IEEE Robotics & Automation Magazine - March 2015 - 93

(b)

Dynamical SyStemS laboratory of new
york UniverSity Polytechnic School of
engineering

(a)

(c)

Figure 7. The pitch performance for the robotic fish. The robotic fish can be set to (a) neutral pitch, (b) maximum downward pitch, or (c) maximum
upward pitch.

Semiautonomous Mode
The semiautonomous mode experiment is conducted
through a test in a laboratory setting at the New York University Polytechnic School of Engineering. The setup consists of a
120 cm # 120 cm # 20-cm water tank with each surface covered with white contact paper to provide a consistent background, similar to [34]. In this case, the water depth is maintained at 18 cm throughout the test and the Microsoft
LifeCam Web camera is placed 142 cm above the water surface so that the image resolution is 2.76 mm/pixel. The PID
controller is set with gains of K p = 5.25 (°/pixel),
K i = 7.5 # 10 -3 [°/(pixel # s)], K d = 7.5 # 10 -4 (°#s/pixel)
corresponding to the proportional, integral, and derivative
terms, respectively. The robotic fish is initially placed next to a
wall of the water tank and tasked with tracking a circular path
constructed by sequentially assigning 24 waypoints with a
radius of 96.8 cm through a MATLAB script. In this test, the
parameters are ( c 1 = 0.25, c 2 =-0.15, k = 4, f = 1.0 Hz ),
corresponding to one of the conditions considered in the
manual mode swimming tests.

Figure 6(b). The dependence of the speed on the tail-beat
amplitude is more evident at higher tail-beat frequencies,
whereby increasing the tail-beat amplitude from amplitude 1
to 3 produces an increase in the average speed of 7.4 cm/s for
a tail-beat frequency of 2 Hz, while only a modest increase of
0.1 cm/s is found for a tail-beat frequency of 0.25 Hz. This
result is in line with findings on other robotic fish designs,
whereby a speed increase can be achieved by increasing the
tail-beat frequency [18], [21] or tail-beat amplitude [37]. Furthermore, when the model parameters are set to ( c 1 = 0.25,
c 2 =-0.15, k = 4, f = 2 Hz ), the robotic fish exhibits an
average speed of 13.7 cm/s, or 0.30 body lengths per second
(BL/s), which is comparable with the speed of other robotic
fish designs based on caudal fin propulsion, ranging from
0.17-1.2 BL/s [38].
In the static pitch test, when the robotic fish is set to neutral buoyancy and the balance mass is at the center of its travel
length, the robotic fish is pitching neither upward nor downward, as shown in Figure 7(a). On the other hand, Figure 7(b)
shows that the robotic fish pitches downward at -17.4° with
respect to the horizontal plane when the balance mass is
shifted to the front. Similarly, Figure 7(c) shows that the

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Dynamical SyStemS laboratory of new york UniverSity Polytechnic School of
engineering

neutral buoyancy with maximum downward pitch and commanded to swim with the parameters ( c 1 = 0.25,
c 2 =-0.15, k = 4, f = 2 Hz ) corresponding to one of the
conditions considered in the swimming tests. The robotic fish
is recorded using the Canon camera as it dives from the surface of the pool to the bottom. The dive rate of the robotic fish
is calculated from the time the robotic fish takes to reach the
bottom of the pool, measured with a stopwatch.

Results
Manual Mode
The effect of varying the wave number on the robotic fish's
speed performance is shown in Figure 6(a). Therein, we find
that the terminal speed of the robotic fish increases as the
wave number increases. Notably, a low wave number indicates a motion similar to thunniform or carangiform, while a
high wave number indicates a motion similar to subcarangiform or anguilliform [31]. Thus, our results suggest that
when the tail beating is set to resemble subcarangiform or
anguilliform swimming, the robotic fish swims faster.
The effects of varying the tail-beat frequency and the
tail-beat amplitude on the robotic fish speed are shown in

Figure 8. A sequence of snapshots of the robotic fish during the
diving test.

march 2015

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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