为3D-3D SLAM设计可证明的不确定性量化方法，确保结果在严格数学保证范围内。
Provably Guaranteed Polytopic Uncertainty Quantification for SLAM
- 用多面体表示不确定性集，实现从建图到位姿跟踪的全程可证明包含。
- 在真实与仿真数据上验证，不确定性边界始终覆盖真实值，且计算高效。
- 适合需要高可靠性保障的自动驾驶、机器人导航等安全关键场景。
在安全关键型机器人应用中，感知环节的不确定性量化（UQ）至关重要。现有方法或缺乏形式化包含保证，或依赖严苛建模假设，或仅关注位姿估计而非完整的SLAM流程。本文提出针对基于3D-3D特征点的SLAM的可证明保证的不确定性量化算法。算法由三个基础模块构成：前向不确定性量化用于建图，后向不确定性量化用于位姿跟踪，以及位姿复合模块。每个模块生成一个经认证的不确定性集合；当输入不确定性界为确定性时，输出集合继承确定性保证，即严格包含真实位姿与特征点。具体地，采用多面体表示不确定性集，支持高效计算并统一处理位姿不确定性。为提升实用性，引入保形预测，基于数据校准测量不确定性至指定置信水平。仿真与实验表明，所提算法兼具强理论保证与实际可用性。代码已开源：https://github.com/LIAS-CUHKSZ/Polytopic-SLAM-Uncertainty-Quantification。
原文摘要 · Abstract (English)
In safety-critical robotics applications, guaranteed and practical uncertainty quantification (UQ) in perception is vital. Many existing works either offer no formal containment guarantee, rely on restrictive modeling assumptions, or focus only on pose estimation rather than a complete SLAM pipeline. This paper presents provably guaranteed UQ algorithms for 3D-3D landmark-based SLAM. The algorithms consist of three basic UQ modules: forward UQ for mapping, backward UQ for pose tracking, and pose compound. Each module produces a certified uncertainty set; when the input uncertainty bounds are deterministic, the output sets inherit deterministic guarantees, i.e., they provably contain the true poses and landmarks. Specifically, we use polytopes to represent uncertainty sets, enabling tractable computations and a unified treatment of pose uncertainty. To enhance algorithms' practical usability, we incorporate conformal prediction to calibrate measurement uncertainty from data with prescribed probability. Simulations and experiments demonstrate that the proposed algorithms provide both strong theoretical guarantees and practical usability. The code is open-sourced at https://github.com/LIAS-CUHKSZ/Polytopic-SLAM-Uncertainty-Quantification.
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