  Recent open-vocabulary robot mapping methods enrich dense geometric maps with
pre-trained visual-language features. While these maps allow for the prediction
of point-wise saliency maps when queried for a certain language concept,
large-scale environments and abstract queries beyond the object level still
pose a considerable hurdle, ultimately limiting language-grounded robotic
navigation. In this work, we present HOV-SG, a hierarchical open-vocabulary 3D
scene graph mapping approach for language-grounded robot navigation. Leveraging
open-vocabulary vision foundation models, we first obtain state-of-the-art
open-vocabulary segment-level maps in 3D and subsequently construct a 3D scene
graph hierarchy consisting of floor, room, and object concepts, each enriched
with open-vocabulary features. Our approach is able to represent multi-story
buildings and allows robotic traversal of those using a cross-floor Voronoi
graph. HOV-SG is evaluated on three distinct datasets and surpasses previous
baselines in open-vocabulary semantic accuracy on the object, room, and floor
level while producing a 75% reduction in representation size compared to dense
open-vocabulary maps. In order to prove the efficacy and generalization
capabilities of HOV-SG, we showcase successful long-horizon
language-conditioned robot navigation within real-world multi-storage
environments. We provide code and trial video data at http://hovsg.github.io/.
