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

Yuzhi Jiang; Yujun Liang; Junhao Li; Han Ding; Lijun Zhu

cs.ROMar 9, 2026

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

Authors: Yuzhi Jiang, Yujun Liang, Junhao Li, Han Ding, Lijun Zhu

Organizations: School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China. · State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China. · School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China.

Abstract

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.

Figures & tables

Fig. 1: Overview of the proposed omnidirectional perceptive locomotion framework deployed on the Unitree G1 humanoid robot. The robot safely performs omnidirectional stair traversal in both indoor and outdoor settings, including forward ascent (a), (c), lateral ascent (b), and backward ascent (d). Orange arrows indicate the direction of motion, and the teal overlay on the stairs illustrates the real-time reconstructed elevation map.

Fig. 2: Overview of the proposed framework. (A) Simulation training: an MLP and a CNN extract proprioceptive and perceptive features, respectively, which are then concatenated. Meanwhile, an unsafe foot penalty function guides the policy to learn safe stair-traversal gaits. (B) Real-world deployment: the trained policy network is directly transferred to the real robot, with a point-cloud mapping and edge-guided elevation map module providing stable and accurate elevation map inputs.

Name	Expression	Weight
Linear Vel. Tracking	$\exp(-4\\|\mathbf{v}_{xy}-\mathbf{v}_{xy}^{\text{cmd}}\\|^{2})$	$5.0$
Angular Vel. Tracking	$\exp(-4\\|\boldsymbol{\omega}_{z}-\boldsymbol{\omega}_{z}^{\text{cmd}}\\|^{2})$	$5.0$
Base Height	$\exp(-400\\|h-h_{\text{tar}}\\|^{2})$	$1.0$
Feet Air Time	$\mathds{1}_{\mathbf{c}_{i}=1}\cdot\min(t_{\text{air}},t_{\text{c}},1.0)$	$7.0$
Base Lin. Vel. Z	$-\\|\mathbf{v}_{z}\\|^{2}$	$-1.0$
Base Ang. Vel. XY	$-\\|\boldsymbol{\omega}_{xy}\\|^{2}$	$-0.05$

TABLE I: Reward function terms

Fig. 3: Illustration of the proposed dense unsafe stepping penalty. The left panel depicts the foot-collision penalty computation, and the right panel depicts the edge-stepping penalty computation.

Fig. 4: Illustration of the spatiotemporal rolling mapping and the protection zone mechanism. The colors of the point cloud indicate temporal confidence levels. The red conical region represents the physical blind zone of the LiDAR, and the light blue cylinder denotes the self-protection zone $\mathcal{Z}_{\text{safe}}$ constructed beneath the base of the robot.

Fig. 5: Comprehensive performance comparison in simulation. (a) Safe stepping rate as a function of stair height for each method. The top row corresponds to forward, backward, and lateral stair ascent, while the bottom row shows the corresponding descent results. (b) Terrain curriculum level progression over the course of training. (c) Forward linear velocity tracking when ascending 15-cm stairs with a commanded velocity of 0.7 m/s.

Fig. 6: Real-world experimental results. (A) The robot traverses stairs in an indoor environment: (a) forward ascent, (b) forward descent, (c) backward descent, and (d) lateral descent. (B) The robot performs long-distance outdoor walking, successfully traversing downhill slopes, flat ground, and stairs. The upper-left inset in each robot image displays the raw elevation map (black dots indicate missing data holes), while the lower-left inset shows the elevation map processed by the proposed reconstruction network.

Net	Loss			G-MSE $\downarrow$	E-MAE $\downarrow$	F-MAE $\downarrow$	F-Rgh $\downarrow$
Net	$\mathcal{L}_{r}$	$\mathcal{L}_{s}$	$\mathcal{L}_{g}$	( $\times 10^{-4}$ )	( $\times 10^{-2}$ )	( $\times 10^{-3}$ )	( $\times 10^{-2}$ )
Baseline				2.05	1.32	5.57	2.57
EGAU				1.99	1.18	5.89	2.26
EGAU	✓			1.54	0.93	5.58	2.36
EGAU	✓	✓		1.46	0.87	5.41	1.87
EGAU	✓	✓	✓	1.23	0.75	4.24	1.32

TABLE II: Ablation results for the reconstruction network and the loss functions

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Climbing hollow stairs remains a challenging problem for quadruped robots due to the high risk of leg trapping, severe depth sparsity, and high-frequency depth-sensing noise. In this paper, we propose StairMaster, a novel three-stage reinforcement learning framework for stable locomotion on such extreme discontinuous terrains. Our architecture integrates a Cross-Attention mechanism to extract structural features from noisy depth data, alongside a Spatial-aware Recurrent Unit (SRU) that maintains robust spatio-temporal memory to mitigate perception blind spots. To bridge the sim-to-real gap in depth perception, we propose a high-fidelity sim-to-real depth sensor modeling pipeline that faithfully replicates real-world sensor artifacts. Additionally, we employ a 3D waypoint-guided active perception reward for proactive sensing, alongside hollow gap kinematic and stair edge penalties to ensure precise foothold placement. We successfully deployed StairMaster on a Unitree Go2 robot, demonstrating its ability to conquer hollow stairs with an unprecedented incline of up to 55

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