Single range observability for cooperative underactuated underwater vehicles

The paper addresses the single range observability analysis of a kinematics model of cooperating underactuated underwater vehicles. Teams of underwater vehicles that communicate with each other may be able to access and exchange their relative distances through, by example, acoustic signal time-of-flight measurements. Such relative distance measurements together with vehicle's attitude and velocity information may be used onboard to implement a navigation filter to estimate the vehicle's relative positions and orientations. A pre-requisite for successfully designing such navigation filters is to assess the systems observability properties. Contrary to the majority of existing studies on single range observability, the paper considers a more realistic underactuated kinematics model for slender body autonomous underwater vehicles rather than a simple point mass model. 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 within the class of interest. The fundamental results reported are also illustrated by numerical simulations providing evidence of different motions generating the same output, namely lacking observability.