IEEE Robotics & Automation Magazine - September 2019 - 29

Spanwise Length/Fin-Base Length

Schematic of
the Cartilage
x
Chordwise

O
z
Fin Base
y

1
0.8
0.6
0.4
0.2
0

0.2
0.4
0.6
0.8
1
Chordwise Length/Fin-Base Length
(b)

Fin-Tip Part

NACA 0012

Fin-Tip Part

Fin Middle

Spanwise

NACA 0015
Fin Middle

Midbody
NACA 0020

(a)

Midbody
(c)
Figure 2. The (a) shape and structures of a cownose ray [19], [20]. (b) The skeletal structure and dorsal shape extraction of a cownose
ray and (c) the shapes of the chordwise sections.

length of the pectoral foil along the chordwise direction
involved in the flapping movements.
The spatial shape of the pectoral foil is another obvious
characteristic that affects propulsion performance. Referring
to the biologic anatomy of the cownose ray, as shown in Figure 2(b), cross sections along the chordwise direction of the
cownose ray's pectoral foil can be approximated to a series of
airfoil shapes developed by the National Advisory Committee
for Aeronautics (NACA), from NACA0020 to NACA0012,
with gradient changes from midbody to the fin tip.
Using visual-processing software developed by our team,
we extracted the movement rules of the cownose ray's special "mobuliform" motion in different swimming modes.
The fin tip, fin base, leading edge, and trailing edge of the
sample cownose ray's pectoral foil were selected as the key
points or lines. Figure 3(a) shows snapshots of a sample
cownose ray's typical flapping cycle in a linear-forward
swim. The cownose ray's key movement features can be
summarized as follows:
● The pectoral foil flaps with frequencies varying from 0.4 to
1.2 Hz, according to the swim conditions. Frequencies
between 0.5 and 0.6 Hz are typically used in linear-forward
swim modes.
● Foil deformation in flapping movements is consistent
with sinusoidal discipline, especially along the chordwise direction.

There are roughly 0.4 driving waves passing on the pectoral foil along the chordwise direction.
● The flapping amplitude of the cownose ray's pectoral foil
is as large as half of the fin-base length.
To handle complicated underwater environments, the cownose ray
When confronted with
has many different swim
modes, including linearobstacles such as reefs,
forward swim, turn, upfloating, and div ing .
seaweed, or predators,
Series snapshots of some
of these modes are shown
cownose rays will merge
in Figure 3(a)-(c). When
confronted with obstacles
different swimming
such as reefs, seaweed, or
predators, cownose rays
postures to realize a quick
will merge different swimming postures to realize
turn or a rolling swim.
a quick turn or a rolling
swim. All the cownose
ray's required swimming
modes are made possible by its large, flat pectoral foils and
its flexible body, which result from the complex biological
structures of the ray's flexible cartilage, muscles, and body.
These natural characteristics, however, are too complicated
●

SEPTEMBER 2019

IEEE ROBOTICS & AUTOMATION MAGAZINE

IEEE Robotics & Automation Magazine - September 2019

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