Homotopy-Aware Corridor Generation without Predefined Reference Paths

2026-07-31

AI Summary

Existing safety corridor generation methods rely on predefined reference paths, which restrict the set of explorable homotopy classes and introduce geometric bias. This work proposes the first reference-path-free, homotopy-aware corridor generation framework that directly constructs sequences of convex sets from free space on a Graph of Convex Sets (GCS). By integrating visibility analysis with a multi-scale adaptive mechanism, the approach enables both local updates and global topological exploration. It further fuses topologically redundant solutions through visibility-based convex set deformation and introduces an incremental GCS structure that preserves homotopy consistency. Experiments demonstrate that the method efficiently constructs graph structures, yields stable trajectory performance, achieves superior homotopy diversity compared to baselines, and exhibits robustness to unknown obstacles in both ground and aerial robotic platforms.

Abstract

Generating safe corridors is essential for collision-free robotic motion planning, yet most existing methods rely on predefined reference paths, which bias corridor geometry and implicitly limit the homotopy classes that can be explored. We propose a reference-path-free corridor generation framework on graphs of convex sets (GCS) that constructs corridors directly as sequences of convex sets, allowing corridor structure to emerge from the free-space representation rather than from a guiding path. To reason about similarity among corridors, we extend visibility-based deformation from paths to convex-set sequences, enabling the fusion of topologically redundant corridors while preserving distinct alternatives. To overcome the limited adaptability of existing GCS methods based on static global decompositions, we further develop an adaptive multi-scale GCS, in which a sampling-based fine-scale graph supports localized updates and a visibility-based coarse-scale graph enables compact global exploration. The two levels maintain topological consistency, allowing incremental updates without full graph reconstruction under environmental uncertainty. Numerical experiments characterize GCS construction, corridor generation, homotopy-aware exploration, and local updates, showing efficient graph construction, stable trajectory-level performance, and shorter-duration homotopy-aware trajectories than existing baselines. Hardware experiments on ground and aerial robots, including deployment with onboard localization, further validate the framework under translated and previously unknown obstacles.

Problem

• corridor generation
• homotopy-aware planning
• reference-path-free
• convex sets
• motion planning

Innovation

• homotopy-aware planning
• graph of convex sets
• reference-path-free corridor generation
• adaptive multi-scale representation
• topological consistency