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

Fig. 1: Illustration of the proposed autonomous exploration framework for multi-floor environments, which consists of four main capabilities: (a) online elevation-aware topological graph construction in multi-floor structures; (b) centerline-constrained viewpoint generation on staircases to prevent the quadruped robot from falling due to yaw variations on stairs; (c) traversable grid-based path searching to compensate for topological failures in stairwells due to sparse and fragmented point clouds; and (d) automatic filtering out structurally inaccessible yet physically traversable regions.

Symbol	Description
$\mathcal{M}^{G}_{occ}$	Global occupancy grid
$\mathcal{M}^{L}_{tomo}$	Local tomography map
$\mathcal{M}^{L}_{grid}$	Local 3D grid map
$\mathcal{M}^{L}_{ter}$	Inflated local 3D terrain map
$\mathcal{S}$	Discrete tomogram slices
$\mathcal{T}_{obs}$	Slice-wise obstacle trees

TABLE I: Nomenclature

Fig. 2: System overview of RAEM. The framework explicitly leverages GPU parallelization for the rapid generation of local tomography map, local 3D grid map, and the extraction of slice-based obstacles. Concurrently, the CPU manages a continuously updated occupancy grid for identifying frontiers. These detected frontiers, combined with the GPU-derived local spatial representations, directly drive the core modules, including elevation-aware topological graph construction, viewpoint generation, and dual path searching. To overcome the challenges posed by degraded tomography maps, RAEM uniquely incorporates a staircase centerline alignment method for safe viewpoint placement and a dual path searching approach to address topological fractures. The global planner subsequently determines the optimal visitation sequence of viewpoints, and the local planner generates trajectory points toward the next goal.

Fig. 3: Traversability analysis of local tomogram slices. Slices are built by projecting the local point cloud onto equidistant horizontal planes, capturing orange ceiling and blue ground layers. The squares represent the cell traversability (green: traversable, red: untraversable) considering the ground conditions and the ceiling height. The red dotted circles highlight cells conservatively marked as untraversable due to strict proximity to structural edges or point cloud map boundaries, despite being physically traversable. Beneath staircases, sparse point cloud observations combined with this conservative labeling generate massive falsely untraversable cells, severely compromising topological building, viewpoint generation, and path searching.

Fig. 4: Illustration of construction processes of the local 3D grid map

\mathcal{M}^{L}_{grid}

. (a)-(c) illustrate the intermediate grid state assignments processed through the structural logic of individual slices. (d) and (e) demonstrate the structural logic across multiple slices, where previously unassigned spatial grids bounded between the ceiling of a lower slice and the ground of an adjacent upper slice are rigorously classified as occupied grids (red) representing solid architectural structures. (f) displays the final integrated map, highlighting a morphological horizontal dilation applied to the traversable grids (indicated by dark green arrows) to significantly reinforce the robustness of path searching for staircases.

Fig. 5: Overview of the slice-based obstacle extraction and distance-to-obstacle query. The multi channel tomogram slices explicitly encode traversable regions (green cubes) and untraversable obstacle boundaries (purple cubes). The untraversable cells within each slice

S_{k}

undergo a dimensional flattening operation, directly projecting the complex spatial structures into a dense 2D point cloud to construct a dedicated planar tree

\mathcal{T}_{obs}^{k}

. For any query point

\mathbf{p}

, its corresponding slice index

k

is mathematically determined based solely on its vertical elevation component

[\mathbf{p}]_{z}

, subsequently enabling rapid and highly efficient distance-to-obstacle evaluations through

\mathcal{T}_{obs}^{k}

.

Fig. 6: Overview of the elevation-aware topological graph construction. (a) A spatial environment featuring overlapping elevation layers. (b) Uniformly sampling candidate locations across the 2D grid plane

(i,j)

. (c) Untraversable or unavailable cells on Plane 0 generate no vertices. (d) and (e) Structurally safe and traversable cells on Plane 1 and Plane 2 successfully instantiate topological vertices at their respective ground elevations. (f) The finalized topological graph interconnecting these generated vertices utilizing bidirectional collision-free spatial edges under maximum allowable edge degree limitations.

