Beyond Geometry: Efficient Topologically-Grounded Navigation in Complex 3D Environments

Ground robot navigation in complex 3D environments is often hindered by geometric ambiguity, where non-traversable structures such as furniture share local geometric properties with navigable ground. Furthermore, the computational cost of searching massive voxel spaces remains a significant challenge. To address these issues, we present a surface extraction framework that constructs a reduced state space of physically reachable standing positions by enforcing ground support, overhead clearance, and seed-based connectivity constraints. Evaluation across five Matterport3D indoor scenes and three PCT benchmark scenes demonstrates over 80% state space reduction and sub-millisecond A* search on the Matterport3D scenes, with 100% planning success across all 300 tested queries.