2026-08-20 · RA-L · 1 citations

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

Published at RA-L (the arXiv record still lists it as a preprint). 1 citations, as of the last refresh.

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 simulates 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 adaptation across a wide range of surface stiffness.

arXiv comment: 8 pages, 9 figures

Ten-minute slide kit

Six slides is the whole talk: what was broken, what people tried, what these authors did, what the numbers say, where it falls over, and the sentence people should remember.

SLIDE 1

The problem

I N recent years, a notable upsurge has been witnessed in the bipedal robotics sector, as it shows great potential for application in deformable and unstructured terrain, which constitutes a significant portion of the Earth's surface. Current bipedal robot locomotion controllers are predominantly optimized for rigid ground, as mainstream simulators [\[1\]](#page-7-0) [\[2\]](#page-7-1) [\[3\]](#page-7-2) rely on rigid-body dynamics that cannot capture the spatiotemporal heterogeneity of deformable terrains. This…

SLIDE 2

What came before

Not recoverable from the parsed text. Read this section in the paper yourself.

SLIDE 3

The method

In the robotics physics community, exploring methods that can accurately and efficiently simulate the deformation and stress of soft substrates upon contact with robots has always Manuscript received: April 28, 2025; Revised: August 30, 2025; Accepted: December 4, 2025. This paper was recommended for publication by Editor Aleksandra Faust upon evaluation of the Associate Editor and Reviewers' comments. This work was supported by General Research Fund under Grant No. 17204222. †Corresponding author lupeng@hku.hk,…

SLIDE 4

What they measured

To assess the advantages of our approach, we compare it with existing state-of-the-art methods for deformable terrain modeling. The data is collected from the policies trained with the same episodes on their respective models: *1) Implicit terrain adaptability:* Different from prior work testing on unquantified grass/sand, we evaluate system performance on standardized materials with defined stiffness grades. Specifically, we consider six distinct terrains, including four manufactured surfaces—rubber tiles, 60d,…

SLIDE 5

Where it breaks

Not recoverable from the parsed text. Read this section in the paper yourself.

SLIDE 6

One-line takeaway

MILD is presented, featuring a physics-grounded discrete-element contact solver that accurately simulates spatially varying foot-terrain interactions and train a terrain-aware locomotion controller via deep reinforcement learning with latent modulation and proprioceptive estimation.

Assembled from the paper's own PDF, parsed with its layout intact so tables and equations survive, 48,618 characters of it, then split on the paper's own section headings. Extractive, not generated: every sentence here is lifted from the paper. Check it before you present it.