Fig. 7: Illustration of viewpoint generation. (a) Raw samples are evaluated where invalid points (green) are discarded, and valid points (red) are vertically projected to surface-level positions (orange). (b) Projected points are categorized according to the specific slice scopes they fall into (e.g., blue and brown subsets). After eliminating points located too close to obstacles (red crosses), the remaining safe points are clustered using collision-free circles to extract candidate viewpoints. (c) The optimal viewpoint

\mathbf{p}_{1}

is selected for maximizing frontier visibility compared to

\mathbf{p}_{2}

and

\mathbf{p}_{3}

. (d) On staircases, an elevation-constrained region expansion from

\mathbf{p}_{1}

extracts the tread centroid to serve as the new viewpoint position.

Fig. 8: Illustration of the dual path searching approach for staircases. (a) Graph-based searching fails due to topological discontinuity. (b) The fallback traversable-grid based searching successfully resolves a valid trajectory (yellow path) to the upper-floor viewpoint.

	Size (m)	Floor Count	Inter-Floor Height (m)
$scene\_1$	18.4 $\times$ 18.4 $\times$ 8.2	3	2.1
$scene\_2$	13.0 $\times$ 22.4 $\times$ 8.2	3	2.5
$scene\_3$	24.0 $\times$ 34.0 $\times$ 7.7	2	3.4
$scene\_4$	17.6 $\times$ 16.8 $\times$ 6.2	4	1.5

TABLE II: Information Of Simulation Scenarios

	scene_1	scene_2	scene_3	scene_4	Real-World
$R_{occ}$	4.0				4.0
$\mathcal{B}_{local}$	12 $\times$ 12 $\times$ 4	12 $\times$ 12 $\times$ 6	12 $\times$ 12 $\times$ 4		12 $\times$ 12 $\times$ 6
$N$	5				5
$r_{tomo}$	0.2				0.2
$d_{min}$	0.5				0.5
$\theta_{s}$	0.6				0.6

TABLE III: Parameter Configurations

Fig. 9: The variation of coverage rate with time duration in exploration progress for (a)

scene\_1

, (b)

scene\_2

, (c)

scene\_3

, and (d)

scene\_4

.

Fig. 10: The variation of coverage rate with traveling distance in exploration progress for (a)

scene\_1

, (b)

scene\_2

, (c)

scene\_3

, and (d)

scene\_4

.

Fig. 11: Visualization of exploration paths generated by RAEM across

scene\_1

,

scene\_2

,

scene\_3

, and

scene\_4

.

		Exploration Time (s)				Trajectory Distance (m)				Occupied Volume (m 3 )				Success Number
		Avg	Std	Max	Min	Avg	Std	Max	Min	Avg	Std	Max	Min	1st Floor	2nd Floor	3rd Floor	4th Floor
$scene\_1$	TARE	63	2	67	59	62	1	65	60	102	3	107	95	20	0	0
	FAEL	41	5	48	32	32	4	37	26	90	11	109	74	20	0	0
	HPHS	41	2	47	37	39	2	46	35	89	1	90	87	20	0	0
	Ours	174	3	184	166	137	2	141	134	389	4	397	379	20	20	20
$scene\_2$	TARE	86	9	108	74	81	8	104	72	109	6	122	100	20	0	0

TABLE IV: Results of Simulations in four Environments

Fig. 12: Evolution of the computation time for a single planning iteration as time progresses in (a)

scene\_1

, (b)

scene\_2

, (c)

scene\_3

, and (d)

scene\_4

.

