Physics-Guided Biomechanical Gait Adaptation for Humanoid Locomotion on Extreme Sloped Terrains

Xuanyu Chen; Mohan Liu; Dengchen Mei; Zhihao Gu; Haitian Zhang; Kaimin Mao; Haiyue Zhu; Shijun Yan; Lin Wang

CoRL 2026

HumoSlope

Physics-Guided Biomechanical Gait Adaptation for Humanoid Locomotion on Extreme Sloped Terrains

A two-stage reinforcement learning framework for robust, proprioception-only humanoid locomotion across extreme and complex slopes.

Xuanyu Chen¹ Mohan Liu¹ Dengchen Mei¹ Zhihao Gu¹ Haitian Zhang¹ Kaimin Mao¹ Haiyue Zhu² Shijun Yan³ Lin Wang^1,†

¹ EmPACT Lab, School of EEE, Nanyang Technological University, Singapore

² Singapore Institute of Manufacturing Technology (SIMTech), Agency for Science, Technology and Research (A*STAR), Singapore

³ Advanced Remanufacturing & Technology Centre (ARTC), Agency for Science, Technology and Research (A*STAR), Singapore

^† Corresponding author

PaperPDF arXiv2607.07830 Codesoon

01 / Main demonstration

Extreme slope locomotion, beyond the lab.

Project video · 03:00

Paper

Abstract

Model-free reinforcement learning has enabled impressive humanoid locomotion; however, control on steep slopes remains largely unexplored. Unlike flat or discrete terrains, sloped terrains impose a persistent gravitational bias that demands simultaneous stability and posture control. Consequently, under generic reward formulations, policies can converge to slow, conservative low-center-of-mass (CoM) crouched gaits. In this work, we propose a novel two-stage physics-guided framework, dubbed HumoSlope, dedicated to robust humanoid locomotion on diverse sloped terrains. Specifically, Stage I establishes a terrain-consistent balance prior by introducing a slope-adaptive Zero Moment Point (ZMP) regularizer evaluated directly on the local inclined support plane rather than a world-horizontal reference. To prevent the resulting policy from defaulting to a crouched posture, Stage II introduces the Biomechanical Slope Gait Adapter (BSGA). Utilizing extracted macroscopic terrain descriptors as privileged, training-only signals, BSGA dynamically gates soft reward priors to modulate CoM height and lower-limb coordination based on the estimated slope geometry—encouraging hip-dominant uphill propulsion and knee-oriented downhill braking. Crucially, the deployed actor remains entirely proprioceptive, requiring no online exteroceptive sensing. Extensive Sim-to-Real experiments demonstrate that our framework effectively mitigates posture degeneration and enables blind, continuous traversal of outdoor grass slopes up to 62.7% (32.1°), validating a physics-guided approach to challenging slope terrain adaptation.

02 / Method

Guided in training, blind at deployment.

Stage I

Slope-Adaptive ZMP Regularization

A terrain-aligned ZMP reward learns a dynamic balance prior that adapts to the local slope.

Stage II

Biomechanical Slope Gait Adapter

Training-time PCA terrain descriptors guide CoM height, uphill hip propulsion, downhill knee braking, and swing-leg motion through soft rewards.

✓

Deployment

Proprioception-only Actor

The terrain descriptor is removed. The final policy acts from onboard proprioceptive observations alone.

03 / Experiments

Experiments

Simulation Results

Compound Slope Tracks

Qualitative experiment comparison showing HumoSlope walking uphill, on flat ground, and downhill; a crouched URL baseline; and the wavy, banked, rough, striped, and composite evaluation terrains. — Compound slope tracks and representative policy behaviors.

Table 1 — Main Results
Method	Input	0% (0°)			17.6% (10°)			36.4% (20°)			57.7% (30°)			Max Grade ↑
Method	Input	SR ↑	MXD ↑	T_trav ↓	SR ↑	MXD ↑	T_trav ↓	SR ↑	MXD ↑	T_trav ↓	SR ↑	MXD ↑	T_trav ↓	Max Grade ↑
URL	Prop.	99.7	32.13	88.0	97.7	31.66	92.7	37.5	17.94	99.4	0.0	2.18	—	47% (25°)
FastTD3	Prop.	100.0	31.50	76.1	100.0	31.49	73.2	77.3	28.32	87.5	0.0	2.02	—	70% (35°)
Gallant	LiDAR	99.7	31.47	51.9	90.7	30.29	53.5	78.9	28.37	54.6	0.0	6.11	—	60% (31°)
Ours	Prop.	100.0	32.19	44.3	100.0	32.19	47.0	100.0	32.18	48.6	77.1	27.54	62.8	73% (36°)

SR (%), MXD (m), and T_trav (s) are averaged over three checkpoints and three friction tiers.

We evaluate HumoSlope on held-out 35 m compound slope tracks with diverse terrain variations. HumoSlope achieves 100% success up to 20° and 77.1% success at 30°, where all baselines fail to complete the track. A separate slope-limit evaluation demonstrates traversal at 36°.

Biomechanical Analysis

CoM Height · Hip-Pitch Torque · Knee Flexion

Biomechanical diagnostics comparing HumoSlope and URL in center-of-mass height, hip-pitch torque along the track, and knee flexion along the track. — CoM height, hip-pitch torque, and knee-flexion diagnostics.

HumoSlope maintains a more upright posture than the URL baseline, avoiding persistent low-CoM crouching. It exhibits increased hip-pitch torque during ascent and greater knee flexion during descent, demonstrating slope-conditioned gait adaptation.

Ablation Study

Table 2 — Ablation Results
Variant	Task Performance			Efficiency / Stability		Posture / Load
Variant	SR ↑	MXD ↑	T_trav ↓	CoT ↓	σ²_yaw ↓	h̄_com	τ^pk_knee
Full	98.2	31.75	53.7	1.380	0.1008	0.669	117.9
Stage I only (no Stage II)	100.0	32.20	67.6	0.925	0.0148	0.535	82.9
w/o slope-adaptive ZMP	55.6	22.08	54.1	1.906	0.3048	0.720	115.5
w/o BSGA critic cue	93.2	30.56	74.1	1.676	0.2009	0.727	83.4
w/o BSGA reward priors	26.9	18.09	71.9	1.603	0.2031	0.722	108.9
w/o BSGA	0.0	9.59	—	1.621	0.3133	0.659	136.4

Stage I establishes a strong stability prior, while Stage II improves traversal speed and posture adaptation. Removing slope-adaptive ZMP or BSGA components substantially degrades performance, confirming their complementary contributions.

04 / Citation

BibTeX

Use the arXiv citation below. The entry will be updated when the official CoRL record becomes available.

@misc{chen2026physicsguidedbiomechanicalgaitadaptation,
  title={Physics-Guided Biomechanical Gait Adaptation for Humanoid Locomotion on Extreme Sloped Terrains},
  author={Xuanyu Chen and Mohan Liu and Dengchen Mei and Zhihao Gu and Haitian Zhang and Kaimin Mao and Haiyue Zhu and Shijun Yan and Lin Wang},
  year={2026},
  eprint={2607.07830},
  archivePrefix={arXiv},
  primaryClass={cs.RO},
  url={https://arxiv.org/abs/2607.07830}
}