💻 computer science

Learning Terrain-Adaptive Humanoid Locomotion on Granular Terrain

This paper presents a physics-grounded granular contact model based on 3D resistive force theory and a terrain-adaptive reinforcement learning framework that enables agile humanoid locomotion on diverse real-world granular terrains, marking the first successful demonstration of such capabilities in the field.

Original authors: Junnosuke Kamohara, Feiyang Wu, Andy Ningan Zong, Daniel I. Goldman, Yashwanth Nakka, Seth Hutchinson, Ye Zhao

Published 2026-09-10

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Junnosuke Kamohara, Feiyang Wu, Andy Ningan Zong, Daniel I. Goldman, Yashwanth Nakka, Seth Hutchinson, Ye Zhao

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Robots have long mastered the art of walking on solid ground, navigating concrete sidewalks and wooden floors with the precision of a human. But step onto a beach, a gravel path, or a field of loose soil, and the rules change entirely. Unlike hard pavement, which offers a firm, unyielding pushback, loose ground like sand or dirt behaves unpredictably. It can act like a solid rock under a quick step, or flow like a thick liquid if the foot sinks too deep. This shifting nature makes it incredibly difficult for a robot to know how much force to apply or how to balance without sinking or slipping. For years, engineers have struggled to teach machines to walk on these unstable surfaces, often relying on simplified models that fail when the ground gives way.

A team of researchers has now developed a new way to teach humanoid robots to walk on loose, granular terrain. Their approach combines a more accurate understanding of how feet interact with sand and gravel with a learning method that allows the robot to sense the ground's stiffness in real time. By training the robot in a highly realistic virtual environment that mimics the physics of sinking and sliding, and then testing it on actual beaches and gravel piles, the team demonstrated that their robot could walk, run, and even jump on soft ground where previous models would have failed. This work represents a significant step toward giving robots the ability to operate in the messy, unstructured environments of the real world.

The core of this achievement lies in how the researchers modeled the interaction between the robot's foot and the ground. Traditional methods often treat the ground as a hard surface that simply stops the foot, or they use rough guesses to estimate how much the foot will sink. The new system, however, uses a physics-based model that calculates the resistance the ground offers as the foot pushes into it. This model accounts for how the angle of the foot, the speed of the movement, and the depth of the penetration all change the force the ground exerts back. Instead of guessing, the system computes these forces based on the physical properties of the material, whether it is dry sand, wet beach sand, or basalt rocks. This allows the robot to experience the same sinking and sliding forces in the simulation that it would feel in reality.

To make this work in practice, the researchers employed a two-stage learning process. First, they trained a "teacher" robot in the simulation that had access to perfect information about the ground, such as its exact stiffness and composition. This teacher learned how to walk efficiently on various surfaces. Then, they trained a "student" robot that could only see what its own sensors could detect, such as the movement of its joints and the forces acting on its body. The student learned to infer the nature of the ground from these internal signals alone, effectively guessing the terrain's properties just by feeling how it moved. Once trained, the student robot could adapt its walking style on the fly, lifting its feet higher when the ground was soft to avoid dragging, or adjusting its stride when the surface was uneven.

The results of this approach were tested in both high-fidelity computer simulations and real-world hardware experiments. In the simulations, the robot was placed on different types of granular terrain, including basalt, dry sand, and poppy seeds, which served as a fine, loose material. The robot trained with the new physics model successfully navigated these surfaces, maintaining balance and following walking commands at speeds up to 2.5 meters per second. In contrast, robots trained with older, simplified models struggled significantly, often falling or failing to move forward on the softer surfaces. The new system not only walked but also managed to run and jump, tasks that require precise timing and force application that are nearly impossible to achieve without a deep understanding of the ground's behavior.

When the team deployed the trained robot on a Unitree G1 humanoid in the real world, the results held up. They tested the robot on a basalt field, a dry sand volleyball court, and a beach. On the hard basalt, the robot walked smoothly. On the dry sand, it maintained its balance even at higher speeds, whereas older models would have lost their footing. Perhaps most impressively, the robot demonstrated the ability to sense when the ground was changing. As it walked from a harder surface onto a patch of softer sand, it automatically adjusted its gait, lifting its feet higher to prevent them from dragging into the loose material. This adaptation happened without any pre-programmed instructions about the specific location; the robot simply reacted to the changing resistance it felt through its legs.

The researchers also observed that the robot's movements became more efficient and gentle on soft ground. By estimating the stiffness of the terrain, the robot learned to apply just enough force to move forward without kicking up excessive amounts of sand or causing its joints to work too hard. This compliant behavior, where the robot absorbs the disturbance of the uneven ground rather than fighting against it, suggests a more natural and energy-efficient way of walking. The study confirms that for robots to truly operate in the wild, they must be able to understand and adapt to the complex, shifting nature of the ground beneath them, moving beyond the rigid assumptions of the past.