Fig. 13: Box plot with logarithmic scale of single computation time of each module for (a)

scene\_1

, (b)

scene\_2

, (c)

scene\_3

, and (d)

scene\_4

.

	scene_1	scene_2	scene_3	scene_4
running on GPU	0.0027 s	0.0028 s	0.0027 s	0.0027 s
running on CPU	0.0268 s	0.0506 s	0.0500 s	0.0504 s

TABLE V: Average Computing Time for Local 3D Grid Map Construction Using CPU and GPU Architectures

Fig. 14: Box plots of the distribution of single execution times for local 3D grid map construction utilizing CPU and GPU across all four simulation scenarios.

	scene_1	scene_2	scene_3	scene_4
clustering	0.0012 s	0.0024 s	0.0026 s	0.0022 s
sampling	0.0015 s	0.0029 s	0.0053 s	0.0051 s

TABLE VI: Average Computing Time of the Sampling and Clustering Viewpoint Generation Schemes

Fig. 15: Box plots of the distribution of single execution times for the sampling and clustering viewpoint generation schemes across all four simulation scenarios.

Fig. 16: Comparative visualization of the quadruped robot ascending staircases. (a) and (b) illustrate the selected staircase regions for evaluation. (c) and (d) demonstrate the erratic climbing trajectories characterized by yaw angle variations generated without the center alignment constraint. (e) and (f) display the nearly straight trajectories produced when the proposed strategy is applied.

Fig. 17: Sequential illustration of a lateral rollover failure caused by the absence of the center alignment constraint. (a) While the quadruped robot climbs facing left, a viewpoint distributed on the right is selected as the next navigation goal, compelling the robot to physically maneuver toward it. (b) and (c) To reach this new target, the robot is forced to substantially alter its yaw angle directly upon the staircase, a dangerous kinematic shift that destabilizes the platform and results in a severe fall.

Fig. 18: Sequential demonstration of the dual path searching mechanism solving a topological disconnection on a corner staircase. (a) A target viewpoint fails to link to the topological graph. (b) The traversable grid-based A-star search activates as a reliable fallback, successfully finding a supplementary path indicated by the solid white line. (c) The local planner generates a navigation trajectory based on this discovered route. (d) The topological graph is fully recovered and reconnected after the robot climbs and densely scans the staircase region in close proximity.

Fig. 19: Hardware configuration of the robotic platform and the trajectory visualization scheme for the real-world experiments. The system comprises a Unitree Go2 quadruped robot equipped with a Mid-360S LiDAR and an onboard NVIDIA Jetson Orin NX computing unit. The accompanying rainbow color gradient applied to the trajectory intuitively illustrates the continuous chronological progression of the exploration process.

	Size (m)	Exp. Time (s)	Traj. Dist. (m)	Max Vel. (m/s)
$stairwell$	5.5 $\times$ 14 $\times$ 21.5	233.9	104.9	1.0
$building\_1$	16 $\times$ 38 $\times$ 8	290.0	132.2	0.75
$building\_2$	51 $\times$ 45 $\times$ 8	375.0	166.0	0.75
$lobby$	35 $\times$ 26 $\times$ 5	247.0	99.9	1.0

TABLE VII: Configuration and Performance Metrics of the Four Real-World Testing Scenarios

Fig. 20: Experimental results in the real-world

stairwell

scene. The proposed framework successfully enables the quadruped robot to autonomously explore from the first floor to the fifth floor.

Fig. 21: Experimental results in the real-world

building\_1

scene. Upon discovering a staircase within the designated exploration boundary, the quadruped robot autonomously climbs to the upper floor to seamlessly continue exploration.

Fig. 22: Experimental results in the real-world

building\_2

scene.

Fig. 23: Experimental results in the real-world

lobby

scene. Despite the sparsely occupied spaces generating numerous frontiers and candidate viewpoints that demand higher computational overhead, the quadruped robot maintains continuous movement, demonstrating the computational stability of the proposed framework.

RAEM: Robust Autonomous Exploration for Multi-Floor Environments with a Quadruped Robot

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