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MILD: Tractable Terrain Modeling for Learning Improved Bipedal Locomotion on Deformable Surfaces

Zeren Luo, Jiahui ZHANG, Zhe Xu, Wanyue Li, Xinqi Li, Xuechao Chen, Zhangguo YU, Annan Tang, Peng Lu

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AI summary

Key figure (auto-extracted from paper)

A physics-grounded discrete-element contact model combined with latent-modulated reinforcement learning enables bipedal robots to robustly adapt to and traverse highly deformable terrains in both simulation and reality.

Bipedal locomotion Deformable terrain Contact modeling Reinforcement learning Granular media Robot simulation

Problem

Current simulators rely on rigid-body dynamics or oversimplified soft-surface models that fail to capture the spatiotemporal heterogeneity of yielding terrains, limiting realistic training data and controller adaptation for bipedal robots.

Approach

The authors introduce MILD, a tractable discrete-element contact solver that models non-uniform foot-terrain interactions, integrated with a terrain-aware reinforcement learning controller that uses latent modulation and proprioceptive estimation to adapt online.

Key results

Tractable discrete-element contact solver capturing eccentric penetration and heterogeneous force distribution
RL controller with latent modulation enabling implicit adaptation to varying terrain compliance
Superior robustness and energy efficiency compared to state-of-the-art simulators and controllers
Successful hardware demonstrations of online terrain identification and adaptation across diverse stiffness levels

Why it matters

Enables reliable bipedal locomotion on complex yielding terrains, advancing applications in disaster response, planetary exploration, and unstructured environment navigation.

Abstract

Enabling robots to walk on yielding terrain is vital for applications ranging from disaster response to planetary exploration. While bipedal robots hold immense potential, their locomotion on deformable surfaces remains limited as current simulators fail to capture the spatiotemporal heterogeneity of such yielding substrates. We present MILD, featuring a physics- grounded discrete-element contact solver that accurately simu- lates spatially varying foot-terrain interactions. Complementing this model, we train a terrain-aware locomotion controller via deep reinforcement learning with latent modulation and proprioceptive estimation. Quantitative comparisons against state-of-the-art methods show our approach generates more diverse and realistic contact scenarios during training, resulting in controllers that exhibit natural adaptation on real deformable surfaces. Through hardware experiments, we demonstrate the system’s capability for online terrain identification and adap- tation across a wide range of surface stiffness.

Index terms

Machine Learning for Robot Control Reinforcement Learning