Advances on a null-space-based approach to range-only underwater steering and positioning

This paper addresses the problem of optimal AUV (Autonomous Underwater Vehicle) motion generation to maximise the range-related information available for vehicle positioning subject to the condition that the overall trajectory will drive the vehicle from an initial to a final target point. To this end we resort to a task prioritisation technique using a nullspace-based projection approach. This allows decoupling the motion objectives from those of maximising an observability based criterion. Preliminary results on this topic have been presented in previous work. Here, a careful singularity analysis of the null space projector operator is formalized and discussed. A saturation management algorithm that copes with vehicle velocity command saturation by properly assigning the velocity vector to the two tasks is also proposed. The stability of the resulting control law is analysed using a Lyapunov-based approach. Robustness against uncertainty in the initial position of the vehicle is also handled by comparing two alternative procedures: the first aims at optimising the worst case scenario, that is, maximising the minimum of the observability metric inside the uncertainty region; the second, a novel approach, aims at optimizing the most frequent observability metric inside the uncertainty region. The work is completed by combining the guidance algorithm with an observer for the estimation of the vehicle's position and its associated uncertainty. Results of numerical simulations show the effectiveness of the proposed strategy.