Minimizing Acoustic Noise: Enhancing Quiet Locomotion for Quadruped Robots in Indoor Applications

Buqing Nie; Yang Zhang; Yue Gao; Zhanxiang Cao

REVIEW 4 major objections 5 minor 33 references

Minimizing Acoustic Noise: Enhancing Quiet Locomotion for Quadruped Robots in Indoor Applications

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A new control policy that slows feet just before ground contact cuts a quadruped's walking noise by about 8 dBA on indoor surfaces, the paper reports.

desk verdict A plausible control-only 8 dBA noise reduction on a real quadruped, but the headline is partly confounded by the quiet factor's speed trade-off and needs matched-actual-speed data. read the letter →

arxiv 2506.23114 v1 pith:UX6WMSBY submitted 2025-06-29 cs.RO

Zhanxiang Cao , Buqing Nie , Yang Zhang , Yue Gao This is my paper · ORCID

classification cs.RO

keywords quadrupedrobotsacousticnoisereductionquietlocomotionfoot-groundimpactreinforcementlearninggaitphaseestimationindoorserviceroboticsfactor

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to show that quadruped robots can be made substantially quieter indoors by changing only the control policy, not the hardware. Its central claim is that foot-ground impacts are the dominant noise source and that a learned controller can be trained to let each foot down softly. The proposed method, MUTE, estimates the phase of each leg's gait cycle and adds a reward that penalizes high foot velocity just before contact, with a dialable quiet factor that trades speed for silence. In experiments on wood, carpet, and tile, MUTE with the quiet factor at its maximum measured about 8 dBA less mean noise than the comparison controllers at the same locomotion speed, roughly a 2.5-fold drop in sound pressure. If this stands, quiet operation in hospitals, offices, and homes would not require new motors or padding; it would be a software property of the walk.

What carries the argument

The load-bearing mechanism is a phase-gated foot-velocity penalty. A network estimates each leg's phase $\hat{\varphi}_t$ from the robot's proprioceptive history, telling the policy when a foot is about to strike. The reward term $r_\varphi = w_d \sum_i e^{\hat{\varphi}_i} v_{f_i,\text{drop}}^2 + w_r \sum_i e^{-\hat{\varphi}_i} v_{f_i,\text{raise}}^2$ penalizes downward foot velocity ever more strongly as the phase nears 1 through its negatively weighted first sum, and the quiet factor $\beta$ in the total reward $r = \beta r_\varphi + (1-k\beta) r_v + r_o$ scales that penalty against the task reward $r_v$, making the noise-speed trade-off explicit and controllable.

What would settle it

Measure the same robot with an independent microphone at a standing person's ear height while it walks on a hard floor, and compare MUTE to the baseline at matched speed; if the ear-height reduction approaches zero even though the trunk-mounted reading still shows roughly 8 dBA, the claimed human-relevant benefit would not survive. A second check would use motion capture of the feet: if two policies with measured impact velocities that are equal still differ by several dBA, then impact velocity alone does not explain the noise difference.

Watch

Extended reading notes

Core claim

The central discovery, as the authors state it, is that acoustic noise during quadruped locomotion is a controllable output of the gait. Sound amplitude is modeled as proportional to the velocity of the foot at the moment of impact, so the objective becomes shaping the foot trajectory to arrive slowly. MUTE learns a policy in simulation using an estimated phase variable $\hat{\varphi}_t$ for each leg; as the phase approaches 1 (contact), a phase reward term imposes a growing penalty on squared drop-foot velocity, while a small reward encourages consistent foot lift. A scalar quiet factor $\beta \in [0,1]$ blends this phase reward with the usual velocity-tracking reward, letting the operator choose between speed and quiet. On wood, carpet, and tile, the method reports an average reduction of approximately 8 dBA compared with the baselines at matched speed, which corresponds to about 2.5 times lower sound pressure, and the reduction persists even when $\beta = 0$.

Load-bearing premise

The reduction depends on foot-ground impact velocity being the dominant and controllable source of the robot's noise, and on the 30-cm-above-ground, robot-mounted microphone capturing the sound field that people actually perceive.

Editorial extensions

If this is right

At matched commanded speed, MUTE lowers mean and peak noise on wood, carpet, and tile, with the largest measured reductions on hard surfaces.
Dialing the quiet factor from 0 to 1 monotonically reduces noise while raising velocity-tracking error only slightly, giving a field-adjustable noise-speed knob.
Because MUTE is quieter than the baselines even at $\beta = 0$, the phase-aware reward appears to improve gait smoothness beyond explicitly trading away speed.
On a 91.7-meter mixed-surface indoor walk, the measured mean noise of 68.25 dBA stays below the 70 dBA hearing-safety threshold, and the paper argues the human-perceived level at ear height would be lower still.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A testable extension the paper does not explore is closed-loop $\beta$ control, where a higher-level planner raises the quiet factor in a hospital corridor at night and lowers it outdoors, treating the quiet factor as a command input rather than a fixed setting.
The paper leaves the human-relevance question open: its microphone rides on the robot near the feet, and the claim that ear-height noise is lower relies on spherical spreading, which reflective floors and A-weighting could weaken in practice.
The same phase-gated contact-velocity reward could transfer to other impact-noise systems, such as bipedal walkers, drone landing controllers, or manipulators setting objects down, whenever contact velocity is a controllable output.
The 8 dBA headline is an average over surfaces and baselines; the paper's surface-by-surface table shows variation of several dBA, so a real deployment would likely need surface-specific tuning to guarantee the advertised reduction.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The paper reports a control-only framework that cuts measured dBA by roughly 8 on a Unitree Go1 across wood, carpet, and tile, using a phase-based foot-velocity penalty and a "quiet factor" beta that trades speed for noise. That is a genuinely useful engineering result—no hardware changes, real robot, multiple surfaces, and trial-level statistics. The combination of a learned phase estimator, foot-velocity rewards, and a scalar trade-off is not something I've seen in the legged-locomotion noise papers.

