness of

SILVER2 can be expressed through 3 equivalent parametrizations (fig. 5 Sb), i.e. the stiffness of the linear

springs used to implement the torsional SEA kSEA, the stiffness of the equivalent torsional spring kROT at the

knee joint and the stiffness of the equivalent linear leg k as in the U-SLIP model. First, the desired stiffness

for the equivalent U-SLIP model k was selected to limit the vertical displacement due to joint compliancy in

static conditions and meet general performance requirements through U-SLIP simulations. Then, the

stiffness of the torsional spring kROT is derived from a moment balance at the knee joint in static conditions.

Finally, the appropriate stiffness of the linear springs used to implement the SEA kSEA was simply derived

from the geometry of the SEA itself. In this work, we targeted an equivalent linear stiffness k=660N/m,

reached when the robot stands on six legs. The resulting linear stiffness of the SEA springs was

kSEA=10kN/m.

Recapping the U-SLIP model during punting phase, the horizontal and vertical dynamics are respectively

described by the following equations:

2 2

¨0

2 2

( ) tt

t

r r x x yk x xXx x x

m M m M x x y

2 2

¨0

2 2

( ) t w

t

r r x x y VgY ky mgy y y

m M m M m M m Mx x y

.

Where m is the mass of the robot, M is the added mass, X is the horizontal damping coefficient due to

water,  Y is the vertical damping coefficient due to water, 0r is the length of the leg at touchdown, tx is the

horizontal position of foot at touchdown, g is the gravity acceleration, V is the volume of the robot,   w is

the density of water. The control input is the elongation of the leg, which we chose to be linear sr r t and it

depends on elongation speed sr , maximum elongation defined as

maxr , and touch down angle α (not shown

in the equations). Once a combination of spring stiffness k and control parameters sr and α which leads to a

robustly stable locomotion was found, we derived specifications for the articulated legs in terms of peak

force obtained from the compression of the linear spring, and time to reach the maximum elongation maxr .

Those specifications became the requirements of a classical mechanical design problem, thus that the

combination of SEA springs, and motors to ensure the timely elongation of the leg were evaluated until the

proper components were selected.

It is worth to mention that the present design methodology, does not consider the actual direction of resulting

forces on the body, which may differ from U-SLIP model. However, this approach resulted effective due to

the good stability of the U-SLIP system for the final choice of the mechanical parameters selected for our

robot. A comparison among the U-SLIP simulations obtained with the parameters reported in table S1 and

the actual trajectories of the robot, as tracked during field tests is shown in fig. S6. The comparison over a

single step (as commonly done in the evaluation of hopping machines, not to let the errors propagate in the

subsequent hops) reveals a good matching between SILVER2 and U-SLIP. In particular, the hopping period

of roughly 5s, and the horizontal and vertical displacements over a period were correctly predicted by the

model. The most notable difference occurs in the horizontal trajectory which, in the case of SILVER2, looks

linear. Such mismatch does not affect the prediction of the average performance of the hop and may be

explained considering the disturbance of currents in real conditions as well as inaccuracies in the

identification of hydrodynamic parameters such as X, Y and M.

Table S1. Parameters of U-SLIP model and values used in simulations. The value of all parameters was obtained by

design, except for the hydrodynamic drags X and Y that were selected as for a box of the size of the robot and M which

was selected as m/2. The rest length of the equivalent single leg r0 is the height of the centre of mass of SILVER2 at

touch down and thus, for the case of articulated legs, depends on the configuration of the legs at touch down. The

volume of the robot V is computed as /u wV m m where mu is the underwater weight of the robot in kg as

measured with a dynamometer.

Parameter Symbol Value

Dry mass m 22 kg

Added mass M 11 kg

Leg’s rest length r0 0.2 m

Leg’s maximum elongation rmax 0.1 m

Horizontal drag X 0.5040

Vertical drag Y 1.0080

Spring stiffness k 660 N/m

Gravity g 9,81

Volume V 0,021 m3

Density of water ρw 1024 kg/m3

Touch down angle α 70°

Extension speed rs 1 m/s

Fig. S6. Comparison between SILVER2 and U-SLIP simulation over a single step.

