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RAEM: Robust Autonomous Exploration for Multi-Floor Environments with a Quadruped Robot
Zikang Yuan, Yuan Ren, Yian Wang, Yixue Wang, Enze Fang, Xuewei Zhang, Junda Cheng, Chi Chen, Chin-Pang Ho, Lijun Zhu, Shaohang Xu, Kwang-Ting Cheng, Xin Yang
TL;DR
Multi-floor exploration challenges planar representations, expensive global tomography replanning, and degraded stairwell observations. RAEM combines local tomography and categorized 3D grids with an elevation-aware global graph, plus stair-specific viewpoint and path strategies, and demonstrates exploration through five floors while remaining scoped primarily to upward traversal.
Problem
Planar traversability representations cannot adequately model overlapping structures and cross-floor connectivity, while global tomography maps are computationally costly for frequent replanning and local stairwell observations can be degraded.
Method
RAEM combines bounded local tomography and categorized local 3D grids for terrain and connectivity analysis with an incrementally updated elevation-aware global topological graph, center alignment, and dual path searching.
Results
Real-world experiments on a Unitree Go2 using a Jetson Orin NX 16GB and one Mid-360S LiDAR achieved complete multi-floor exploration, including a five-floor stairwell.
Takeaways & Limitations
RAEM supports continuous autonomous exploration across multi-floor environments, including corner staircases and a five-floor stairwell, with heterogeneous CPU–GPU online computation.
Takeaways & Limitations
The framework primarily addresses upward staircase exploration; downward traversal remains unaddressed because of sensing blind spots and greater descending locomotion demands.
Abstract
from arXiv · showhide
In this paper, we propose RAEM, a robust autonomous exploration framework for quadruped robots operating in multi-floor environments. Most existing ground-robot exploration approaches rely on planar traversability representations, which cannot adequately represent the overlapping structures and cross-floor connectivity of multi-floor buildings. Although tomography-based representations provide effective traversability modeling for multi-floor navigation, maintaining a global tomography map incurs substantial computational overhead for online exploration with frequent replanning. Moreover, sparse and fragmented LiDAR observations in stairwells can degrade local traversability estimation, leading to irregular viewpoint placement and temporary topological disconnections. To address these challenges, RAEM adopts a hybrid local-global traversability representation, in which a local tomography map and an explicitly categorized local 3D grid map are used for online terrain analysis and connectivity evaluation, while an elevation-aware global topological graph is incrementally constructed from these local spatial representations for efficient cross-floor exploration planning. We further introduce a staircase center alignment strategy to reduce abrupt yaw variations during climbing and a dual path searching mechanism to recover guidance paths when the global topology is locally disconnected. Extensive simulation and real-world experiments demonstrate robust and computationally stable autonomous exploration across multi-floor structures, including continuous exploration of a five-floor stairwell.
I. INTRODUCTION
RAEM addresses the mismatch between planar ground-robot representations and multi-floor exploration by combining local spatial analysis with global topological planning. It also targets stairwell perception failures through center-aligned viewpoints and fallback path searching, and demonstrates multi-floor exploration in simulation and on a five-floor stairwell.
- Motivation: Global tomography maps model multi-floor traversability but impose substantial computational overhead during frequent frontier-driven replanning and depend on complete high-fidelity observations.Incrementally built local observations can be sparse because ground robots’ low-mounted LiDAR sensors have limited viewpoints in stairwells.
- RAEM Framework: RAEM uses a hybrid local–global representation that combines local tomography and categorized local 3D grids with an incrementally updated elevation-aware global topological graph.The local maps support terrain analysis, connectivity evaluation, viewpoint generation, and path searching, while the graph supports efficient cross-floor planning.
- Stairwell Robustness: Center alignment places stair viewpoints at stair-tread centers, reducing yaw instability caused by irregular viewpoint distributions during climbing.Connected traversable grids at consistent heights are grouped by region growing before viewpoint positions are updated to geometric centers.
- Stairwell Robustness: Dual path searching uses local traversable grids to generate guidance paths when sparse observations temporarily fracture global topological connectivity.As the robot climbs, accumulating point-cloud density can restore connectivity, while unreachable viewpoints are discarded.
- Evaluation: Real-world experiments with a Unitree Go2, one Mid-360S LiDAR, and an NVIDIA Jetson Orin NX 16GB achieved complete multi-floor exploration, including a five-floor stairwell.Simulations also covered quadrangular spiral and corner staircases.
