Real-time Spatial-temporal Traversability Assessment via Feature-based Sparse Gaussian Process

Zhenyu Hou^1†, Senming Tan^1†, Zhihao Zhang^1†

Long Xu^1,2, Mengke Zhang^1,2, Zhaoqi He¹

Chao Xu^1,2*, Fei Gao^1,2, Yanjun Cao^1,2*

¹Huzhou Institute of Zhejiang University ²State Key Laboratory of Industrial Control Technology, Zhejiang University

^†Equal contribution (co-first authors). ^*Corresponding authors.

Zhenyu Hou is actively seeking Ph.D. opportunities—please get in touch!

Teaser

A narrated walkthrough of the FSGP-BGK traversability assessment pipeline is in preparation and will be shared here soon. Stay tuned for demonstrations highlighting feature extraction, spatial-temporal fusion, and autonomous navigation on uneven terrain.

Abstract

Terrain analysis is critical for the practical application of ground mobile robots in real-world tasks, especially in outdoor unstructured environments. We propose FSGP-BGK, a spatial-temporal traversability assessment framework that extracts geometric features directly from LiDAR point clouds using a feature-driven sparse Gaussian process (SGP) and fuses real-time and historical data via a Bayesian Gaussian kernel (BGK). GPU-accelerated feature extraction, inducing-point regression, and BGK smoothing produce dense, uncertainty-aware traversability maps. Extensive simulations across diverse terrain scenarios and real-world tests on a differential-drive platform demonstrate superior accuracy, robustness, and efficiency compared to state-of-the-art baselines.

Simulation traversability map and real-world testing environment — (a) Simulation results and the corresponding traversability map; (b) Real-world testing environment, where the yellow line indicates areas that are easy to traverse.

Highlights

Feature-driven SGP pipeline

GPU-accelerated KNN, curvature, and gradient extraction compress LiDAR point clouds into an informative inducing set, enabling precise SGP-based elevation and slope estimation with quantified uncertainty.

Spatial-temporal BGK fusion

A Bayesian Gaussian kernel blends real-time predictions with historical traversability maps using decay-aware confidence weighting, yielding smooth and stable cost layers.

Integrated navigation stack

Traversability costs guide A* search, MINCO trajectory optimization, and closed-loop control, forming a complete autonomy workflow for uneven terrain navigation.

Validated performance

Evaluated on 2,500 simulated scenes and outdoor deployments, FSGP-BGK cuts mean error by up to 52% and runtime by 3× versus elevation maps while preserving low variance.

Overview of the FSGP-BGK traversability pipeline — Overview of the proposed terrain traversability mapping and navigation framework. From left to right, localization and LiDAR point cloud data are fed into the Feature Extraction module, where curvature and gradient features are computed for each point. These features are then processed by a Sparse Gaussian Process (SGP) model with induced points, yielding local height predictions, variance, and gradient information. Next, a spatial-temporal Bayesian Gaussian Kernel (BGK) fusion step integrates these predictions with historical maps to produce a refined traversability cost map. Finally, we employ A* for trajectory search, MINCO for trajectory optimization, and a controller for trajectory tracking, thereby generating the necessary control commands for the autonomous vehicle to navigate uneven terrain safely and efficiently.

Method Overview

Feature Extraction

GPU-accelerated KNN, curvature, and gradient computation condense LiDAR point clouds into a sparse but informative inducing set. PCA decorrelates features before regression for stable learning. We extract local curvature κ and gradient g from point clouds, identifying feature points with high curvature or large gradients that indicate critical terrain structures such as ridges, valleys, and cliffs.

Sparse Gaussian Process (SGP) Regression

An inducing-point SGP predicts elevation, slope magnitude, curvature, and variance on a dense grid, supporting uncertainty-aware traversability scoring. The SGP model uses inducing points Z to reduce computational complexity while maintaining high accuracy. For each test point X*, we interpolate local curvature and gradient using inverse distance weighting, then feed these features into the trained GP model to predict terrain elevation and uncertainty.

Sparse Gaussian Process regression with inducing points — SGP regression framework: Inducing points enable efficient computation of predictive mean and variance for terrain elevation, slope, and curvature estimation.

Spatial-Temporal BGK Fusion

Bayesian Gaussian kernel smoothing injects temporal decay and variance-weighted confidence, yielding smooth, history-aware traversability maps ready for planning. The BGK method fuses historical traversability estimates M_{τ,t-1} with preliminary predictions M_{τ,pre} using temporal decay weight ω_t = exp(-λ(t-t₀)) and uncertainty-based confidence weight ω_σ = 1/(σ²_{τ,t-1}+ε). This approach effectively integrates multi-frame observations while maintaining computational efficiency.

