Learning Terrain-Adaptive Humanoid Locomotion on Granular Terrain

Junnosuke Kamohara, Feiyang Wu, Andy Ningan Zong, Daniel I. Goldman, Yashwanth Nakka, Seth Hutchinson, Ye Zhao · N/A · 2026

Summary

Abstract Summary

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/

Key Points

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.

Preliminaries

We utilize 3D RFT [ 13 ] to model the contact forces between the humanoid foot and the granular terrain. RFT assumes that the contact force on an intruding body is the sum of forces per area per depth $\bm{\alpha}$ acting on infinitesimal elements: $\mathbf{F}=\int_{S}\bm{\alpha}/z/\mathds{1}_{z 2 . Thus, we first derive the contact force and moment acting on each finite element.

Method

This section details our terrain-adaptive RL framework, which builds on the granular contact model introduced above. We formulate the velocity-tracking task for humanoid locomotion as a Markov Decision Process (MDP).

At each timestep $t$, the agent receives the observation $\mathbf{o}_{t}$, performs an action $\mathbf{a}_{t}$ according to its current policy $\pi(\cdot/\mathbf{o}_{t})$, and obtains a scalar reward $R_{t}$.

Method — Learning Terrain-Adaptive Humanoid Locomotion on Granular Terrain — Figure 3: System diagram of our proposed terrain-adaptive humanoid locomotion. It has two-stage training where privileged teacher network is first trained with VAE terrain encoder and MLP policy. Then, this teacher policy is distilled to deployable student policy by teacher-student RL.

Results

We evaluate the performance of the proposed control system for robust walking and running on different types of granular terrain in both simulation and real-world experiments. We first evaluate the fidelity of our contact model in isolation through a single rigid body intrusion experiment, comparing horizontal travel distance, ground penetration, and ground reaction forces against the material point method (MPM).

Sources and Demonstrations

Figures are reproduced from Kamohara et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.