C. Cross-Floor Navigation
RAEM represents cross-floor traversability through local tomography and categorized 3D grids that update an elevation-aware global graph. Its heterogeneous GPU–CPU pipeline supplies spatial representations and frontiers to topology construction, viewpoint generation, path searching, and trajectory planning.
- Representation: Augmented elevation maps and complex multi-floor representations address overhangs and varying terrain but can remain unsuitable for global building navigation or incur severe processing overhead.The cited prior approaches include slice-based surface lists and 3D occupancy-grid traversability estimates.
- Global Representations: The global occupancy grid represents known and unknown space and supplies newly detected frontiers, while the global graph G = {V, E} encodes traversability through vertices and connective edges.The graph is an undirected representation of connectivity across the environment.
- Local Representations: Locally, the tomography map and 3D grid map support graph updating, viewpoint generation, and path searching, while the inflated terrain map supplies collision-clearance constraints to the local planner.The local tomography map contains N discrete slices and supports slice-wise obstacle extraction.
- System Overview: GPU processing constructs the local tomography map, categorized 3D grid, and slice-based obstacle trees from registered point clouds, then streams them to CPU modules.The CPU updates the global occupancy grid, identifies frontiers, and uses the GPU-derived grid for elevation-aware graph construction and downstream planning.
- Planning: The global planner determines the visitation sequence and guidance path, while the local planner uses the inflated local terrain map to generate executable quadruped trajectory points.This division links frontier detection and topology updates to local motion generation.
B. Frontier Detection
RAEM detects frontiers from updated free–unknown boundaries while constructing a compact local tomography map for online terrain analysis. The map combines layered elevation information with traversability costs, but conservative labeling can create false obstacles beneath staircases.
- Frontier Detection: Frontiers are extracted at free–unknown boundaries within the updated occupancy bounding box and appended to the frontier set Qf.
- Traversability Analysis: Sparse observations beneath staircases combined with conservative edge labeling produce many falsely untraversable cells, compromising topology building, viewpoint generation, and path searching.The red dotted circles identify physically traversable cells marked untraversable near structural edges or map boundaries.
- Local Tomography Map: The local tomography map contains N equidistant 2.5D slices distributed above and below the robot-centered horizontal plane.Each slice uses spatial resolution rtomo and stores ground elevation, ceiling elevation, and traversal cost channels.
- Local Tomography Map: Each slice derives complementary ground and ceiling layers by projecting lower and upper point groups onto its horizontal plane.Cells without projected points receive invalid elevation values.
- Traversability Analysis: Traversability evaluates vertical clearance, ground gradients, and the percentage of safe neighboring cells before assigning traversal costs.Traversable cells additionally incorporate posture deformation and terrain roughness penalties under physical and safety thresholds.
D. Local 3D Grid Map Construction
RAEM converts local tomography slices into an explicitly categorized 3D grid map to represent traversable, free, occupied, and unknown space. GPU-parallel construction and permissive geometric labeling support connectivity and path searching.
- Local 3D Grid Map Construction: The local 3D grid map supplements 2.5D slices because slices alone cannot evaluate spatial connectivity or recover paths across topological fractures.
- Implementation: A GPU architecture assigns one thread to each vertical column and queries multiple tomogram channels during dense 3D map construction.
- State Assignment: Each grid stores one of four states: unknown, occupied, free, or traversable, with columns processed upward from the lowest vertical grid.Ground and ceiling surfaces become occupied; the first grid above ground becomes traversable, while higher unobstructed grids become free.
- State Assignment: Unassigned grids between a lower slice’s ceiling and an adjacent upper slice’s ground are classified as occupied structural regions.
- Map Refinement: A horizontal dilation expands traversable grids only when the vertically adjacent grid beneath is traversable or occupied.The operation reinforces the representation in geometrically complicated areas.
- Map Refinement: The map relies only on ceiling and ground elevations, omitting conservative traversal costs to produce a more permissive traversable space.
E. Slice-Based Obstacle Extraction
RAEM extracts slice-wise obstacle boundaries from untraversable tomogram cells and organizes them into planar trees. Elevation selects the relevant tree for efficient nearest-obstacle distance queries.
- Obstacle Extraction: Untraversable cells in each slice are flattened into a dense 2D point cloud representing obstacle boundaries.
- Obstacle Extraction: The flattened obstacle points are stored in a dedicated planar tree T_k^obs for rapid distance queries across slice elevations.