Hopping

Fig. S7. Control of hopping locomotion. A) Schematics showing the forces transferred to the body of the robot by the

legs. B) Sideways hopping control. Left, top view; middle, front view with legs in retracted position; right, front view

with legs in extended position. The asymmetry of extended positions between the two sides of the robot generates

propulsion in the direction of negative x-axis. C) Rotating hopping control. Left, top view; middle, front view with legs

is retracted position; right, front view with legs in extended position. The position of coxa joints of all legs generates a

momentum around z-axis.

The hopping locomotion demonstrated in the paper is based on two simple control primitives, which in turn

are defined by two positions in which a leg can be. With a reference to joint angles depicted in fig. S2, each

leg Li can be in the retracted position qir =[ci

r fir t

ir] or in the extended position qi

e =[cie f

ie t

ie]. The action of

going from qir to qi

e, corresponds to the extension primitive, whereas the reverse action corresponds to the

retraction primitive.

In addition to an open loop control layer in which the extension and retraction primitives are clock driven

(when the touch-down-clock elapses, the extension primitive is triggered; when the lift-off-clock elapses, the

retraction primitive is triggered), an additional layer harnesses the feedback from the contact sensors to

trigger the primitives as follows:

If touch down is detected or touch-down-clock elapses:

Extend all legs

Reset touch-down-clock

If lift off is detected or lift-off-clock elapses:

Retract all legs

Reset lift-off-clock

When Li is in contact with the ground, it exerts a force Fi to the body at the attachment point of Li with

direction and intensity which depend on qir, q

ie and on the extension trajectory. In the present work the latter

aspect was not systematically modelled and values for qir and q

ie were tuned heuristically. Furthermore, the

extension trajectory consisted in a linear trajectory for every joint at the maximum velocity allowed by the

hardware. Note that a linear trajectory for every joint does not result in a linear trajectory of the foot.

In this work, we used a gait in which all legs extend altogether when contact is detected on any feet. In this

condition and neglecting any rotation around axis x and y due to body geometry, we can assume that legs get

in contact with the ground and exert a force to the body at the same time. As shown in fig. S7A, the overall

force exerted to the body by the action of legs is thus F =

6

1

i

i

i

c F

, where ci is zero if Li is not in contact with

the ground and 1 otherwise. Similarly, the overall momentum around z-axis is M =

6

1

i

i

i

c M

with Mi

depending on the projection of Fi on plane XY.

Sideways locomotion in the direction of x-axis was obtained as depicted in fig. S7B, with coxa angles

arranged to generate an overall null momentum around z-axis, and asymmetry in the extended position of the

legs on the two sides of the robot to generate a force in the direction of negative x-axis. The trajectories

presented in fig. S6 were obtained with the following joint angles qir = [0, 50, 130] i=1-6, qj

e = [0, 9, 141]

i=1-3, qke = [0, 20, 85] k=4-6 , which correspond to the poses reported in fig. S 7B middle and right.

Rotations in place was obtained as depicted in fig. S7C, with radially symmetric pushing directions to cancel

out forces on the XY-plane, and coxa angles arranged to generate momentum around z.

By taking the U-SLIP model as a reference, the tuning knobs of the hopping locomotion are inter-limbs

coordination, touch down angle α and the extension law r of the equivalent single leg, which are dictated by

the extended and retracted position of each leg qir, q

ie and on the joint velocity selected to transition from one

to the other. In particular, as depicted in fig. S7A, α results from the vector sum of the forces generated by

the legs in contact with the ground.

Fig. S8. Parametric analysis of U-SLIP performance with respect to touch down angle and spring stiffness. Each

curve is obtained with a different value of equivalent linear spring stiffness from k =110N/m to k=660N/m. A)

Horizontal velocity vx of U-SLIP increases for smaller values of α and larger values of k. B) Conversely, cost of

transport CoT increases for higher values of α and smaller values of k. For simulations that reached stable periodic

hopping 𝐶𝑜𝑇 = 𝐸𝑙𝑜 − 𝐸𝑡𝑑 𝑚𝑔𝑣𝑥⁄ , where 𝐸𝑙𝑜 is the energy at lift off, 𝐸𝑡𝑑 is the energy at touch down and 𝑣𝑥 is the mean

horizontal velocity as in A.

