In this paper, we propose RAEM, a robust autonomous exploration framework for quadruped robots operating in multi-floor environments. Most existing ground-robot exploration approaches rely on planar traversability representations, which cannot adequately represent the overlapping structures and cross-floor connectivity of multi-floor buildings. Although tomography-based representations provide effective traversability modeling for multi-floor navigation, maintaining a global tomography map incurs substantial computational overhead for online exploration with frequent replanning. Moreover, sparse and fragmented LiDAR observations in stairwells can degrade local traversability estimation, leading to irregular viewpoint placement and temporary topological disconnections. To address these challenges, RAEM adopts a hybrid local-global traversability representation, in which a local tomography map and an explicitly categorized local 3D grid map are used for online terrain analysis and connectivity evaluation, while an elevation-aware global topological graph is incrementally constructed from these local spatial representations for efficient cross-floor exploration planning. We further introduce a staircase center alignment strategy to reduce abrupt yaw variations during climbing and a dual path searching mechanism to recover guidance paths when the global topology is locally disconnected. Extensive simulation and real-world experiments demonstrate robust and computationally stable autonomous exploration across multi-floor structures, including continuous exploration of a five-floor stairwell.

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