Orientation control of multiple underwater vehicles with symmetry-breaking potentials

We present a control strategy for stable orientation alignment of autonomous vehicles traveling together as a coordinated group in three-dimensional space. The control law derives from an artificial potential that depends only on the relative orientation of pairs of vehicles. The result is a controlled system of coupled rigid bodies with partially broken rotational symmetry. Semidirect product reduction theory is used to study the closed-loop dynamics, and the energy-Casimir method is applied to the reduced dynamics to prove stability of an alignment of vehicles translating in parallel along the same body axis. For clarity, the theory is described in detail for the case of two underwater vehicles, and the extension to an arbitrary number of underwater vehicles is summarized.