Multiple autonomous surface vehicle motion planning for cooperative range-based underwater target localization

Abstract Range-based target localization is an important class of problems that arise in an increasing number of scientific and commercial missions at sea. Underwater target localization refers to the task of estimating the positions of fixed or moving underwater targets by using range measurements between the targets and one or more autonomous surface vehicles (ASVs), called trackers , undergoing trajectories that are known in real time. In this context, the trackers must execute sufficiently exciting maneuvers so as to maximize the range-based information available for multiple target localization. In this paper, adopting an estimation theoretical setting, we first propose a general methodology for tracker motion planning that results from maximizing the determinant of an appropriately defined Fisher information matrix (FIM) subject to inter-vehicle collision avoidance and vehicle maneuvering constraints. Then, for the single-target single-tracker problem (which is the dual problem of the classical single-beacon navigation problem), we provide a family of analytical solutions for the optimal tracker trajectories and complement the results with a practical experiment using a tracker when the target undergoes trajectories that are straight lines, pieces of arcs, or a combination thereof. In the methodology adopted for system implementation the tracker runs three key algorithms simultaneously, over a sliding time window: (i) tracker motion planning, (ii) tracker motion control, and (iii) target motion estimation based on range data acquired on-line. In order to simplify the types of trajectories that the tracker must undergo in the single target localization problem, we extend the above set-up to the case where the tracker works in cooperation with another vehicle, called companion , that can also measure ranges to the target and share this info with the tracker. The latter may have access to the position of the companion or, in some cases, only to the range between the two vehicles. We consider three different operating scenarios where the motion of the tracker is chosen so as to increase the accuracy with which the position of the target can be estimated. The scenarios reflect the situations where the motion of the companion vehicle satisfies one of three conditions: (i) the motion is not defined a priori and can also be optimized, (ii) the motion is fixed a priori and is known to the tracker (scenario in which the tracker benefits from the extra information acquired by the companion vehicle, which tracks a desired trajectory in the context of a separate, independent mission), and (iii) the motion is not known a priori and must be learned in the course of the mission. Simulation results illustrate the methodology adopted for cooperative target localization.