## Orientation Control of Multiple Underwater Vehicles

### Troy R. Smith, Heinz Hanssmann and Naomi Ehrich Leonard

*Proc. of the 40th IEEE Conference on Decision and Control*,
Orlando, FL, December 2001, 4598--4603.
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.