在极简传感下实现不稳定的系统状态主动定位。
Active Localization of Unstable Systems with Coarse Information
- 结合集合估计与Voronoi分区控制，动态选择信息丰富区域。
- 理论保证初始状态不确定性指数收敛，适用于不稳定系统。
- 适合机器人定位中粗粒度感知场景，如关键帧、分割等。
我们研究了在粗粒度、单比特传感条件下不稳定系统的状态定位与控制问题。为理解此类极简反馈带来的根本限制，本文识别出在系统不稳定且测量极度稀疏时仍可恢复初始状态的充分条件。基于这些条件，提出一种主动定位算法，将集合估计器与基于Voronoi划分的控制策略相结合，可严格保证初始状态的估计精度，并确保智能体始终处于信息丰富的区域。在所推导条件下，该方法能保证初始状态不确定性的指数收缩，数值实验进一步验证了其有效性。研究成果为机器人定位中常见的粗粒度抽象（如关键帧、分割图、线特征）提供了理论支持。
原文摘要 · Abstract (English)
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.
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