Stabilization of steady motions of an underwater vehicle

We show how to stabilize underwater vehicle dynamics for a six degree-of-freedom vehicle modeled as a neutrally buoyant, submerged rigid body in an ideal fluid. Stabilization is achieved by applying external torques to the vehicle that mimic the kind of torques that are naturally induced when the vehicle´s center of gravity is lower than its center of buoyancy. This approach makes the controlled system resemble the uncontrolled system in structure, and we can mimic our analysis of open-loop stability of a bottom-heavy underwater vehicle to study closed-loop stability of the controlled vehicle. We show that the closed-loop system has Lie-Poisson form and prove closed-loop stability using extensions to the energy-Casimir method. A resulting property of the control law is robustness to model parameter uncertainty