Single range observability for cooperative underactuated underwater vehicles

The paper describes the single range observability issues related to a kinematics model of cooperating underwater vehicles. The paper extends previous results building on an augmented state technique allowing to reformulate the nonlinear observability problem in terms of a linear time varying one. As a result, all possible (globally) unobservable motions are characterized in terms of the systems initial conditions and velocity commands. These results are functional to the design of observers for the navigation of cooperating marine robots having an underactuated model as the one considered. The fundamental results reported are also illustrated by numerical simulations providing evidence of different motions generating the same output, i.e. lacking observability.