Provably Guaranteed Polytopic Uncertainty Quantification for SLAM

2026-05-27

AI Summary

Existing SLAM methods struggle to provide provable inclusion guarantees for pose and map uncertainties in safety-critical scenarios. This work proposes the first provably correct uncertainty quantification framework tailored for 3D–3D landmark-based SLAM, delivering uncertainty sets in polyhedral form with deterministic inclusion guarantees through three core modules: forward mapping, backward pose tracking, and pose composition. The approach offers, for the first time, theoretically rigorous guarantees over the entire SLAM pipeline while integrating conformal prediction to enable data-driven probabilistic calibration—thus balancing strong theoretical assurances with practical utility. Extensive simulations and real-world experiments validate the method’s effectiveness, and the implementation is publicly released.

Abstract

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.

Problem

• uncertainty quantification
• SLAM
• polytopic uncertainty
• guaranteed containment
• safety-critical robotics

Innovation

• polytopic uncertainty quantification
• provably guaranteed SLAM
• conformal prediction
• 3D landmark-based SLAM
• certified uncertainty sets