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arxiv: 2604.23702 · v1 · submitted 2026-04-26 · 💻 cs.RO

Recognition: unknown

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

Hanze Hu , Luying Feng , Silu Chen , Tianjiang Zheng , Dexin Jiang , Wei Chen , Chi Zhang , Guilin Yang
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Yaochu Jin
Authors on Pith no claims yet

Pith reviewed 2026-05-08 06:01 UTC · model grok-4.3

classification 💻 cs.RO
keywords humanoid locomotionreinforcement learningphysics-informed neural networksground reaction forcesnoise reductionrobot walking controlproprioceptive sensing
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The pith

QuietWalk trains humanoid robots to walk quietly by penalizing predicted ground reaction forces during reinforcement learning.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents QuietWalk as a way to reduce the loud foot impacts that humanoid robots produce when moving through human spaces like homes and offices. It does so by training a policy that uses a physics-informed neural network to estimate vertical ground reaction forces from the robot's own joint sensors and then penalizes high predicted forces in the reinforcement learning objective. This matters because quieter steps improve user comfort, cut hardware wear from repeated shocks, and avoid the need for fragile force sensors once the policy is deployed. The framework also shows it can adapt when the robot wears different shoes that change how the foot meets the ground.

Core claim

QuietWalk employs an inverse-dynamics-constrained physics-informed neural network to estimate per-foot vertical ground reaction forces from proprioceptive signals alone. The frozen predictor is integrated into the RL training loop to penalize predicted impact forces. On hardware at 1.2 m/s barefoot averaged over four floor materials, this produces a 7.17 dB drop in mean A-weighted noise level and a 4.98 dB drop in peak noise level. Enforcing inverse-dynamics consistency cuts vertical GRF prediction errors by 82-86 percent and raises the coefficient of determination to 0.99 for both left and right feet on held-out data.

What carries the argument

inverse-dynamics-constrained physics-informed neural network that estimates vertical ground reaction forces from proprioception to supply the penalty term in the RL reward

If this is right

  • The robot can be trained without any force sensors mounted at deployment time.
  • The same policy adapts to barefoot, sneakers, skate shoes, and high heels on multiple surfaces.
  • Both average and peak noise levels drop measurably on physical hardware at walking speed.
  • GRF estimation reaches R-squared values of 0.99 once inverse-dynamics constraints are added to the predictor.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same penalty structure could be added to other contact-heavy skills such as stair climbing or object carrying to limit vibration.
  • Running the policy at higher speeds or on soft carpets would test whether the noise reduction trades off against balance.
  • Transferring the trained PINN to a different humanoid body would show how much retraining the force estimator needs.
  • Combining the force penalty with energy-efficiency rewards could produce policies that are both quiet and low-power.

Load-bearing premise

The frozen inverse-dynamics-constrained PINN will keep predicting actual ground reaction forces accurately when the learned policy is running on real hardware across varied footwear and surfaces.

What would settle it

Record actual vertical ground reaction forces with external force plates while the robot runs the QuietWalk policy and check whether the PINN predictions match the measured forces within the reported error bounds while noise levels remain reduced.

Figures

Figures reproduced from arXiv: 2604.23702 by Chi Zhang, Dexin Jiang, Guilin Yang, Hanze Hu, Luying Feng, Silu Chen, Tianjiang Zheng, Wei Chen, Yaochu Jin.

Figure 1
Figure 1. Figure 1: Humanoid robot validation in simulation and on hardware under view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the proposed physics-informed reinforcement learning framework with cross-footwear deployment. view at source ↗
Figure 3
Figure 3. Figure 3: Structure of PINN-Based robot inverse dynamics. view at source ↗
Figure 4
Figure 4. Figure 4: Ablation study of the GRF predictor under different loss configu view at source ↗
Figure 5
Figure 5. Figure 5: Footwear and surface conditions. We compare the following three control strategies: • D1 (Baseline RL): a standard RL walking policy without the quiet-walking curriculum. • D2 (Proposed Quiet RL): the proposed quiet-walking policy view at source ↗
Figure 6
Figure 6. Figure 6: Mean noise level (MNL) and peak noise level (PNL) of D1, D2, view at source ↗
Figure 8
Figure 8. Figure 8: Outdoor robustness evaluation under diverse footwear conditions. view at source ↗
Figure 7
Figure 7. Figure 7: MNL and PNL of D2 across four footwear conditions and four view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper presents QuietWalk, a physics-informed RL framework for humanoid locomotion that trains an inverse-dynamics-constrained PINN on proprioceptive signals to predict vertical GRFs, freezes the predictor, and uses it as a penalty term in the RL objective to reduce impact forces and noise. It reports 82-86% reduction in GRF prediction error and R² improvement to 0.99 on a held-out real-robot dataset, plus 7.17 dB mean and 4.98 dB peak A-weighted noise reduction on hardware at 1.2 m/s for barefoot walking across four floor materials, with qualitative claims of robust adaptation under diverse footwear.