- Distance Query: For a query point, the algorithm selects a slice using its vertical elevation and queries that slice’s obstacle tree with the point’s planar coordinates.
- Distance Query: The distance evaluation returns the minimum obstacle distance, supporting safety checks for topological vertex generation and viewpoint selection.
F. Elevation-Aware Topological Graph Construction
RAEM incrementally updates an elevation-aware global topological graph from local maps and obstacle trees. It samples candidate positions across elevation layers, filters them by traversability, clearance, and spacing, then connects collision-free vertices.
- Graph Construction: The graph construction uses the local tomography map, local 3D grid map, slice-wise obstacle trees, and the current global graph as inputs.
- Edge Connection: Bidirectional edges are added only when candidate vertices satisfy distance and collision-free constraints, subject to maximum edge degree limitations.
- Graph Construction: Existing vertices within radius Rtopo of the robot are extracted before new vertices are generated.
- Vertex Generation: For each sampled planar location, the algorithm checks every tomogram slice and can generate vertices at distinct ground elevations.A candidate is retained only when the cell is traversable, obstacle clearance exceeds dsafe, and spacing from existing vertices exceeds rmin.
- Vertex Generation: Untraversable, unavailable, or insufficiently clear cells generate no vertex, while safe candidates are added to Vnew after the spacing test.
G. Viewpoint Generation
RAEM generates frontier viewpoints through clustered sampling rather than exhaustive evaluation, then aligns staircase viewpoints to improve traversal safety.
- RAEM adopts a cluster-first strategy that groups raw frontier samples before generating and selecting viewpoints, keeping computational complexity stable.This avoids the cost of uniformly evaluating many candidate points against every frontier.
- Raw samples are filtered for validity, projected onto surface-level positions, grouped by tomogram slice scope, and clustered after obstacle-clearance filtering.Collision-free circles merge nearby safe points into spatial clusters.
- Within each spatial cluster, the point with the greatest obstacle distance becomes the representative candidate viewpoint.This selects safer representatives after collision-free-circle clustering.
- The optimal viewpoint is selected by maximizing the number of visible frontiers within its associated frontier cluster.Visibility is evaluated using collision-free line-of-sight checks.
1) Frontier Clustering:
Frontiers are maintained as spatially coherent clusters that are updated incrementally as the map changes, while insignificant clusters are discarded.
- New frontiers and frontiers invalidated by map updates are placed in a queue and reclustered by geometric proximity.Existing clusters intersecting the update region are removed before their frontiers re-enter the queue.
- Clusters containing too few frontier cells are discarded, producing the finalized set of newly aggregated frontier clusters.
- For each frontier cluster, candidate samples are initialized around its centroid in a predefined cylindrical pattern.
3) Optimal Viewpoint Selection:
Staircase center alignment replaces potentially unsafe viewpoint locations with centroids of bounded, coplanar tread regions.
- The refined staircase viewpoint is the geometric centroid of the converged bounded tread cluster.The centroid shifts the viewpoint away from potentially dangerous stair edges.
- A viewpoint is classified as staircase terrain when its height differs from the robot position by more than one map-grid resolution.This condition activates center alignment.
- Region growing starts from the viewpoint’s seed grid and aggregates neighboring grids representing the contiguous stair tread.Growth follows coplanarity and elevation constraints and stops at the maximum cluster size γ.
- Figure 8 shows that grid-based fallback search can recover a valid trajectory to an upper-floor viewpoint when graph search is disconnected.
H. Dual Path Searching
RAEM combines graph search with traversable-grid fallback search to handle staircase disconnections, then uses elevation-aware costs to order viewpoint visits.
- Sparse or fragmented staircase point clouds can isolate upper-floor and staircase vertices, preventing graph edges and causing graph-based A-star search to fail.
- When the primary topological-graph search fails, RAEM performs grid-based A-star search restricted to grids labeled traversable.
- Bidirectional path caching preserves successful forward and reversed paths to reduce repetitive volumetric planning during cost-matrix construction.
- Viewpoints unreachable by both search stages are excluded from the cost matrix and subsequent visitation-sequence optimization.
- The transition cost multiplies trajectory length by an elevation penalty, encouraging exploration of the current floor before ascending.The elevation penalty activates when the height difference exceeds the local grid resolution.
- A two-opt heuristic balances penalized transition weights against information gains to produce an efficient, kinematically stable visitation sequence.
