Towards a Framework for Tracking Multiple Targets: Hybrid Systems meets Computational Geometry

TL;DR

This paper presents a hybrid systems framework for tracking a mobile intruder in a polygonal environment using diagonal guards, providing conditions for effective tracking based on reachability analysis.

Contribution

It introduces a hybrid automaton model for guard-intruder tracking and derives necessary and sufficient conditions for successful tracking using critical regions.

Findings

Conditions for tracking with n/4 guards derived

Hybrid automaton model effectively captures tracking dynamics

Reachability analysis provides concrete tracking guarantees

Abstract

We investigate a variation of the art gallery problem in which a team of mobile guards tries to track an unpredictable intruder in a simply-connected polygonal environment. In this work, we use the deployment strategy for diagonal guards originally proposed in [1]. The guards are confined to move along the diagonals of a polygon and the intruder can move freely within the environment. We define critical regions to generate event-triggered strategies for the guards. We design a hybrid automaton based on the critical regions to model the tracking problem. Based on reachability analysis, we provide necessary and sufficient conditions for tracking in terms of the maximal controlled invariant set of the hybrid system. We express these conditions in terms of the critical curves to find sufficient conditions for n/4 guards to track the mobile intruder using the reachability analysis.