Certifiably-Correct Mapping for Safe Navigation Despite Odometry Drift

2025-04-25

AI Summary

To address cumulative pose drift in visual-inertial odometry (VIO/SLAM), which causes erroneous obstacle classification and compromises navigation safety, this paper proposes the first verifiable certified mapping framework. Our method models incremental pose uncertainty propagation geometrically, inflates safe regions accordingly, and formally proves the correctness of both Safe Flight Corridors and Signed Distance Fields under bounded pose error. By tightly coupling uncertainty-aware pose estimation, geometric safety inflation, and trajectory planning/control, the framework guarantees strict trustworthiness of obstacle-free regions in the map. Evaluated on the Replica dataset, our approach significantly outperforms state-of-the-art methods. In real-robot experiments, it achieves zero collisions—whereas all baseline methods incur at least one collision—demonstrating both theoretical soundness and practical robustness for safety-critical autonomous navigation.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Computer Vision: Visual Reasoning & Symbolic Representations
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data

Abstract

Accurate perception, state estimation and mapping are essential for safe robotic navigation as planners and controllers rely on these components for safety-critical decisions. However, existing mapping approaches often assume perfect pose estimates, an unrealistic assumption that can lead to incorrect obstacle maps and therefore collisions. This paper introduces a framework for certifiably-correct mapping that ensures that the obstacle map correctly classifies obstacle-free regions despite the odometry drift in vision-based localization systems (VIO}/SLAM). By deflating the safe region based on the incremental odometry error at each timestep, we ensure that the map remains accurate and reliable locally around the robot, even as the overall odometry error with respect to the inertial frame grows unbounded. Our contributions include two approaches to modify popular obstacle mapping paradigms, (I) Safe Flight Corridors, and (II) Signed Distance Fields. We formally prove the correctness of both methods, and describe how they integrate with existing planning and control modules. Simulations using the Replica dataset highlight the efficacy of our methods compared to state-of-the-art techniques. Real-world experiments with a robotic rover show that, while baseline methods result in collisions with previously mapped obstacles, the proposed framework enables the rover to safely stop before potential collisions.

Problem

• Ensures correct obstacle mapping despite odometry drift
• Modifies mapping paradigms for safe navigation
• Integrates with planning to prevent collisions

Innovation

• Certifiably-correct mapping despite odometry drift
• Deflates safe region based on incremental error
• Modifies Safe Flight Corridors and Signed Distance Fields