SE(2) Navigation Mesh

2026-07-01

AI Summary

Existing navigation methods struggle to efficiently model the heading-constrained traversable regions for non-circular robots in complex multi-level environments. This work proposes an SE(2) navigation mesh that, for the first time, integrates the SE(2) pose space into navigation representation by explicitly encoding heading-dependent traversability through a heading-stratified polygonal structure, while supporting online incremental updates from streaming point clouds. The approach combines footprint-mask-based traversability evaluation with a hierarchical A*-String Pulling-A* path planner to jointly optimize position and heading. Experiments demonstrate that the method improves traversable area coverage by over 50% in simulation, yields superior path quality compared to sampling-based baselines in constrained scenarios, and achieves real-time performance and stable navigation in physical robot deployments.

Abstract

Global navigation for ground robots in complex multi-level environments requires representations that accurately capture traversable regions while enabling efficient path planning. Current approaches present key limitations: Point clouds and volumetric occupancy maps lack explicit surface structure for traversability estimation, whereas direct pathfinding on dense triangle meshes is computationally prohibitive. Navigation meshes mitigate these challenges through polygonal abstraction of the underlying mesh, but assume yaw-invariant traversability, rendering them unsuitable for non-circular robots in constrained spaces. We propose SE(2) Navigation Mesh (SE(2) NavMesh), a polygonal representation of traversable regions that encodes yaw-dependent traversability. Our method evaluates traversability using footprint masks and constructs a graph over yaw-specific layers with explicit translational and rotational connectivity. Grounded in this representation, we develop an A*-String Pulling-A* (ASA) pathfinding strategy that hierarchically optimizes robot position and heading. We also present an online method that incrementally updates the SE(2) NavMesh from streaming point clouds during concurrent geometry reconstruction. In simulation, the SE(2) NavMesh captures over 50% more traversable area than classical NavMeshes, and the SE(2) NavMesh + ASA pipeline consistently outperforms sampling-based baselines in constrained environments. Extensive real-world experiments on a physical robot validate real-time online generation and successful navigation across multiple environments.

Problem

• SE(2) Navigation Mesh
• traversability
• global navigation
• non-circular robots
• constrained environments

Innovation

• SE(2) Navigation Mesh
• yaw-dependent traversability
• footprint mask
• ASA pathfinding
• online incremental update