Active Localization of Unstable Systems with Coarse Information

TL;DR

This paper develops an active localization method for unstable systems using minimal, single-bit sensing, providing conditions for initial state recovery and guaranteeing exponential uncertainty reduction.

Contribution

It introduces a novel set-based estimator combined with Voronoi-based control for localization under coarse, sparse measurements, with theoretical guarantees.

Findings

Guarantees exponential contraction of initial-state uncertainty.

Provides conditions for initial state recovery despite instability.

Supports results with numerical experiments.

Abstract

We study localization and control for unstable systems under coarse, single-bit sensing. Motivated by understanding the fundamental limitations imposed by such minimal feedback, we identify sufficient conditions under which the initial state can be recovered despite instability and extremely sparse measurements. Building on these conditions, we develop an active localization algorithm that integrates a set-based estimator with a control strategy derived from Voronoi partitions, which provably estimates the initial state while ensuring the agent remains in informative regions. Under the derived conditions, the proposed approach guarantees exponential contraction of the initial-state uncertainty, and the result is further supported by numerical experiments. These findings can offer theoretical insight into localization in robotics, where sensing is often limited to coarse abstractions such as keyframes, segmentations, or line-based features.