A stochastic hybrid control law for a localization task based on active sensing

A localization task by a mobile agent is considered, where the sensing and the motion actions are performed exclusively with respect to each other, meaning that sensing the target is not available during the agent movement. To formalize this scenario the system is modeled on the 1D line and a control law with a timer and a logic variable, to allow switching between the operating modes of sensing the target and moving towards it, is designed. A Stochastic Hybrid System in standard form is obtained, satisfying the Stochastic Hybrid Basic conditions, and the overall closed-loop system behavior is then studied. An extension to the 2D plane is also proposed and its behavior is analyzed. Finally, the 2D control law is tested for a simulated Search & Rescue task in an unknown indoor environment under some simplifying hypotheses.