This paper presents a novel robust controller design for formation control of autonomous underwater vehicles (AUVs). We consider a nonlinear three-degree-of-freedom dynamic model for the horizontal motion of each AUV. By using the Jacobi transform, the horizontal dynamics of AUVs are explicitly expressed as dynamics for formation shape and formation center, and are further decoupled by feedback control. We treat the coupling terms as perturbations to the decoupled system. An H-infinity state feedback controller is designed to achieve robust stability of the closed loop formation and translation dynamics. By incorporating an orientation controller, the formation shape under control converges and the formation center tracks a desired trajectory simultaneously. Simulation results demonstrate the effectiveness of the controllers.

References

References
1.
Olfati-Saber
,
R.
,
Fax
,
J.
, and
Murray
,
R. M.
, 2007, “
Consensus and Cooperation in Networked Multi-Agent Systems
,”
Proc. IEEE
,
95
, pp.
215
233
.
2.
Porfiri
,
M.
,
Roberson
,
D.
, and
Stilwell
,
D. J.
, 2007, “
Tracking and Formation Control of Multiple Autonomous Agents: A Two-Level Consensus Approach
,”
Automatica
,
43
, pp.
1318
1328
.
3.
Lewis
,
M.
, and
Tan
,
K.-H.
, 1997, “
High Precision Formation Control of Mobile Robots Using Virtual Structures
,”
Auton. Rob.
,
4
, pp.
387
403
.
4.
Zhang
,
F.
, 2010, “
Geometric Cooperative Control of Particle Formations
,”
IEEE Trans. Autom. Control
,
55
(
3
), pp.
800
803
.
5.
Zhang
,
F.
, and
Leonard
,
N. E.
, 2010, “
Cooperative Control and Filtering for Cooperative Exploration
,”
IEEE Trans. Autom. Control
,
55
(
3
), pp.
650
663
.
6.
Fahimi
,
F.
, 2008, “
Full Formation Control for Autonomous Helicopter Groups
,”
Robotica
,
26
, pp.
143
156
.
7.
Hou
,
S.
, and
Cheah
,
C.
, 2009, “
PD Control Scheme for Formation Control of Multiple Autonomous Underwater Vehicles
,”
IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, pp.
356
361
.
8.
Choi
,
S.
,
Takashige
,
G.
, and
Yuh
,
J.
, 1994, “
Experimental Study on an Underwater Robotic Vehicle: ODIN
,”
Proceedings of the 1994 Symposium on Autonomous Underwater Vehicle Technology
, pp.
79
84
.
9.
Cui
,
R.
,
Ge
,
S. S.
,
How
,
B. V. E.
, and
Choob
,
Y. S.
, 2010, “
Leader–Follower Formation Control of Underactuated Autonomous Underwater Vehicles
,”
Ocean Eng.
,
37
, pp.
1491
1502
.
10.
Bφhaug
,
E.
,
Pavlov
,
A.
, and
Pettersen
,
K. Y.
, 2006, “
Cross-Track Formation Control of Underactuated Autonomous Underwater Vehicles
,”
Group Coordination and Cooperative Control
, pp.
35
54
,
Springer
,
Berlin
.
11.
Bφhaug
,
E.
,
Pavlov
,
A.
, and
Pettersen
,
K. Y.
, 2006, “
Cross-Track Formation Control of Underactuated Surface Vessels
,”
Proceedings of the 45th IEEE Conference on Decision and Control
, pp.
5955
5961
.
12.
Klein
,
D. J.
,
Lee
,
P.
,
Morgansen
,
K. A.
, and
Javidi
,
T.
, 2008, “
Integration of Communication and Control Using Discrete Time Kuramoto Models for Multivehicle Coordination Over Broadcast Networks
,”
IEEE J. Sel. Areas Commun.
,
26
(
4
), pp.
695
705
.
13.
Klein
,
D. J.
,
Bettale
,
P. K.
,
Triplett
,
B. I.
, and
Morgansen
,
K. A.
, 2008, “
Autonomous Underwater Multivehicle Control With Limited communication: Theory and Experiment
,”
Second IFAC Workshop Navigation, Guidance and Control of Underwater Vehicles
.
14.
Zhang
,
F.
,
Goldgeier
,
M.
, and
Krishnaprasad
,
P. S.
, 2003, “
Control of Small Formations Using Shape Coordinates
,”
Proceedings of the 2003 IEEE International Conference on Robotics and Automation
, pp.
14
19
.
15.
Belta
,
C.
, and
Kumar
,
V.
, 2004, “
Abstraction and Control for Groups of Robots
,”
IEEE Trans. Rob.
,
20
(
5
), pp.
865
875
.
16.
Yang
,
H.
, and
Zhang
,
F.
, 2010, “
Geometric Formation Control for Autonomous Underwater Vehicles
,”
2010 IEEE International Conference on Robotics and Automation
, pp.
4288
4293
.
17.
Yang
,
H.
, and
Zhang
,
F.
, 2011, “
Robust Control of Horizontal Formation Dynamics for Autonomous Underwater Vehicles
,”
2011 IEEE International Conference on Robotics and Automation
, pp.
3364
3369
.
18.
Okamoto
,
A.
,
Edwards
,
D.
, and
Anderson
,
M.
, 2004, “
Robust Control of a Platoon of Underwater Autonomous Vehicles
,”
Proceedings of Oceans’04 MTS/IEEE Techno-Ocean’04
, pp.
505
510
.
19.
Yang
,
E.
, and
Gu
,
D.
, 2007, “
Nonlinear Formation-Keeping and Mooring Control of Multiple Autonomous Underwater Vehicles
,”
IEEE/ASME Trans. Mechatron.
,
12
(
2
), pp.
164
178
.
20.
Feng
,
Z.
, and
Allen
,
R.
, 2004, “
Reduced Order H Control of an Autonomous Underwater Vehicle
,”
Control Eng. Pract.
,
12
, pp.
1511
1520
.
21.
Fossen
,
T. I.
, 1994,
Guidance and Control of Ocean Vehicles
,
1st ed.
,
John Wiley and Sons
,
Chichester
.
22.
Antonelli
,
G.
, 2006,
Underwater Robots-Motion and Force Control of Vehicle-Manipulator Systems
,
2 ed.
,
Springer-Verlag
,
Berlin
.
23.
Zhou
,
K.
, and
Doyle
,
J. C.
, 1997,
Essentials of Robust Control
,
1 ed.
,
Prentice Hall
,
NJ
.
24.
Reyhanoglu
,
M.
, 1996, “
Control and Stabilization of an Underactuated Surface Vessel
,”
Proceedings of the 35th Conference on Decision and Control
, pp.
2371
2376
.
You do not currently have access to this content.