Observability Analyses and Trajectory Planning for Tracking of an Underwater Robot using Empirical Gramians1

Abstract In marine robotics, estimation of the position and orientation of an underwater agent requires lots of research efforts. Especially the realization of robot teams has opened new horizons, allowing for relative navigation based on relative range measurements between the agents. Hence, there is the need for a better understanding of optimal sensor placement related to the positions of the robots relative to each other, and for improvement of observability, based on the concrete mission scenario. In this paper, we study the tracking of a moving target by a Reference Objects (RO) capable of performing acoustic range measurements. We employ the well-known theory of the Empirical Gramians, to evaluate different scenarios and their influence on the observability properties. Emphasis will be put on the computation of a trajectory for the RO that optimizes the observability criterion. We will compare our results with others found in literature that were derived by different procedures, to proof the usability of the Empirical Gramian approach for the area of underwater robotics.