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Accurate perception, state estimation and mapping are essential for saferobotic navigation as planners and controllers rely on these components forsafety-critical decisions. However, existing mapping approaches often assumeperfect pose estimates, an unrealistic assumption that can lead to incorrectobstacle maps and therefore collisions. This paper introduces a framework forcertifiably-correct mapping that ensures that the obstacle map correctlyclassifies obstacle-free regions despite the odometry drift in vision-basedlocalization systems (VIO}/SLAM). By deflating the safe region based on theincremental odometry error at each timestep, we ensure that the map remainsaccurate and reliable locally around the robot, even as the overall odometryerror with respect to the inertial frame grows unbounded.  Our contributions include two approaches to modify popular obstacle mappingparadigms, (I) Safe Flight Corridors, and (II) Signed Distance Fields. Weformally prove the correctness of both methods, and describe how they integratewith existing planning and control modules. Simulations using the Replicadataset highlight the efficacy of our methods compared to state-of-the-arttechniques. Real-world experiments with a robotic rover show that, whilebaseline methods result in collisions with previously mapped obstacles, theproposed framework enables the rover to safely stop before potentialcollisions.

Certifiably-Correct Mapping for Safe Navigation Despite Odometry Drift