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

Falling is an inherent risk for humanoid robots operating in unstructured environments. Existing reinforcement learning methods that leverage expert motion priors are predominantly trained on flat-ground fall-recovery tasks and typically rely on hard switching between separate recovery and locomotion controllers. As a result, such policies struggle to achieve smooth and robust recovery behaviors when deployed on complex terrains such as slopes and gravel. This paper presents \textbf{CG-MuTra}, a unified continuously-gated multi-scale discriminator framework for multi-terrain adaptive fall recovery. CG-MuTra introduces a proprioceptively-derived continuous gate $α= f(z_{\mathrm{root}}, s)$ that softly blends three discriminators operating at different temporal horizons: frame-level stability ($Φ_{\mathrm{frame}}$, $H=1$), temporal smoothness ($Φ_{\mathrm{seq}}$, $H=5$), and gait periodicity ($Φ_{\mathrm{gait}}$, $H=10$). This design enables seamless recovery-to-locomotion transitions without explicit mode switching. Furthermore, we propose a Terrain-Pose Risk Coupling Sampler (TPRCS) that explicitly couples dangerous edge initial poses with terrain dynamics during training, forming a closed-loop synergy with the terrain-privileged shaping term $Ξ_κ$. We validate CG-MuTra on a Unitree G1 humanoid across grass, slopes ($10^\circ$--$15^\circ$), and gravel in both simulation and hardware. Experimental results demonstrate that CG-MuTra achieves smooth, highly robust fall recovery and locomotion transitions across multiple terrains while maintaining a single deployable policy.

Humanoid locomotion on granular terrain remains a significant challenge due to its complex foot-terrain interaction dynamics that are difficult to model. Existing approaches either ignore granular contact dynamics or incorporate simplified normal force models with heuristic tangential components. In this work, we present a physics-grounded granular contact model based on three-dimensional resistive force theory (3D RFT) and efficiently simulate granular terrain for reinforcement learning (RL) training. Unlike traditional rigid contact models and simplified granular contact models with ad-hoc heuristics, our contact solver produces physically accurate granular intrusion dynamics without resorting to heuristics. It captures realistic penetration and tangential drag during training, enabling the policy to learn behaviors that transfer reliably to real-world granular terrain where rigid contact models fail. To adapt to varying terrain conditions, we train a terrain-adaptive locomotion controller via teacher-student RL, using a variational autoencoder to encode terrain information into a compact latent representation. Simulation studies using material point method (MPM) with NVIDIA Newton demonstrate that our method generalizes to unseen granular terrains, achieves a significantly higher success rate than baselines, and demonstrates zero-shot terrain identification and adaptation. We further validate our approach through extensive hardware experiments across diverse real-world granular terrains including basalt, dry sand, and beach sand. To the best of our knowledge, this is the first demonstration of agile humanoid locomotion on real-world granular terrain. Project page: https://humanoid-gm-locomotion.github.io/HUMANOID-GM/

Humans primarily rely on walking and running to traverse complex terrains. Similarly, humanoid robots should be able to smoothly transition between walking and running while maintaining natural and stable locomotion. However, unifying gait transition and multi-terrain adaptation within a single policy remains challenging due to gradient interference between tasks and the distribution shift caused by terrain variations. Although Mixture-of-Experts (MoE) architectures can mitigate multi-skill interference, direct joint training often fails to achieve clear expert specialization. To address these challenges, we propose CoRe-MoE, a two-stage reinforcement learning framework that decouples gait generation from terrain adaptation. In the first stage, a stable locomotion policy is learned to produce natural walking and running behaviors with smooth transitions. In the second stage, a terrain-aware MoE branch is introduced, and the gating network is trained with a contrastive objective to learn structured terrain representations and promote expert specialization. The final action is obtained through weighted fusion of the base gait policy and the terrain-aware branch, enabling the policy to preserve stable locomotion while adapting to complex terrains. Extensive simulation results demonstrate that the proposed method outperforms baseline approaches in terms of success rate, locomotion stability, and multi-terrain adaptability. Furthermore, zero-shot deployment on a Unitree G1 humanoid robot validates the effectiveness of our framework, achieving robust walking and running across stairs, slopes, steps, obstacles, and unstructured outdoor terrains while maintaining accurate foothold control and dynamic stability.