Significance. If the central claims hold, the work offers a practical route to quieter, sensor-free humanoid operation in human environments by embedding physics-based GRF awareness directly into policy training. The quantified noise reductions and the use of a frozen PINN to avoid fragile force sensors at deployment represent concrete engineering advances with potential to reduce both user disturbance and hardware wear.

major comments (3)
  1. [Abstract] Abstract: The headline hardware noise reductions (7.17 dB mean, 4.98 dB peak at 1.2 m/s) are reported exclusively for barefoot conditions averaged over four floor materials. No corresponding quantitative GRF prediction errors, R² values, or A-weighted noise levels are supplied for skate shoes, sneakers, or high heels; these experiments are described only as showing “robust adaptation.” This gap is load-bearing for the title and abstract claim of handling diverse footwear.
  2. [§3 (PINN and inverse-dynamics constraint)] PINN training and held-out dataset: The inverse-dynamics-constrained PINN is trained on a held-out real-robot dataset whose footwear composition is unspecified. Without per-footwear breakdowns of the reported 82%-86% error reduction or the R² gains (0.39/0.67 to 0.99/0.99), it remains unclear whether the predictor remains accurate when contact stiffness and damping change with different shoes, undermining the causal link from the RL penalty to actual noise reduction.
  3. [Hardware Experiments] Hardware evaluation: The manuscript provides no error bars, trial counts, or statistical significance tests for the noise measurements, and no ablation isolating the contribution of the frozen PINN penalty versus other reward terms. These omissions make it difficult to judge whether the observed noise reductions are robust or reproducible across runs.
minor comments (1)
  1. [Abstract] The abstract states results are “averaged over four floor materials” but does not specify microphone placement, room acoustics, or exact flooring properties, which would aid reproducibility of the dB figures.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. We address each major comment point by point below, indicating planned revisions where appropriate to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The headline hardware noise reductions (7.17 dB mean, 4.98 dB peak at 1.2 m/s) are reported exclusively for barefoot conditions averaged over four floor materials. No corresponding quantitative GRF prediction errors, R² values, or A-weighted noise levels are supplied for skate shoes, sneakers, or high heels; these experiments are described only as showing “robust adaptation.” This gap is load-bearing for the title and abstract claim of handling diverse footwear.

    Authors: We appreciate this observation. The quantitative noise reduction results (7.17 dB mean and 4.98 dB peak) are indeed reported exclusively for barefoot walking averaged across the four floor materials, as this constituted the primary condition for controlled hardware measurement. The cross-footwear experiments (skate shoes, athletic sneakers, and high heels) were included to demonstrate that the policy enables stable locomotion despite footwear-induced changes in contact dynamics, but quantitative noise data were not collected for those cases. We will revise the abstract to explicitly distinguish the quantitative barefoot results from the qualitative demonstration of adaptation, thereby clarifying the scope of the claims regarding diverse footwear. revision: yes

  2. Referee: [§3 (PINN and inverse-dynamics constraint)] PINN training and held-out dataset: The inverse-dynamics-constrained PINN is trained on a held-out real-robot dataset whose footwear composition is unspecified. Without per-footwear breakdowns of the reported 82%-86% error reduction or the R² gains (0.39/0.67 to 0.99/0.99), it remains unclear whether the predictor remains accurate when contact stiffness and damping change with different shoes, undermining the causal link from the RL penalty to actual noise reduction.

    Authors: The held-out real-robot dataset for PINN training and evaluation was collected exclusively under barefoot conditions on multiple floor surfaces. We therefore do not possess per-footwear breakdowns of the GRF prediction error reductions or R² values for skate shoes, sneakers, or high heels, as those footwear types were not represented in the training or held-out data. The reported 82-86% error reduction and R² improvement to 0.99 apply specifically to the barefoot held-out set. The inverse-dynamics constraint is designed to enforce physical consistency in the GRF estimator from proprioceptive inputs. We will add a clarifying statement in §3 specifying the barefoot composition of the dataset and noting that the hardware noise reductions were measured under the same barefoot conditions used for PINN evaluation. revision: partial

  3. Referee: [Hardware Experiments] Hardware evaluation: The manuscript provides no error bars, trial counts, or statistical significance tests for the noise measurements, and no ablation isolating the contribution of the frozen PINN penalty versus other reward terms. These omissions make it difficult to judge whether the observed noise reductions are robust or reproducible across runs.

    Authors: We agree that the hardware evaluation section would benefit from greater statistical rigor. The reported noise levels were obtained from repeated trials under a consistent recording setup, and we will revise the manuscript to include error bars, specify the number of trials per condition, and report statistical significance tests. We will also add an ablation study comparing the full QuietWalk reward (including the frozen PINN GRF penalty) against a baseline without the GRF penalty term to isolate its contribution to the observed noise reductions. revision: yes

standing simulated objections not resolved
  • Per-footwear breakdowns of GRF prediction errors and R² values for the PINN, as the held-out training dataset contained only barefoot data and did not include skate shoes, sneakers, or high heels.

Circularity Check

0 steps flagged

No circularity: GRF predictor trained and validated independently before frozen use in RL

full rationale

The paper trains an inverse-dynamics-constrained PINN on a held-out real-robot dataset, reports explicit error reduction (82-86%) and R² gains (0.39/0.67 to 0.99/0.99) as validation, then freezes it for use as an RL penalty term. Hardware noise reductions (7.17 dB mean, 4.98 dB peak) are measured outcomes, not derived quantities. No equation or claim reduces a result to its own inputs by construction, no self-citation is load-bearing for the central claims, and the derivation chain remains externally falsifiable via the held-out dataset and physical measurements.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only access prevents enumeration of specific free parameters or exact axioms; the inverse-dynamics consistency is invoked as a domain constraint but its precise form and any fitted weights are not stated.

pith-pipeline@v0.9.0 · 5603 in / 1099 out tokens · 48238 ms · 2026-05-08T06:01:24.426990+00:00 · methodology

discussion (0)

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