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Research Papers

Tail-Enabled Spiraling Maneuver for Gliding Robotic Fish

[+] Author and Article Information
Feitian Zhang

Smart Microsystems Lab,
Department of Electrical
and Computer Engineering,
Michigan State University,
East Lansing, MI 48823
e-mail: zhangzft@gmail.com

Fumin Zhang

School of Electrical and Computer Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: fumin@gatech.edu

Xiaobo Tan

Smart Microsystems Lab,
Department of Electrical
and Computer Engineering,
Michigan State University,
East Lansing, MI 48823
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 May 5, 2013; final manuscript received February 20, 2014; published online May 8, 2014. Assoc. Editor: Alexander Leonessa.

J. Dyn. Sys., Meas., Control 136(4), 041028 (May 08, 2014) (8 pages) Paper No: DS-13-1184; doi: 10.1115/1.4026965 History: Received May 05, 2013; Revised February 20, 2014

Gliding robotic fish, a new type of underwater robot, combines both strengths of underwater gliders and robotic fish, featuring long operation duration and high maneuverability. In this paper, we present both analytical and experimental results on a novel gliding motion, tail-enabled three-dimensional (3D) spiraling, which is well suited for sampling a water column. A dynamic model of a gliding robotic fish with a deflected tail is first established. The equations for the relative equilibria corresponding to steady-state spiraling are derived and then solved recursively using Newton's method. The region of convergence for Newton's method is examined numerically. We then establish the local asymptotic stability of the computed equilibria through Jacobian analysis and further numerically explore the basins of attraction. Experiments have been conducted on a fish-shaped miniature underwater glider with a deflected tail, where a gliding-induced 3D spiraling maneuver is confirmed. Furthermore, consistent with model predictions, experimental results have shown that the achievable turning radius of the spiraling can be as small as less than 0.4 m, demonstrating the high maneuverability.

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Figures

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Fig. 2

Illustration of the reference frames and hydrodynamic forces

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Fig. 1

The mass distribution of the gliding robotic fish (side view)

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Fig. 8

Spiraling radius with respect to the tail angle, with fixed movable mass displacement of 0.5 cm and fixed excess mass of 30 g

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Fig. 9

Spiraling radius with respect to the excess mass, with fixed movable mass displacement of 0.5 cm and fixed tail angle of 45 deg

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Fig. 3

Contours of the static pressure with tail angle at 45 deg

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Fig. 5

Convergence time in seconds for spiraling dynamics with respect to different initial values of states in roll angle φ, pitch angle θ, and translational velocity v1 along the Oxb direction, for the control inputs of rp = 5 mm,m0 = 30 g, and δ = 45 deg. The corresponding equilibrium state values are θ = -42.1281 deg,φ = -34.2830 deg, and v1 = 0.2801 m/s. (a) Display in orthogonal slice planes and (b) display in a half sphere surface.

Grahic Jump Location
Fig. 4

Convergence test results for Newton's method with respect to initial conditions. Color yellow (light) means that convergence to the steady-state spiraling equilibrium is achievable with the corresponding initial values; color blue (dark) means that there is no convergent solution or the convergent solution is not at the steady-state spiraling equilibrium. In the test, the used set of control inputs is rp = 5 mm,m0 = 30 g,δ = 45 deg; and the corresponding equilibrium state values are θ = -42.1281 deg,φ = -34.2830 deg,ω3i = 0.4229 rad/s,V = 0.2809 m/s,α = -0.9014 deg,β = 4.2414  deg. (a) Convergence with respect to the roll angle, pitch angle, and spiraling speed; (b) convergence with respect to the angle of attack, sideslip angle, and angular speed.

Grahic Jump Location
Fig. 6

Convergence time in seconds for spiraling dynamics with respect to different initial values of states in angular velocities, for the control inputs of rp = 5 mm,m0 = 30 g, and δ = 45 deg, displayed in orthogonal slice planes. The corresponding equilibrium state values are ω1 = 0.2837 rad/s,ω2 = -0.1767 rad/s, and ω3 = 0.2592 rad/s.

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Fig. 7

Snap shots of the robot spiraling in the experiment tank. A full video of this maneuver can be accessed at2

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