Energy shaping and dissipation: Underwater vehicle stabilization using internal rotors

This dissertation concerns nonlinear feedback stabilization of mechanical systems using energy-based methods. Nonlinear techniques are appealing because they can yield large regions of attraction for feedback-stabilized equilibria. Energy-based methods are particularly attractive for mechanical systems because these methods preserve a physical view of a system's dynamics and because they yield Lyapunov functions. For conservative systems, proof of stability typically requires the existence of a Lyapunov function. For systems with damping, Lyapunov functions can be used to design feedback dissipation to ensure or enhance asymptotic stability and to obtain more global conclusions.; Both as a case study of a particular control methodology and as a practical contribution in the area of underwater vehicle control, we consider stabilization of an underwater vehicle using internal rotors as actuators. The methodology used to develop stabilizing control laws consists of three steps. The first step involves shaping the kinetic energy of the conservative dynamics. For the underwater vehicle, the control term in this step may be interpreted as modifying the system inertia. In the second step, feedback dissipation is designed based on a Lyapunov function developed in the first step. In the third step, it is verified that the effect of external damping due to viscous forces does not destroy the stability results. This method is applied first to a vehicle whose centers of gravity and buoyancy coincide and then to a vehicle with noncoincident centers of gravity and buoyancy.; The method of controlled Lagrangians, developed in recent years, is a generalization of the idea of kinetic energy shaping. The method applies to underactuated mechanical systems (systems with more degrees of freedom than independent actuators). Motivated by the results of the investigation into the effect of external damping on an underwater vehicle with internal rotors, we study the effect of damping on more general systems which have been stabilized, in the conservative approximation, using the method of controlled Lagrangians. A significant result of this inquiry is that, for certain classes of systems, damping in the unactuated directions enhances stability by driving the unactuated dynamics to their desired equilibrium value. Damping in the controlled directions may be detrimental but can be directly compensated for through feedback. Thus, with an appropriate choice of feedback dissipation, these systems may be asymptotically stabilized even in the presence of physical damping.