In fig. S8 we reported a parametric analysis of U-SLIP that highlights the influence of touch down angle α

spring stiffness k on the horizontal velocity vx and cost of transport CoT of the system. Values of α resulting

in unstable behaviour are not shown. Velocity can be increased by selecting smaller values of α or higher

values of 𝑘. Conversely, CoT increases for higher values of α and smaller values of 𝑘. It is worth noticing

that the stiffness of each leg is fixed by design through the choice of kSEA, however, the equivalent stiffness

of SILVER2 depends on the number of legs in contact with the ground at each time. For this reason, in fig.

S8 we reported six values of 𝑘 = 𝑛110 N/m, corresponding to the stiffness of the equivalent virtual leg

obtained by hopping on n=1-6 legs. The results of simulations provide insights on the effects of inter-limbs

coordination on the performance of the robot, indeed hopping on six legs results in faster and more efficient

locomotion, whereas for example, hopping on three legs in a sort of dynamic alternating tripod may result in

slower and less efficient locomotion. Finally, the formula used for CoT in simulations is different from the

one used to estimate it on the real robot which also accounts for energy dissipated to power the

microcontroller and sensors and for this reason, no comparison can be made.

Table S2. Free parameters of omnidirectional walking gait

Equations of leg kinematics. The coordinates of the tip of the foot of Li xi, yi, zi can be expressed as a function

of the joint angles as follows:

0 2 3 1

0 2 3 1

2 3

cos cos cos sin

cos cos sin cos

sin sin

i i i i i i

i i i i i i

i i i i

x l l f l f t c l c

y l l f l f t c l c

z l f l f t

Equations of leg inverse kinematics. For a given position of the tip of the foot, the joint angles can be found

as follows:

𝜌𝑖 = √𝑥𝑖2 + 𝑦𝑖

2

𝛽𝑖 = 𝑎𝑡𝑎𝑛2(𝑦𝑖 , 𝑥𝑖)

𝛾𝑖 = 𝑎𝑡𝑎𝑛2(𝑙1, √𝜌𝑖2 − 𝑙1

2)

𝑐𝑖 = 𝛽𝑖 − 𝛾𝑖

𝑟𝑖 = 𝑥𝑖 cos 𝑐𝑖 + 𝑦𝑖 sin 𝑐𝑖 − 𝑙0

𝑎𝑖 = √𝑟𝑖2 + 𝑧𝑖

2

𝑓𝑖 = acos (𝑙2

2 + 𝑎𝑖2 − 𝑙3

2

2𝑙2𝑎𝑖) + 𝑎𝑡𝑎𝑛2(𝑧𝑖 , 𝑟𝑖)

𝑡𝑖 = π − acos (𝑙2

2 − 𝑎𝑖2 + 𝑙3

2

2𝑙2𝑙3)

Equations of leg trajectories. Subscript 𝑖 is not reported for the sake of readability. When the foot is in

contact with the ground (stance phase) the trajectory is a segment. When the foot is not in contact with the

ground, the trajectory is a hemi-ellipse. Here ns and nf are the number of points into which the trajectory is

quantized.

𝑥𝑠 = 𝑙𝑖𝑛𝑠𝑝𝑎𝑐𝑒(𝑥𝑐 −𝑠2

cos 𝛼 , 𝑥𝑐 +𝑠2

cos 𝛼 , 𝑛𝑠)

𝑦𝑠 = 𝑙𝑖𝑛𝑠𝑝𝑎𝑐𝑒(𝑦𝑐 −𝑠2

𝑠𝑖𝑛𝛼, 𝑦𝑐 +𝑠2

𝑠𝑖𝑛𝛼, 𝑛𝑠)

𝑧𝑠 = −ℎ 𝑜𝑛𝑒𝑠(1, 𝑛𝑠)

𝑥𝑓 = 𝑙𝑖𝑛𝑠𝑝𝑎𝑐𝑒(𝑥𝑐 +𝑠2

cos 𝛼 , 𝑥𝑐 −𝑠2

𝑐𝑜𝑠𝛼, 𝑛𝑓)

