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.

References

References
1.
Eriksen
,
C. C.
,
Osse
,
T. J.
,
Light
,
R.
,
Wen
,
R. D.
,
Lehmann
,
T. W.
,
Sabin
,
P. L.
,
Ballard
,
J. W.
, and
Chiodi
,
A. M.
,
2001
, “
Seaglider: A Long-Range Autonomous Underwater Vehicle for Oceanographic Research
,”
IEEE J. Oceanic Eng.
,
26
(
4
), pp.
424
436
.10.1109/48.972073
2.
Sherman
,
J.
,
Davis
,
R. E.
,
Owens
,
W. B.
, and
Valdes
,
J.
,
2001
, “
The Autonomous Underwater Glider “Spray,”
IEEE J. Oceanic Eng.
,
26
(
4
), pp.
437
446
.10.1109/48.972076
3.
Webb
,
D. C.
,
Simonetti
,
P. J.
, and
Jones
,
C. P.
,
2001
, “
Slocum: An Underwater Glider Propelled by Environmental Energy
,”
IEEE J. Oceanic Eng.
,
26
(
4
), pp.
447
452
.10.1109/48.972077
4.
Kato
,
N.
,
2000
, “
Control Performance in the Horizontal Plane of a Fish Robot With Mechanical Pectoral Fins
,”
IEEE J. Oceanic Eng.
,
25
(
1
), pp.
121
129
.10.1109/48.820744
5.
Low
,
K. H.
,
2006
, “
Locomotion and Depth Control of Robotic Fish With Modular Undulating Fins
,”
Int. J. Autom. Comput.
,
4
, pp.
348
357
.10.1007/s11633-006-0348-6
6.
Triantafyllou
,
M. S.
, and
Triantafyllou
,
G. S.
,
1995
, “
An Efficient Swimming Machine
,”
Sci. Am.
,
273
(
3
), pp.
64
70
.10.1038/scientificamerican0395-64
7.
Yu
,
J.
, and
Wang
,
L.
,
2005
, “
Parameter Optimization of Simplified Propulsive Model for Biomimetic Robot Fish
,”
Proceedings of the 2005 IEEE International Conference on Robotics and Automation
, pp.
3306
3311
.
8.
Hu
,
H.
,
Liu
,
J.
,
Dukes
,
I.
, and
Francis
,
G.
,
2006
, “
Design of 3D Swim Patterns for Autonomous Robotic Fish
,”
Proceedings of the 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems
, pp.
2406
2411
.
9.
Morgansen
,
K. A.
,
Triplett
,
B. I.
, and
Klein
,
D. J.
,
2007
, “
Geometric Methods for Modeling and Control of Free-Swimming Fin-Actuated Underwater Vehicles
,”
IEEE Trans. Rob.
,
23
(
6
), pp.
1184
1199
.10.1109/LED.2007.911625
10.
Chen
,
Z.
,
Shatara
,
S.
, and
Tan
,
X.
,
2010
, “
Modeling of Biomimetic Robotic Fish Propelled by an Ionic Polymer-Metal Composite Caudal Fin
,”
IEEE/ASME Trans. Mechatronics
,
15
(
3
), pp.
448
459
.10.1109/TMECH.2009.2027812
11.
Anderson
,
J.
, and
Chhabra
,
N.
,
2002
, “
Maneuvering and Stability Performance of a Robotic Tuna
,”
Integr. Comp. Biol.
,
42
(
1
), pp.
118
126
.10.1093/icb/42.1.118
12.
Yu
,
J.
,
Tan
,
M.
,
Wang
,
S.
, and
Chen
,
E.
,
2004
, “
Development of a Biomimetic Robotic Fish and Its Control Algorithm
,”
IEEE Trans. Syst., Man, Cybern., Part B
,
34
(
4
), pp.
1798
1810
.10.1109/TSMCB.2004.831151
13.
Epstein
,
M.
,
Colgate
,
J.
, and
MacIver
,
M.
,
2006
, “
Generating Thrust With a Biologically-Inspired Robotic Ribbon Fin
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
, pp.
2412
2417
.
14.
Kodati
,
P.
,
Hinkle
,
J.
,
Winn
,
A.
, and
Deng
,
X.
,
2008
, “
Microautonomous Robotic Ostraciiform (Marco): Hydrodynamics, Design, and Fabrication
,”
IEEE Trans. Rob.
,
24
(
1
), pp.
105
117
.10.1109/TRO.2008.915446
15.
McIsaac
,
K.
, and
Ostrowski
,
J.
,
2003
, “
Motion Planning for Anguilliform Locomotion
,”
IEEE Trans. Rob. Autom.
,
19
(
4
), pp.
637
652
.10.1109/TRA.2003.814495
16.
