Stabilizing underwater vehicle motion using internal rotors

As a case study of a particular control methodology and as a practical contribution in the area of underwater vehicle control, we consider the problem of stabilizing an underwater vehicle using internal rotors as actuators. The control design method comprises three steps. The first step involves shaping the kinetic energy of the conservative dynamics. For the underwater vehicle, the control term from this step may be interpreted as modifying the system inertia. In the second step, we design feedback dissipation using a Lyapunov function constructed in the first step. In the third step, we include a general model for the viscous force and moment on the vehicle and we show that these effects enhance stability. We first apply this method to a vehicle whose centers of buoyancy and gravity coincide and then to a vehicle with noncoincident centers of buoyancy and gravity.

[1]  Naomi Ehrich Leonard,et al.  Dynamics of the Kirchhoff equations I: coincident centers of gravity and buoyancy , 1998 .

[2]  Naomi Ehrich Leonard,et al.  Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping , 2001, IEEE Trans. Autom. Control..

[3]  Francesco Bullo,et al.  Stabilization of relative equilibria for underactuated systems on Riemannian manifolds , 2000, Autom..

[4]  R. Ortega,et al.  The matching conditions of controlled Lagrangians and IDA-passivity based control , 2002 .

[5]  Alan Weinstein,et al.  Geometric Models for Noncommutative Algebras , 1999 .

[6]  J. Marsden,et al.  Introduction to mechanics and symmetry , 1994 .

[7]  Romeo Ortega,et al.  Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment , 2002, IEEE Trans. Autom. Control..

[8]  Alessandro Astolfi,et al.  Asymptotic stabilization of selected equilibria of the underactuated Kirchhoff's equations , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[9]  Jerrold E. Marsden,et al.  Stabilization of relative equilibria , 2000, IEEE Trans. Autom. Control..

[10]  Naomi Ehrich Leonard,et al.  Underwater vehicle stabilization by internal rotors , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[11]  Bernard Etkin,et al.  Dynamics of Atmospheric Flight , 1972 .

[12]  Naomi Ehrich Leonard,et al.  Controlled Lagrangians and the stabilization of Euler–Poincaré mechanical systems , 2001 .

[13]  H. J.,et al.  Hydrodynamics , 1924, Nature.

[14]  Perinkulam S. Krishnaprasad,et al.  Lie-Poisson structures, dual-spin spacecraft and asymptotic stability , 1985 .

[15]  Naomi Ehrich Leonard,et al.  The equivalence of controlled lagrangian and controlled hamiltonian systems , 2002 .

[16]  Naomi Ehrich Leonard,et al.  Model-based feedback control of autonomous underwater gliders , 2001 .

[17]  Jerrold E. Marsden,et al.  Stabilization of rigid body dynamics by internal and external torques , 1992, Autom..

[18]  M. Spong,et al.  Stabilization of Underactuated Mechanical Systems Via Interconnection and Damping Assignment , 2000 .

[19]  Thor I. Fossen,et al.  Guidance and control of ocean vehicles , 1994 .

[20]  A. J. Schaft,et al.  Stabilization of Hamiltonian systems , 1986 .

[21]  J. Bellingham,et al.  Autonomous Oceanographic Sampling Networks , 1993 .

[22]  Naomi Ehrich Leonard,et al.  Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem , 2000, IEEE Trans. Autom. Control..

[23]  Naomi Ehrich Leonard,et al.  Modification of Hamiltonian Structure to Stabilize An Underwater Vehicle , 2000 .

[24]  Roger L. Simpson,et al.  Unsteady Crossflow Separation Location Measurements on a Maneuvering 6:1 Prolate Spheroid , 1998 .

[25]  Naomi Ehrich Leonard,et al.  Global asymptotic stabilization of an underwater vehicle using internal rotors , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[26]  Naomi Ehrich Leonard Stabilization of underwater vehicle dynamics with symmetry-breaking potentials , 1997 .

[27]  S. Hoerner Fluid-Dynamic Lift , 1985 .

[28]  Naomi Ehrich Leonard Stability of a bottom-heavy underwater vehicle , 1997, Autom..