Online Interval Depth Localization of an Underwater Robot with Ballast

Abstract

This paper presents an efficient online method to simulate a dynamical system with interval uncertainties. These uncertainties can be either on the initial state vector, on the time-dependent inputs, or on the evolution function. Compared to other techniques used for the guaranteed integration of differential inclusion, the presented approach is online and requires a small and fixed number of operations at each sampling time. An illustration related to underwater robotics will be provided. The application involves a robot with a ballast that can move from the surface to the sea floor. We would like to guarantee that the robot will reach a given depth at a given time.