Tracking Control for an Ellipsoidal Submarine Driven by Kirchhoff's Laws

In this paper, we study the control of an ellipsoid immersed in an infinite volume of ideal fluid. The dynamics of the uncontrolled body are given by Kirchhoff's laws. The control system is underactuated: one control is an acceleration along an axis of the ellipsoid and two are angular accelera...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2008-02, Vol.53 (1), p.339-349
Main Authors: Chambrion, T., Sigalotti, M.
Format: Article
Language:English
Subjects:
Acceleration
Attitude control
Automatic control
Backstepping
Control systems
Ellipsoids
Fluid dynamics
Force control
hydrodynamics
Ideal fluids
Kirchhoff law
Mathematics
Mechanical systems
Optimization and Control
position control
Solids
Stability
Submarines
underwater vehicle control
Underwater vehicles
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Summary:In this paper, we study the control of an ellipsoid immersed in an infinite volume of ideal fluid. The dynamics of the uncontrolled body are given by Kirchhoff's laws. The control system is underactuated: one control is an acceleration along an axis of the ellipsoid and two are angular accelerations around the other two axes. By adopting a backstepping viewpoint, we prove that the position and the attitude of the solid can be forced to approximately follow any given path, using fast-oscillating controls. Moreover, we prove that the controlled mechanical system (which includes the impulses) is completely controllable in an arbitrary small time.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2007.914958