On stabilization by means of the Energy-Casimir method

Recently a stabilization result on the angular velocity equations of the rigid body has been derived by means of the Energy-Casimir method. In this paper an alternative derivation of this result is given based on a topological condition on the level surfaces defined by the constants of motion. This condition is then reinterpreted, leading to a relaxed form of the Energy-Casimir theorem. The theorem is applied to the angular velocity equations of a rigid body.     

Stabilization of underwater vehicle dynamics with symmetry-breaking potentials

We show how to stabilize, in stages, arbitrary steady translations of an underwater vehicle with feedback that derives from a potential and deliberately breaks symmetry in the dynamics. First, rotational symmetry is broken to ensure stability in the momentum parameters. Then, translational symmetry is broken to prevent drift. Stability of the closed-loop system is proved using the energy-Casimir method. A resulting property of the control law is robustness to model parameter uncertainty.