A null-space-based behavioral approach to single range underwater positioning

This paper addresses the problem of driving an underwater vehicle to a desired position while optimizing the performance of a single-range based localization system. Indeed, the performance of single-range based localization techniques is strongly dependent on the vehicle's motion that needs to be sufficiently rich to yield a good measure of observability. We present a prioritized task oriented technique to combine a point-to-point guidance task with an observability optimization task. In particular, the minimum singular value of the Fisher Information Matrix is adopted as the observability metric. Task prioritization is achieved through a null-space-based projection technique that is also combined with a saturation management algorithm to cope with velocity command saturations. The stability of the resulting control law is analysed following a Lyapunov-based approach. Robustness against uncertainty in the initial position of the vehicle is also handled resorting to a procedure that maximises the minimum (worst-case) observability metric. Numerical simulations are reported confirming the effectiveness of the proposed strategy.