Robust obstacle segmentation is essential for the safety of intelligent robots, where LiDAR-based perception systems play a fundamental role in the robot-environment interaction. While extensive LiDAR-based approaches have demonstrated high performance on common obstacles in urban scenarios, their results on tiny obstacles such as curbs, gravel, and potholes remain unsatisfactory due to the significant similarity between tiny obstacles and inherent road undulations. Moreover, their segmentation accuracy even deteriorates sharply when the LiDAR scans suffer from degradation in challenging off-road scenes. To overcome these bottlenecks, we propose LOGOS, a LiDAR-only unified tiny obstacle segmentation system, which models the road surface as a continuous mixture of 2D Gaussian primitives and distinguishes tiny obstacles via high-presicion elevation estimation. Unlike existing Gaussian splatting methods that rely on iterative RGB training, LOGOS is a backpropagation-free LiDAR-only approach. It directly estimates Gaussian parameters via a freespace-aware initialization by incrementally pruning non-road primitives using smoothness constraints. Subsequently, pointwise signed distances are computed via a novel normal-aware elevation splatting function, ensuring robustness to both flat and sloped terrains. We evaluate LOGOS on a highly heterogeneous benchmark of point cloud frames collected from urban mobility scenarios and mining haulage off-road environments. These data are practically acquired using different LiDAR sensors and exhibit large variations in point density, terrain roughness, and obstacle types. Experiments on the road and off-road scenes demonstrate that LOGOS significantly outperforms other state-of-the-art methods, particularly in degraded point cloud regions and challenging off-road scenarios, while maintaining real-time efficiency.

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