STAG: A Sparse Traversability-Aware Graph Representation from Grid-Based Costmaps for Robotic Navigation

Autonomous navigation across large off-road environments remains a challenging problem. Onboard sensors perceive only the immediate surroundings, yet safe and efficient routes depend on terrain features that extend well beyond the sensor horizon. Geo-spatial data sources such as satellite imagery, aerial LiDAR, and vector maps can close this gap, but learning traversability from them is difficult: dense labels are unavailable at scale, and existing methods rely on short-range sensing. We propose an efficient formulation that learns a continuous traversability map from overhead data, supervised directly by human-driven GPS trajectories and shaped by supervised geometric priors from LiDAR. Alongside the model, we release a dataset, curated from public sources, consisting of 299 scenes spanning $\sim\!1{,}244\,\mathrm{km}^{2}$ of diverse terrain, paired with $1{,}130\,\mathrm{km}$ of human driving. In field trials on a Clearpath Warthog across seven routes at two sites,our method achieves trajectories within $5.5\%$ of human path length and reduces operator interventions by $\sim\!85\%$ compared to local-planner-only autonomy.

Mission-level autonomy for disaster response, search and rescue, and tactical UGV operations requires repeated path and mission planning as terrain conditions, agent types, and objectives change. Pixel-grid search is costly for repeated kilometer-scale queries, while semantic abstractions must maintain valid costs and connectivity as conditions change. We present HOPHY (Hierarchical Off-Road Planning using Hypergraphs), a reusable hierarchical terrain representation that organizes map-scale terrain into geometrically connected semantic regions (GSNodes), connectivity-preserving critical regions (Coarse Regions), and typed hyperedges for terrain, agent, and weather context. Hyperedge intersections select affected regions and incident edges for state updates without rebuilding the hierarchy. Across real off-road maps spanning kilometer-scale areas, HOPHY achieves 100% planning success and less than 0.01% median cost deviation from the oracle (pixel A*), with substantially lower query and replanning latency than the evaluated pixel and abstraction baselines. Applied to a multi-robot task-allocation (MRTA) problem, these gains reduce total computation by 79x over pixel A* and 7.2x over the fastest abstraction baseline, with mission makespan comparable to pixel A*. Finally, we demonstrate HOPHY on a physical Clearpath Jackal that successfully executes a 1.5-km, eight-task mission across mixed-surface outdoor terrain and a blockage-triggered replanned route.

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.