Technical Summary: Learning Terrain-Adaptive Humanoid Locomotion on Granular Terrain

Problem Statement
Humanoid locomotion on deformable granular terrain (e.g., sand, gravel, loose soil) remains a significant challenge due to complex, nonlinear foot-terrain interaction dynamics that are difficult to model. Unlike rigid ground, granular media exhibit multi-phase behavior, acting as solids or fluids depending on loading conditions, which generates large contact forces and causes severe sinkage and slip. Existing approaches generally fall into two categories with distinct limitations:

Model-based methods: Often rely on simplified resistive force theory (RFT) or terradynamics embedded in trajectory optimization. While physically grounded, these methods are typically validated on small-scale robots in controlled settings and struggle with the stochastic perturbations of outdoor environments.
Learning-based methods: Reinforcement learning (RL) approaches often use domain randomization over rigid contact models, failing to capture granular physics explicitly. Alternatively, recent works incorporating granular models often rely on ad-hoc heuristics, stitching together separate normal force models with tangential friction heuristics (e.g., Coulomb friction), which lack consistent physical grounding.

Methodology
The authors propose a physics-grounded framework that integrates a three-dimensional resistive force theory (3D RFT) contact model into an RL training pipeline, coupled with a terrain-adaptive teacher-student architecture.

3D RFT Contact Model: The core innovation is a contact solver based on 3D RFT, which calculates resistive forces on infinitesimal surface elements of the robot's foot. The model computes the force per area per depth ( $\alpha$ ) as a function of the body's velocity angle, orientation, and penetration depth. Unlike prior works that use simplified normal models with heuristic tangential components, this model derives both normal and tangential drag forces from a single, experimentally validated 3D formulation. This allows the simulation to capture realistic penetration and lateral drag without ad-hoc design choices. The model is implemented using NVIDIA Warp to enable high-frequency simulation (hundreds of thousands of frames per second) suitable for RL training.
Terrain-Adaptive Teacher-Student RL: To address the variability of real-world granular materials, the authors employ a teacher-student RL framework:
- Teacher Policy: Trained with access to privileged information, including ground-truth terrain material properties (specifically the media-dependent scaling coefficient). A Variational Autoencoder (VAE) is used to encode this privileged terrain information into a compact latent representation. The teacher learns to adapt its gait (swing foot clearance, frequency) based on this ground truth.
- Student Policy: A deployable policy trained via behavior cloning and representation matching. The student receives only proprioceptive history (joint positions, velocities, IMU data) and must infer the terrain latent variable to condition its actions. The student encoder is trained to mimic the teacher's latent output, effectively learning to estimate terrain stiffness from proprioception alone.
Training Pipeline: The system is trained in IsaacLab using Proximal Policy Optimization (PPO). A curriculum is employed where the robot first learns on hard terrain before transitioning to soft granular surfaces. Domain randomization is applied to material properties (density, friction coefficients) to ensure robustness.

Key Contributions

Integration of 3D RFT: The paper introduces a 3D RFT-based granular contact model into the simulation pipeline, replacing heuristic tangential models with a physically consistent formulation that captures realistic intrusion dynamics.
Terrain-Adaptive Policy: The authors develop a locomotion controller that adapts to varying terrain stiffness by learning to infer terrain properties from proprioceptive history, enabling adaptive swing foot clearance and gait frequency modulation.
Dynamic Multi-Gait Demonstration: The work demonstrates agile humanoid locomotion, including walking, running, circular walking, and jumping, across diverse granular terrains in both simulation and real-world hardware.

Results

Simulation Validation:
- Contact Model Accuracy: Comparisons against high-fidelity Material Point Method (MPM) simulations show that the 3D RFT model produces horizontal travel distances and sinkage profiles closest to the ground truth, outperforming rigid models, heuristic RFT, and jammed granular cone models.
- Policy Performance: Policies trained with the 3D RFT model achieved significantly higher success rates and lower tracking errors than those trained with rigid or heuristic models, particularly in challenging scenarios like deep sand and rough terrain.
- Dynamic Motion: The method successfully enabled jumping on simulated granular terrain, a capability where rigid-contact-trained policies failed due to inability to compensate for ground slip.
Hardware Experiments:
- The policy was deployed on a Unitree G1 humanoid robot across basalt, dry sand, and beach sand.
- Robustness: The 3D RFT-trained policies maintained stable locomotion at speeds up to 2.5 m/s on sand, whereas rigid-contact policies failed at speeds above 1.5 m/s.
- Adaptation: The teacher-student policy demonstrated superior velocity tracking compared to baselines. Analysis of ankle torques revealed that the proposed method achieved compliant ankle control, minimizing terrain disturbance and "stamping" motions.
- Terrain Transition: During transitions from stiff to soft terrain, the policy successfully increased swing foot clearance to prevent foot dragging, a behavior the baseline PPO (without terrain estimation) failed to execute, resulting in balance loss.

Significance and Claims
The paper claims to present the first demonstration of agile humanoid locomotion on real-world granular terrain. The authors emphasize that their approach overcomes the limitations of previous methods by providing a contact model that is physically grounded without resorting to heuristics. By successfully transferring a policy trained with a 3D RFT contact model to real-world environments, the work validates that explicit modeling of granular contact dynamics is critical for robust legged locomotion. Furthermore, the successful zero-shot terrain identification and adaptation via the student policy demonstrate that robots can learn to infer complex terrain properties from proprioception, enabling reliable operation in unstructured, deformable environments.

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