𝑦𝑓 = 𝑙𝑖𝑛𝑠𝑝𝑎𝑐𝑒(𝑦𝑐 +𝑠2

𝑠𝑖𝑛𝛼, 𝑦𝑐 −𝑠2

𝑠𝑖𝑛𝛼, 𝑛𝑓)

𝑧𝑓 = −(ℎ − ∆𝑧 sin (𝜋𝑡𝑓)

Where (xc,yc) are the coordinates of the midpoint of the segment followed by the foot during the stance

phase. For each leg (xc,yc) lies on the circle centered in OB with radius w (fig. SA).

Parameter Symbol

Walking direction α

Step length s

Gait period T

Gait width w

Gait height h

Ground clearance ∆z

Phase lag φ

Duty cycle β i

Both gaits were resilient to damages to the leg: in one situation, a foot detached from the leg, and the overall

behaviour was slightly affected by increasing the pitching motion of the robot, but without impairing

locomotion,

Data analysis

For each trials the following signals were extracted:

1. Current absorbed c(tc), [A];

2. Acceleration vector ax(ta), ay(ta), az(ta), [m/s2];

3. Yaw angle ψ(ta), [deg];

4. Pressure data p(tp), [mbar];

Each trial starts at ti and ends at te. Current sensor, pressure sensor and IMU all had different sampling

frequencies so that for each signal there is an associated time vector.

The vertical position z [mm] was obtained from the pressure data p, by taking as a reference the datasheet of

the pressure sensor, through the following conversion:

  10   refz p p

Where pref is the atmospheric pressure at sea level measured at the beginning of the trial.

The statistics reported in the main text were obtained from the signals using Matlab as follows:

1. Mean current absorbed c mean c ;

2. Max current absorbed max c ;

3. Max vertical acceleration max zabs a ;

4. 1 2 ) ( 1 2e iSlope P t P P t P , where z was fitted to a line using polyfit function.

The resulting angular coefficient and constant term are respectively P(1) and P(2);

5. Mean turning rate   max max / e imin t t ;

6. Mean hopping frequency / e if length apex t t , where apex is a vector with the local

maxima of z, obtained with findpeaks funtion;

7. Mean hopping height z mean dz , where dz apex lowest , where lowest is a vector of

the same dimension of apex with the local minima of z, obtained with findpeaks funtion.

Missions

Table S3. Data of the tests presented. Ground types are identified as in the paper. Cross identifies if a certain type of

action was performed during the specific mission. Immersion time is the overall time the robot was in water, while

operational is the time when robot was performing an action, and on-board signals were recorded.

Ground

type

Date [D M,

Y]

Average

depth [m]

Immersion

time [min]

Operational

time [min]

Hopping Walking Rotating Sampling

P 07/03/2019 2 120 35 X X

P 11/03/2019 2 120 33 X X X

R 20/03/2019 0,5 36 25 X

X

R 21/03/2019 0,5 80 28 X X X

R 09/04/2019 0,5 38 24 X

R 20/05/2019 0,6 40 31 X

S 04/06/2019 0,8 59 33 X

X X

R 07/06/2019 1,5 15 10

X

Omnidirectional walking

Fig. S9. Control of omnidirectional walking locomotion. A) Schematics showing body frame (origin OB), world

frame (origin Ow) and the frame of a generic leg (origin Oi) with an example of foot trajectory. B) Schematics of leg

frame with definition of leg angles ci, fi, ti, leg segments, and auxiliary axis ri for the definition of the coxa plane.

Segments l0 and l1 correspond to the L-shaped component connecting the shaft of the coxa motor to the canister of the

femur motor, l2 is the first link of the leg and l3 accounts for the lengths of the third link of the leg and the foot. C) Top

view of leg frame with coxa angle ci defining the coxa plane. D) Coxa plane frame with femur and tibia angles, fi and ti.

