Active Localization of Unstable Systems with Coarse Information

2026-02-05

AI Summary

This work proposes the first active localization and control method that guarantees exponential convergence of the initial state estimation error under the challenging conditions of single-bit coarse-grained feedback and unstable system dynamics. By integrating set-valued state estimation with a Voronoi-partition-based active sensing strategy, the approach steers the agent persistently into information-rich regions, enabling reliable recovery of the initial state of an unstable system even with extremely sparse measurements. Theoretical analysis establishes sufficient conditions for ensuring exponential convergence, and numerical experiments validate the efficacy of the proposed method. This study offers a novel paradigm for robot localization in resource-constrained scenarios where conventional high-resolution sensing is infeasible.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• active localization
• unstable systems
• coarse sensing
• single-bit feedback
• initial state recovery

Innovation

• active localization
• coarse sensing
• unstable systems
• set-based estimation
• Voronoi partition