通过占用地图估计中退化局部保证下的融合实现有限样本共形覆盖恢复
Finite-Sample Conformal Coverage Recovery via Fusion under Degraded Local Guarantees in Occupancy Map Estimation
AI总结：
研究针对多机器人环境映射中高斯过程占用映射缺乏有限样本预测保证、共形预测局部保证退化的问题，开发分布式融合算法，通过机器人交换e值及接收器融合，实现恢复目标覆盖水平，提升地图效率。
AI中文摘要：
准确可靠的环境映射是多机器人自主的基本要求。高斯过程占用映射等连续映射技术缺乏有限样本预测可靠性保证。共形预测可为每个机器人的局部地图提供无分布覆盖保证，但实际中该局部保证会退化。本文在给定这些退化的每个智能体保证的情况下，开发了一种分布式融合算法，机器人仅与邻居交换轻量级标量e值，接收器使用每个邻域的误覆盖预算和不确定性衰减融合算子进行融合。证明了融合后的集值地图能恢复目标用户指定的覆盖水平，模拟实验表明融合预测器能可靠达到理论覆盖边界，更密集的通信拓扑可提高地图效率。
英文摘要：
Accurate and reliable environmental mapping is a fundamental requirement for multi-robot autonomy. While continuous mapping techniques like Gaussian Process Occupancy Mapping (GPOM) provide rich spatial correlation and uncertainty estimates, they lack formal, finite-sample guarantees on their predictive reliability. Conformal prediction can equip each robot's local map with a distribution-free coverage guarantee, but this local guarantee degrades in practice: temporal correlation along a robot's trajectory breaks the exchangeability on which conformal calibration relies, and each robot observes only a spatially limited, non-uniform portion of the environment. Taking these degraded per-agent guarantees as given, we develop a distributed fusion algorithm that recovers the desired coverage across the team. Robots exchange only lightweight scalar e-values with their neighbors, and a receiver fuses them using a per-neighborhood miscoverage budget and an uncertainty-attenuated fusion operator. We prove that the fused set-valued map recovers the target user-specified coverage level regardless of the communication graph topology or the underlying sensor noise distribution. However, a drawback is that wherever the fused evidence is insufficient, the map declines to commit and returns both labels (free and occupied), leaving a significant fraction of the domain unclassified rather than thresholded into a single decision. Simulated multi-agent mapping experiments demonstrate that the fused predictor reliably meets its theoretical coverage bounds, and illustrate that denser communication topologies significantly enhance map efficiency by shrinking this unclassified fraction.