The omnidirectional walking gait allows the robot to translate in direction α without any rotation nor

displacements around z-axis according to the set of parameters reported in table S2. The control is based on

the inverse kinematics of the segmented leg. Equations of direct and inverse kinematics for the leg of

SILVER2 are reported below, with symbols defined in fig. S9. The contribution of the SEA is neglected. All

legs follow identical trajectories in their respective frame (except for mirror symmetries between the L1,L2,L6

and L3,L4,L5) with a phase lag of φi set by the operator.

The omnidirectional walking gait hereby presented is a very general implementation, and many different

locomotion strategies can be obtained through different parameters settings. For example, the classic

alternating tripod implemented on hexapod robots is obtained by setting the phase lags to φi=0, i=1,3,5,

φj=180°, j = 2,4,6 and β > 0.5. Additionally, the duration of the phase in which both tripods are in contact

with the ground can be increased by increasing β. Other inter-limb coordination strategies can be obtained by

tuning phase lags and duty cycle, however, in the present paper, only the alternating tripod was used due its

recognized stability and efficacy in hexapod robot locomotion. The locomotion speed in dictated by step

length s and gait period T as s/T, while the robot stance can be set through gait width w and gait height h.

Finally, the ground clearance controls how much the feet are lifted in the swing phases and higher values are

to be preferred on irregular terrain to reduce the risk of tripping.

D 08/06/2019 6 56 18 X

X X

R 25/06/2019 0,5 43 14

X

X

M 13/07/2019 11,5 48 22 X X X

R 23/07/2019 0,5 37 16

X

total 692 289

average 58 24

Missions were performed in several sites, in different period of the year (table S3). Mission time varied

significantly depending on requirements and setup operations, but generally lasted around 2 hours. This time

includes the time to transport SILVER2 on the boat or rubber boat, to reach the immersion site, to deploy and

to recover the robot, and eventually to return to the base. Team was composed of three members on average:

two on the boat, one acting as SILVER2 pilot, and a third one in water, in free diving.

Immersion time reports the period when the robot was actually immersed in water, while operational time

identifies the period when the robot was undertaking some actions and recording the ROS bag. Occasionally,

corrupted ROS bags were saved: these are not included in the reported time. Operational and Immersion time

may differ due to the pilot experience and mission requirements. The User interface, largely based on RQT

and service calls, is not effective for online control, thus when mission requirements changed during the

operation, or when additional movements or experiments where asked, the gait parameters have to be

manually changed.

Long exposure algorithm

Fig. S10. Reconstructed long-exposure images. A) Top left: initial frame, top right: last frame, bottom: cumulative

frame. B) Top left: initial frame, top right: last frame, bottom: cumulative frame.

We proved the stability of our passive station keeping strategy by the low value of acceleration data, and by

visual feedback from the cameras mounted on the robot. To visualize stability with respect to a changing and

hydrodynamic environment, long-exposure images  cI were reconstructed from frames I of the actual

videos with the following procedure:

~ 1d dcI k I I k I cI k

Where dI is a logical 2-D mask obtained from the difference on grayscale images of the current frame

gI k with the previous cumulated (long-exposure) image 1gcI k , as:

1d g gI I k cI k

With the value 1 for 8-bit unsigned integer images.

Example images of first, last and cumulative frame are reported in fig. S8 and fig. S9.

Movie S1. Hopping locomotion. View from outside water camera. The hopping locomotion of SILVER2

is shown from the pier. In this video the robot approaches a significantly high obstacle and negotiates it

without external intervention from the pilot.

Movie S2. Hopping locomotion. View from seabed and on-board cameras. The hopping locomotion is

shown from a camera placed in the rocky seabed (approximate depth of about 0.5m). The punting and

swimming phases are highlighted. The hopping locomotion is also shown from the robot’s point of view,

while hopping onto the sand dunes ground.

Movie S3. Walking locomotion. View from seabed camera. The walking locomotion is shown from a side

view. It is possible to notice how fishes are not disturbed by the gait, and they move all around the robot

Movie S4. Sea life. View from on-board camera. A few clips of sea life recorded from the camera of the

robot are reported, either while the robot was moving or when it was standing.

Movie S5. Approaching procedure. View from outside water and seabed camera. The approaching

procedure is shown with clips from outside water and from the seabed. The use of static locomotion allows

to get close to the target without the risk of accidentally hitting it.