Robust bipedal locomotion on flowable slopes via foot-driven terrain manipulation
Authors: Deniz Kerimoglu, Junnosuke Kamohara, Jiyeon Maeng, Ziwon Yoon, Seth Hutchinson, Ye Zhao, Daniel I. Goldman
Abstract
Bipedal robots are challenging to control because they operate close to instability, where small variations in foot-terrain contact can rapidly destabilize locomotion. On rigid terrain, bipedal robots mitigate this fragility by using well-established contact mechanics and control strategies. On flowable surfaces such as granular slopes, foot contact can induce large surface deformations and solid-fluid-like transitions, coupling terrain effects with robot dynamics, leading to underperformance or failure. This is partly due to the lack of reliable methods to represent the dynamics of flowable terrain, making it difficult to account for terrain effects in locomotion design. Here, we investigate how controlling terrain response can improve bipedal locomotion on granular slopes by studying the terradynamics of cleated feet, thin plates emanating from the foot soles. Systematic studies of a small-scale (1.4 kg) robophysical biped reveal that cleats with sparse and dense spacing lead to excessive terrain yielding and resistance, respectively, degrading performance and leading to failure. An intermediate cleat spacing distributes interaction forces to maintain substrate stresses near (or below) the yield threshold, enabling walking on granular slopes up to 30 degrees. Guided by these principles, we design a foot that actively adjusts cleat depth and accommodates both rigid and granular terrain. We also demonstrate that the principles of effective foot-terrain interaction translate to a larger (15 kg) autonomous biped. Our study presents an alternative to conventional body-centric robot control approaches, which regulate terrain-induced effects through body motion, by instead regulating terrain interactions through limb-centric approach.
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/
Junnosuke Kamohara, Feiyang Wu, Andy Ningan Zong +4
Model-free reinforcement learning has enabled impressive humanoid locomotion; however, control on steep slopes remains largely unexplored. Unlike flat or discrete terrains, sloped terrains impose a persistent gravitational bias that demands simultaneous stability and posture control. Consequently, under generic reward formulations, policies can converge to slow, conservative low-center-of-mass (CoM) crouched gaits. In this work, we propose a novel two-stage physics-guided framework, dubbed HumoSlope, dedicated to robust humanoid locomotion on diverse sloped terrains. Specifically, Stage I establishes a terrain-consistent balance prior by introducing a slope-adaptive Zero Moment Point (ZMP) regularizer evaluated directly on the local inclined support plane rather than a world-horizontal reference. To prevent the resulting policy from defaulting to a crouched posture, Stage II introduces the Biomechanical Slope Gait Adapter (BSGA). Utilizing extracted macroscopic terrain descriptors as privileged, training-only signals, BSGA dynamically gates soft reward priors to modulate CoM height and lower-limb coordination based on the estimated slope geometry -- encouraging hip-dominant uphill propulsion and knee-oriented downhill braking. Crucially, the deployed actor remains entirely proprioceptive, requiring no online exteroceptive sensing. Extensive Sim-to-Real experiments demonstrate that our framework effectively mitigates posture degeneration and enables blind, continuous traversal of outdoor grass slopes up to 62.7% (32.1∘), validating a physics-guided approach to challenging slope terrain adaptation.
Deploying legged robots in extra-terrestrial environments includes many challenges due to complex terrain interactions, energy, and thermal constraints. For effective mechanical design of a lunar exploration quadrupedal robot, careful consideration of motor torques, energy expenditure, and cost of transport is required. The lunar surface is composed of granular regolith, which impacts the locomotion of legged robots and their performance. Locomotion algorithms trained with rigid contact assumptions are also ineffective when applied to environments with soft contacts, such as granular surfaces, which can result in instability and poor tracking. In this report, the physical modelling of the granular lunar surface-robot foot contacts is applied to a simulation environment with locomotion trained using Reinforcement Learning. A comparison is conducted between the policy trained on rigid contact and soft contact environments, analysing the gait and locomotion performance metrics. The analysis demonstrates that soft contacts simulating regolith surfaces pose additional challenges for Reinforcement Learning based training, result in a qualitatively different gait, and increase the overall energy expenditure.