Bayesian Gaussian Kernel fusion of historical and real-time data — BGK fusion mechanism: Temporal decay and variance-weighted confidence weighting enable smooth integration of historical traversability maps with real-time predictions.

Planning & Control

The traversability cost map feeds A* for global path planning and MINCO for trajectory optimization; the resulting paths are tracked by a differential-drive controller (DDR-opt) in both simulation and field tests. The complete autonomous navigation framework integrates localization, mapping, planning, and control into a unified system for real-time terrain-aware navigation.

Real-time Performance

FSGP-BGK attains 33.84 ms average runtime per update with reduced GPU memory usage compared to direct multi-frame accumulation, enabling deployment on embedded GPUs. The GPU-accelerated pipeline processes feature extraction, SGP inference, and BGK fusion efficiently, achieving 20 Hz traversability map updates on real robotic platforms.

Simulation & Benchmark Studies

We conducted comprehensive quantitative evaluations across five terrain types (Hilly, Forest, Ruin, Road, Indoor) with 2,500 procedurally generated point clouds. Each scenario includes 15% intentional occlusion to mimic real-world LiDAR limitations. Our method is benchmarked against classical SGP and elevation map (EM) baselines.

Accuracy Improvements: FSGP-BGK lowers mean traversability error by 52.5% on hilly terrain and 37.9% on forest terrain relative to baseline SGP, while achieving the lowest variance across all categories.
Scalability: Inducing-point ablations (50 vs. 500 points) reveal that BGK fusion sustains accuracy gains even with dense inducing sets, demonstrating robustness across different computational budgets.
Computational Efficiency: Compared with elevation-map interpolation, FSGP-BGK achieves nearly three times faster runtime (33.84 ms vs. 107.85 ms) with reduced uncertainty.
Temporal Consistency: Mean error steadily decreases over time, highlighting enhanced terrain estimation accuracy through integration of historical observations.

Experimental results showing mean error and variance across different terrain types — Quantitative evaluation across five terrain types: FSGP-BGK consistently achieves the lowest mean error and variance compared to SGP and FSGP baselines.

Comparative analysis of FSGP-BGK versus baseline methods — Performance comparison: FSGP-BGK demonstrates superior accuracy and stability across diverse terrain scenarios with varying inducing point configurations.

Numerical performance metrics and statistical analysis — Detailed numerical results: Mean error and variance metrics for FSGP-BGK, FSGP, and SGP across all terrain categories, demonstrating consistent improvements.

Real-world Validation

We deploy FSGP-BGK on an Agilex Scout Mini differential-drive platform equipped with a Livox MID-360 LiDAR, an Intel Core i7 compute unit, and an RTX 2060 GPU. The system maintains 20 Hz traversability updates and accurately highlights small obstacles that baseline SGP fails to capture, while consuming less GPU memory. The robot successfully navigates complex outdoor unstructured environments with real-time terrain-aware path planning and control.

In Isaac Sim simulation, traversability-aware maps enable smooth trajectory optimization and tracking with MINCO, confirming that the cost map integrates seamlessly with downstream planning algorithms. The framework demonstrates robust performance across diverse terrain types and sensor conditions.

Agilex Scout Mini robot platform with LiDAR and GPU compute unit — Robotic platform: Agilex Scout Mini equipped with Livox MID-360 LiDAR, Intel Core i7, and RTX 2060 GPU for real-time traversability assessment and autonomous navigation.

Real-world terrain navigation with traversability-aware path planning — Autonomous navigation in complex terrain: The robot uses FSGP-BGK traversability maps for real-time path planning and obstacle avoidance in unstructured outdoor environments.

Robot deployment in field testing — Field deployment: Real-world testing of FSGP-BGK on uneven terrain with natural obstacles and vegetation.

Robot navigation in complex environment — Autonomous navigation: The robot successfully traverses challenging terrain using real-time traversability assessment.

Resources

Paper (PDF)

Code Repository

Contact: xiagelearn@gmail.com, yanjunhi@zju.edu.cn

BibTeX

@inproceedings{hou2025fsgpbgk,
  title={Real-time Spatial-temporal Traversability Assessment via Feature-based Sparse Gaussian Process},
  author={Hou, Zhenyu and Tan, Senming and Zhang, Zhihao and Xu, Long and Zhang, Mengke and He, Zhaoqi and Xu, Chao and Gao, Fei and Cao, Yanjun},
  booktitle={IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)},
  year={2025}
}