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

2026-05-17

AI Summary

Ground robots often struggle to navigate efficiently in complex 3D environments due to geometric ambiguities and the high computational cost of large-scale voxel-based search. This work proposes a topology-constrained framework for extractable standable surfaces, which jointly models ground support, overhead clearance, and seed connectivity constraints to construct a physically traversable and highly compressed state space. By resolving navigation ambiguities arising from geometric similarity, the method achieves over 80% state-space reduction on the Matterport3D and PCT datasets, enables A* path planning with average runtime under 1 millisecond, and attains a 100% success rate across 300 navigation tasks, significantly enhancing both planning efficiency and robustness.

Abstract

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.

Problem

• geometric ambiguity
• 3D navigation
• computational cost
• voxel space
• robot navigation

Innovation

• topologically-grounded navigation
• state space reduction
• surface extraction
• 3D robot navigation
• geometric ambiguity