Saimek
,
S.
, and
Li
,
P.
,
2004
, “
Motion Planning and Control of a Swimming Machine
,”
Int. J. Robo. Res.
,
23
(
1
), pp.
27
53
.10.1177/0278364904038366
17.
Kelly
,
S.
,
1998
, “
The Mechanics and Control of Robotic Locomotion With Applications to Aquatic Vehicles
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
18.
Tan
,
X.
,
2011
, “
Autonomous Robotic Fish as Mobile Sensor Platforms: Challenges and Potential Solutions
,”
Marine Technol. Soc. J.
,
45
(
4
), pp.
31
40
.10.4031/MTSJ.45.4.2
19.
Graver
,
J. G.
,
2005
, “
Underwater Gliders: Dynamics, Control, and Design
,” Ph.D. thesis, Princeton University, Princeton, NJ.
20.
Bhatta
,
P.
,
2006
, “
Nonlinear Stability and Control of Gliding Vehicles
,” Ph.D. thesis, Princeton University, Princeton, NJ.
21.
Mahmoudian
,
N.
,
2009
, “
Efficient Motion Planning and Control for Underwater Gliders
,” Ph.D. thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
22.
Mahmoudian
,
N.
,
Geisbert
,
J.
, and
Woolsey
,
C.
,
2010
, “
Approximate Analytical Turning Conditions for Underwater Gliders: Implications for Motion Control and Path Planning
,”
IEEE J. Oceanic Eng.
,
35
(
1
), pp.
131
143
.10.1109/JOE.2009.2039655
23.
Zhang
,
S.
,
Yu
,
J.
,
Zhang
,
A.
, and
Zhang
,
F.
,
2011
, “
Steady Three Dimensional Gliding Motion of an Underwater Glider
,”
IEEE International Conference on Robotics and Automation
(
ICRA
), pp.
2392
2397
.10.1109/ICRA.2011.5979703
24.
Zhang
,
S.
,
Yu
,
J.
,
Zhang
,
A.
, and
Zhang
,
F.
,
2013
, “
Spiraling Motion of Underwater Gliders: Modeling, Analysis, and Experimental Results
,”
Ocean Eng.
,
60
, pp.
1
13
.10.1016/j.oceaneng.2012.12.023
25.
Zhang
,
F.
,
Zhang
,
F.
, and
Tan
,
X.
,
2012
, “
Steady Spiraling Motion of Gliding Robotic Fish
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), pp.
1754
1759
.10.1109/IROS.2012.6385860
26.
Schwartz
,
M.
,
2005
,
Encyclopedia of Coastal Science
, Vol.
24
,
Kluwer Academic Publishers
,
Norwell, MA
.
27.
Leonard
,
N. E.
, and
Graver
,
J. G.
,
2001
, “
Model-Based Feedback Control of Autonomous Underwater Gliders
,”
IEEE J. Oceanic Eng.
,
26
(
4
), pp.
633
645
.10.1109/48.972106
28.
Bhatta
,
P.
, and
Leonard
,
N.
,
2008
, “
Nonlinear Gliding Stability and Control for Vehicles With Hydrodynamic Forcing
,”
Automatica
,
44
(
5
), pp.
1240
1250
.10.1016/j.automatica.2007.10.006
29.
Zhang
,
F.
,
Thon
,
J.
,
Thon
,
C.
, and
Tan
,
X.
,
2012
, “
Miniature Underwater Glider: Design, Modeling, and Experimental Results
,”
Proceedings of the 2012 IEEE International Conference on Robotics and Automation
, pp.
4904
4910
.
30.
Greenwood
,
D. T.
,
1988
,
Principles of Dynamics
,
Prentice Hall
,
Englewood Cliffs, NJ
.
31.
Milgram
,
J.
,
2007
, “
Strip Theory for Underwater Vehicles in Water of Finite Depth
,”
J. Eng. Math.
,
58
(
1
), pp.
31
50
.10.1007/s10665-006-9101-y
32.
Panton
,
R. L.
,
2005
,
Incompressible Flow
,
Wiley
,
New York
.
33.
Anderson
,
J. D.
,
1998
,
Aircraft Performance and Design
,
McGraw-Hill
,
New York
.
34.
Seo
,
D.
,
Jo
,
G.
, and
Choi
,
H.
,
2008
, “
Pitching Control Simulations of an Underwater Glider Using CFD Analysis
,”
OCEANS 2008-MTS/IEEE Kobe Techno-Ocean
, pp.
1
5
.10.1109/OCEANSKOBE.2008.4530978
35.
Kelley
,
C.
,
2003
,
Solving Nonlinear Equations With Newton's Method
,
Society for Industrial Mathematics
,
Philadelphia, PA
.
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