J. Local Planner
RAEM adapts a local planner for quadruped navigation using vertical adherence and rolling-window obstacle awareness, then evaluates exploration across four simulated multi-floor scenes. The framework completes stable exhaustive exploration while keeping planning cost below 0.1 s in corridor-and-staircase scenes and above 0.2 s in sparse scenes.
- J. Local Planner: RAEM modifies Ego-Planner with a vertical z-axis penalty and a rolling-window local inflated 3D grid map.These changes constrain trajectories near the ground and preserve immediate obstacle awareness with constant memory overhead.
- J. Local Planner: The evaluation uses Gazebo simulations of four scenes spanning two- to four-floor buildings with varied staircase and obstruction layouts.The platform is a Unitree A1 with a Mid-360 LiDAR, evaluated on an Intel Core i7 12700H and RTX 3050Ti system.
- J. Local Planner: 20 independent trials show RAEM achieves stable and exhaustive exploration across all four simulation environments.TARE and FAEL complete only the first floor, while HPHS fails to stably complete some first-floor explorations and records no successful attempt in scene 4.
- J. Local Planner: Below 0.1 s average planning iterations occur in scenes 1–2, while scenes 3–4 exceed 0.2 s because sparse spaces generate more frontiers and viewpoints.The increased computation in scenes 3–4 is also associated with a larger viewpoint-sorting workload.
C. Ablation Study of GPU Acceleration
RAEM’s ablations examine GPU acceleration, viewpoint generation, staircase center alignment, and dual path searching. The results link heterogeneous computing and frontier clustering to lower computational cost, while alignment and fallback path search improve staircase robustness.
- C. Ablation Study of GPU Acceleration: CPU construction of the local 3D grid map requires approximately 18 times more computational time than the GPU implementation.The comparison supports using heterogeneous computing to reduce dense 3D grid update overhead.
- D. Ablation Study of Viewpoint Generation Scheme: In sparse scenes 3–4, sampling-based viewpoint generation costs approximately twice as much as frontier clustering.Sampling associates each frontier with candidate viewpoints, whereas clustering selects one optimal viewpoint per frontier cluster.
- E. Ablation Study of Center Alignment for Staircases: Center alignment significantly alleviates yaw variation during staircase climbing and produces nearly straight trajectories.Without the constraint, arbitrary viewpoint placement can induce lateral oscillation and a rollover occurred once in 20 trials.
- F. Ablation Study of Dual Path Searching: The dual path search succeeds in all 20 attempts, whereas the purely topological method succeeds only 12 times.The fallback uses traversable grid-based A-star search when staircase topology is disconnected, then restores graph connectivity.
G. Real-World Experiment
RAEM is evaluated in real-world multi-floor scenes, including stairwells, buildings, and a sparsely occupied lobby. The experiments demonstrate continuous autonomous exploration, robust staircase climbing, and computational stability under challenging perception and planning conditions.
- Experimental setup: The real-world platform used a Unitree Go2 with a head-mounted Mid-360S LiDAR configured with a 45° downward pitch and a 4.0 m sensing range.Computations were executed directly on the robot’s onboard NVIDIA Jetson platform.
- Real-world stairwell: RAEM autonomously explored from the first floor to the fifth floor, climbing four consecutive corner staircases in a real-world stairwell.The trial tested robustness under map noise and localization errors; failures in viewpoint generation or path searching would have terminated exploration.
- Real-world buildings: RAEM completed exploration across both targeted floors in building 1 and building 2 despite highly sparse LiDAR observations near newly discovered staircases.The building 2 trial also introduced a physical barricade near the task’s conclusion to obstruct a prolonged forward corridor.
- Computational stability: In the sparsely occupied lobby, RAEM maintained continuous movement without waiting for planning results despite numerous frontiers and candidate viewpoints.The scene was selected because expansive open areas generate higher computational overhead.
- Scope boundary: The framework primarily addresses upward staircase exploration and does not explicitly support downward cross-floor traversal.The stated boundary reflects both downward-stair perception blind spots from fixed LiDAR mounting and higher locomotion demands during descent.
- Framework evaluated: RAEM combines local tomography and categorized local 3D grid maps with an elevation-aware global topological graph for efficient cross-floor exploration planning.Staircase center alignment reduces abrupt yaw variations, while dual path searching provides alternative guidance when sparse observations disrupt topology.