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Research Papers

Dynamic Modeling of Robotic Fish With a Base-Actuated Flexible Tail

[+] Author and Article Information
Jianxun Wang

Department of Electrical and
Computer Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: wangji19@msu.edu

Philip K. McKinley

Department of Computer Science
and Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: mckinley@cse.msu.edu

Xiaobo Tan

Department of Electrical and
Computer Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: xbtan@msu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 8, 2013; final manuscript received July 17, 2014; published online August 28, 2014. Assoc. Editor: Evangelos Papadopoulos.

J. Dyn. Sys., Meas., Control 137(1), 011004 (Aug 28, 2014) (11 pages) Paper No: DS-13-1266; doi: 10.1115/1.4028056 History: Received July 08, 2013; Revised July 17, 2014

In this paper, we develop a new dynamic model for a robotic fish propelled by a flexible tail actuated at the base. The tail is modeled by multiple rigid segments connected in series through rotational springs and dampers, and the hydrodynamic force on each segment is evaluated using Lighthill's large-amplitude elongated-body theory. For comparison, we also construct a model using linear beam theory to capture the beam dynamics. To assess the accuracy of the models, we conducted experiments with a free-swimming robotic fish. The results show that the two models have almost identical predictions when the tail undergoes small deformation, but only the proposed multisegment model matches the experimental measurement closely for all tail motions, demonstrating its promise in the optimization and control of tail-actuated robotic fish.

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Figures

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Fig. 1

Schematic representation of the robotic fish in planar motion

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Fig. 2

Illustration of the coordinate system for flexible tail (top view)

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Fig. 3

Passive flexible tail modeled by Euler–Bernoulli linear beam approach

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Fig. 4

Passive flexible tail modeled by multiple rigid segments

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Fig. 5

A free-swimming robotic fish prototype used for model validation

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Fig. 6

Experimental setup for measuring the Young's modulus of the flexible tail

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Fig. 7

Experimental results for measuring the Young's modulus of the flexible tail

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Fig. 8

Displacement of the tail tip generated by the model using different number of rigid segments

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Fig. 9

Computation time needed to simulate the model using different numbers of rigid segments

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Fig. 10

Comparison between model predictions and experimental measurement of the speed versus tail-beat frequency. The amplitude is fixed at 13.6 deg

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Fig. 11

Comparison between model predictions and experimental measurement of the speed versus tail-beat frequency, with the new tail. The amplitude is fixed at 13.6 deg

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Fig. 12

Comparison between multisegment model predictions and experimental measurement for forward swimming (including transients): (a) time trajectory of X-coordinate of the robot; (b) time trajectory of the Y-coordinate of the robot; (c) path of the robot in the XY-plane. For both the experiment and simulations, the amplitude and frequency of the tail beat are fixed at 13.6 deg and 0.9 Hz, respectively.

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Fig. 13

Experimental setup to capture the dynamic shape of a flexible tail actuated at the base (top view).

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Fig. 14

Comparison between experimental measurement of the time-dependent tail shape with model predictions. The tail beats at 0.4 Hz with 0 deg bias and 14 deg amplitude. The solid line, dashed line with circles and the dashed-dotted line imply the experimental measurement, predictions from multisegment model and Euler–Bernoulli beam model, respectively.

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Fig. 15

Comparison between experimental measurement of the time-dependent tail shape with model predictions. The tail beats at 0.9 Hz with 0 deg bias and 13.6 deg amplitude. The solid line, dashed line with circles, and the dashed-dotted line imply the experimental measurement, predictions from multisegment model and Euler–Bernoulli beam model, respectively.

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