# QuietWalk: Physics-Informed Reinforcement Learning for Ground Reaction Force-Aware Humanoid Locomotion Under Diverse Footwear

arXiv: https://arxiv.org/abs/2604.23702 · HTML: https://mlsanity.com/paper/2604.23702/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for robot locomotion and manipulation, one of 15 directions in Deep reinforcement learning methods.
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 26 Apr 2026.

## Placed in

- Deep reinforcement learning methods / [RL for robot locomotion and manipulation](https://mlsanity.com/deeprl/rl-for-robot-locomotion-and-manipulation/)

## Builds on (most cited first, 17 of 17)

- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Real-World Humanoid Locomotion with Reinforcement Learning](https://mlsanity.com/paper/2303.03381/) (2023)
- [Rapid Locomotion via Reinforcement Learning](https://mlsanity.com/paper/2205.02824/) (2022)
- [Legged Locomotion in Challenging Terrains using Egocentric Vision](https://mlsanity.com/paper/2211.07638/) (2022)
- [Reinforcement Learning for Versatile, Dynamic, and Robust Bipedal Locomotion Control](https://mlsanity.com/paper/2401.16889/) (2024)
- [DreamWaQ: Learning Robust Quadrupedal Locomotion With Implicit Terrain Imagination via Deep Reinforcement Learning](https://mlsanity.com/paper/2301.10602/) (2023)
- [Adapting Rapid Motor Adaptation for Bipedal Robots](https://mlsanity.com/paper/2205.15299/) (2022)
- [Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling](https://mlsanity.com/paper/2109.06407/) (2021)
- [Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks](https://mlsanity.com/paper/2308.12716/) (2023)
- [Physics-informed Neural Networks to Model and Control Robots: a Theoretical and Experimental Investigation](https://mlsanity.com/paper/2305.05375/) (2023)
- [Olaf: Bringing an Animated Character to Life in the Physical World](https://mlsanity.com/paper/2512.16705/) (2025)
- [Learning Quiet Walking for a Small Home Robot](https://mlsanity.com/paper/2502.10983/) (2025)
- [Exploring Consequential Robot Sound: Should We Make Robots Quiet and Kawaii-et?](https://mlsanity.com/paper/2104.02191/) (2021)
- [QuietPaw: Learning Quadrupedal Locomotion with Versatile Noise Preference Alignment](https://mlsanity.com/paper/2503.05035/) (2025)
- [Analytical Model and Experimental Testing of the SoftFoot: an Adaptive Robot Foot for Walking over Obstacles and Irregular Terrains](https://mlsanity.com/paper/2401.05318/) (2024)
- [Minimizing Acoustic Noise: Enhancing Quiet Locomotion for Quadruped Robots in Indoor Applications](https://mlsanity.com/paper/2506.23114/) (2025)

## Abstract (arXiv)

Humanoid robots operating in human-centered environments (e.g., homes, hospitals, and offices) must mitigate foot--ground impact transients, as impact-induced vibration and noise degrade user experience and repeated impacts accelerate hardware wear. However, existing low-noise locomotion training often relies on kinematic proxy objectives or fragile force sensors, and footwear-induced changes in contact dynamics introduce distribution shifts that hinder policy generalization.We present QuietWalk, a physics-informed reinforcement learning framework for ground-reaction-force-aware humanoid locomotion under diverse footwear conditions. QuietWalk employs an inverse-dynamics-constrained physics-informed neural network (PINN) to estimate per-foot vertical ground reaction forces (GRFs) from proprioceptive signals, and integrates the frozen predictor into the RL training loop to penalize predicted impact forces without requiring force sensors at deployment.On a held-out real-robot dataset, enforcing inverse-dynamics consistency reduces vertical GRF prediction errors by 82%-86% compared with a purely supervised predictor and improves the coefficient of determination from 0.39/0.67 to 0.99/0.99 for the left/right feet. On hardware at 1.2 m/s (barefoot; averaged over four floor materials), QuietWalk reduces mean A-weighted noise level by 7.17 dB and peak noise level by 4.98 dB under a consistent recording setup. Cross-footwear experiments (barefoot, skate shoes, athletic sneakers, and high heels) across multiple surfaces further demonstrate robust adaptation to footwear-induced contact variations.