Biomimetic Design of a Soft Robotic Fish for High Speed Locomotion
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active segment and the passive head, as is shown in Fig. 5. Both the compliant
and active segments consist of multiple sub-segments to achieve sufficiently fluent motion. The passive compliant segment and active segment consist of 4 and
5 sub-segments respectively, with a length of 30 mm each. The rotation of the
active segment is modeled to be constant over all sub-segments and varies over
time following a sinusoidal function with a frequency of 1.59 Hz and amplitude
of 5.73
◦ for each sub-segment.
The passive compliant segments were modeled having a consistent spring
stiffness of 0.001 Nm/deg and a damping coefficient which was gradually reduced
along the compliant segmentation from 0.005 Nm(deg/s) to 0.00075 Nm(deg/s)
to simulate the decrease in surface area interacting with the surrounding water.
The body length was varied between 73.34 mm and 880 mm, corresponding
to a ratio of head mass to total mass of 0.3 and 0.8 respectively. The distance
between the centre of the caudal fin and the centre of rotation is used to express
the maneuverability of the fish. The larger this distance is, the less maneuverable
the fish is. The head sway stability is expressed as the angle between the passive
head and the neutral line (indicated in blue in Fig. 5). A larger angle corresponds
to a fish with lower sway stability. Lower sway stability leads to less efficient
swimming, as energy is lost when the head is not aligned in the swimming
direction. The results are shown in Fig. 6. A clear trade-off can be found between
the maneuverability and sway stability. The tuna is an efficient long-distance
swimmer with less need for quick maneuvers. Therefore, it has a relatively long
body. We chose a similar length distribution for our robotic fish design (see
Fig. 3(c)). At the same time, the relatively high length of the passive head
provides space for the motor and gearbox.
2.4 Body Shape and Pectoral, Anal, and Dorsal Fins
The body shape and the pectoral, anal, and dorsal fins of the fish greatly influence its stability and sway (see Fig. 3(d)). The vertically compressed elliptical
body shape is inspired by the tunafish, and can be found in a large portion of fish
species. Although the shape is not intuitive from a hydrodynamical point of view
as minimizing drag around a given volume would result in a body of revolution,
the advantage of this adaptation is the damping of the larger side surface area
minimizing swaying motion during sideways oscillation of the tail [8]. Moreover,
the shape also reduces rolling and creates a larger distance between the center
of rotation and dorsal and anal fins, preventing change in vertical angle [15]. In
fast swimming fish e.g. marlin, sailfish and mahimahi a large side surface area at
a distance as far as possible from the center line of yaw rotation (defined by the
line between the center of mass and buoyancy) is also a common adaptation.
2.5 Caudal Fin Shape
The shape of caudal fin is critical for high-speed and efficient swimming. The
caudal fin is illustrated in Fig. 3(d). When flapping the fin back and forth through
the active and passive compliant tail, a pressure difference is generated between
371
active segment and the passive head, as is shown in Fig. 5. Both the compliant
and active segments consist of multiple sub-segments to achieve sufficiently fluent motion. The passive compliant segment and active segment consist of 4 and
5 sub-segments respectively, with a length of 30 mm each. The rotation of the
active segment is modeled to be constant over all sub-segments and varies over
time following a sinusoidal function with a frequency of 1.59 Hz and amplitude
of 5.73
◦ for each sub-segment.
The passive compliant segments were modeled having a consistent spring
stiffness of 0.001 Nm/deg and a damping coefficient which was gradually reduced
along the compliant segmentation from 0.005 Nm(deg/s) to 0.00075 Nm(deg/s)
to simulate the decrease in surface area interacting with the surrounding water.
The body length was varied between 73.34 mm and 880 mm, corresponding
to a ratio of head mass to total mass of 0.3 and 0.8 respectively. The distance
between the centre of the caudal fin and the centre of rotation is used to express
the maneuverability of the fish. The larger this distance is, the less maneuverable
the fish is. The head sway stability is expressed as the angle between the passive
head and the neutral line (indicated in blue in Fig. 5). A larger angle corresponds
to a fish with lower sway stability. Lower sway stability leads to less efficient
swimming, as energy is lost when the head is not aligned in the swimming
direction. The results are shown in Fig. 6. A clear trade-off can be found between
the maneuverability and sway stability. The tuna is an efficient long-distance
swimmer with less need for quick maneuvers. Therefore, it has a relatively long
body. We chose a similar length distribution for our robotic fish design (see
Fig. 3(c)). At the same time, the relatively high length of the passive head
provides space for the motor and gearbox.
2.4 Body Shape and Pectoral, Anal, and Dorsal Fins
The body shape and the pectoral, anal, and dorsal fins of the fish greatly influence its stability and sway (see Fig. 3(d)). The vertically compressed elliptical
body shape is inspired by the tunafish, and can be found in a large portion of fish
species. Although the shape is not intuitive from a hydrodynamical point of view
as minimizing drag around a given volume would result in a body of revolution,
the advantage of this adaptation is the damping of the larger side surface area
minimizing swaying motion during sideways oscillation of the tail [8]. Moreover,
the shape also reduces rolling and creates a larger distance between the center
of rotation and dorsal and anal fins, preventing change in vertical angle [15]. In
fast swimming fish e.g. marlin, sailfish and mahimahi a large side surface area at
a distance as far as possible from the center line of yaw rotation (defined by the
line between the center of mass and buoyancy) is also a common adaptation.
2.5 Caudal Fin Shape
The shape of caudal fin is critical for high-speed and efficient swimming. The
caudal fin is illustrated in Fig. 3(d). When flapping the fin back and forth through
the active and passive compliant tail, a pressure difference is generated between