Omnidirectional Humanoid Locomotion on Stairs via Unsafe Stepping Penalty and Sparse LiDAR Elevation Mapping

Humanoid robots, characterized by numerous degrees of freedom and a high center of gravity, are inherently unstable. Safe omnidirectional locomotion on stairs requires both omnidirectional terrain perception and reliable foothold selection. Existing methods often rely on forward-facing depth cameras, which create blind zones that restrict omnidirectional mobility. Furthermore, sparse post-contact unsafe stepping penalties lead to low learning efficiency and suboptimal strategies. To realize safe stair-traversal gaits, this paper introduces a single-stage training framework incorporating a dense unsafe stepping penalty that provides continuous feedback as the foot approaches a hazardous placement. To obtain stable and reliable elevation maps, we build a rolling point-cloud mapping system with spatiotemporal confidence decay and a self-protection zone mechanism, producing temporally consistent local maps. These maps are further refined by an Edge-Guided Asymmetric U-Net (EGAU), which mitigates reconstruction distortion caused by sparse LiDAR returns on stair risers. Simulation and real-robot experiments show that the proposed method achieves a near-100\% safe stepping rate on stair terrains in simulation, while maintaining a remarkably high safe stepping rate in real-world deployments. Furthermore, it completes a continuous long-distance walking test on complex outdoor terrains, demonstrating reliable sim-to-real transfer and long-term stability.