The soft spot is the headline. The 8 dBA average in Table II is at a common 0.5 m/s command, not at matched actual speed. Eq. (6) deliberately scales the velocity-tracking reward down by (1-k*beta)=0.8 at beta=1, and Fig. 6 confirms velocity tracking error climbs with beta. So part of the measured gap likely comes from MUTE beta=1 simply walking slower. The authors do include a matched-actual-speed plot on wood (Fig. 4), which is the right control, but that figure doesn't cover all three surfaces and doesn't produce the 8 dBA average. The contribution statement "equivalent locomotion speeds" is therefore stronger than the evidence. The fix is straightforward: report actual speeds from the logs for every trial, or re-run with speed matched, and caveat the averaged claim or re-report as a speed-noise trade-off.

Other issues are minor. No code or raw recordings, so it's not independently checkable. The microphone at 30 cm on the trunk captures the near field; the perceptual benefit at ear height is inferred, not measured. No significance tests on the dBA differences, though the std devs are reported. These are all revisable in review.

Overall the core mechanism is plausible and the direction of the result is credible. This is incremental—it doesn't change how legged locomotion is understood—but it's a solid application paper that could be useful to anyone deploying quadrupeds indoors. I'd send it to peer review and ask for the matched-speed data plus a clearer statement of what the 8 dBA does and does not mean.

Referee Report

4 major / 5 minor

Summary. The paper proposes MUTE, a learned quadruped locomotion controller that combines LSTM-based phase estimation, a phase-dependent foot-velocity penalty in the reward, and a scalar 'quiet factor' β that trades speed against noise. Policies are trained in simulation with PPO and deployed on a Unitree Go1 EDU without further tuning. Real-world experiments measure mean and peak A-weighted sound levels on wood, carpet, and tiles at a 0.5 m/s command, and also include a speed sweep and a long-distance mixed-surface walk. The central claim is that MUTE achieves an average noise reduction of approximately 8 dBA compared with DreamWaQ and built-in MPC baselines at equivalent locomotion speeds.

Significance. If the quantitative claim is substantiated, this is a valuable contribution to an underexplored area: noise-aware locomotion control for legged robots. The paper's strengths are its real-robot evaluation on three surfaces, comparison against two baselines, a tunable trade-off parameter (β), and a long-duration deployment test. The evaluation is not circular: the acoustic measurements are external outcomes and are not used to fit the policy. However, the headline result currently rests on commanded rather than measured speed, the measurement chain is under-specified, and no statistical inference is provided. These issues are fixable but need to be addressed before the claim of an 8 dBA reduction at equivalent speeds can be accepted.

major comments (4)

[§III-D, Table II; Contribution 3] The headline 'equivalent locomotion speeds' is not supported by the reported data. Table II reports only the commanded 0.5 m/s and no measured actual speed per method, while Eq. (6) with k=0.2 explicitly scales the velocity-tracking reward by (1−kβ)=0.8 when β=1, and Fig. 6 shows velocity-tracking squared error increasing with β. The average 7.78 dBA reduction of MUTE β=1 over DreamWaQ (64.80 vs 72.58 dBA) could therefore partly reflect slower actual walking. Fig. 4 uses EKF-based actual speed, but it is a separate experiment on wood and is not linked to the Table II trials. Please report per-method actual speeds (or matched-speed runs) for the Table II conditions, or re-scope the claim as a tunable speed–noise trade-off.
[§III-E, Fig. 6; §III-D] The numerical support for the trade-off is incomplete. The velocity tracking squared error at β=1 is about 0.012 m²/s², corresponding to an RMS error of roughly 0.11 m/s on a 0.8 m/s command, which is not self-evidently a 'minor compromise.' Moreover, no statistical tests or confidence intervals are provided for any MNL/PNL difference; the five-trial mean ± std in Table II does not establish that the 8 dBA gap is significant or that the ordering across methods is reliable. Please add paired tests or bootstrap intervals and report actual speed or velocity error in physical units.
[§III-A, §III-B, Eq. (10); §I-C] The measurement chain is under-specified for an absolute dBA claim. No microphone model, calibration procedure, frequency-weighting implementation, or ambient-noise levels during trials are given; the sensor is mounted on the robot and samples at 20 Hz, which is slow for capturing impact transients, so the PNL values may be underestimated. The assertion in §I-C that motor/fan noise is 'relatively minor' is not backed by measurements, and a robot-mounted sensor may pick up such contributions. Raw recordings or a calibration check are needed to rule out systematic bias in the 8 dBA number.
[§II, Eq. (9); §III-D] The causal mechanism is assumed rather than demonstrated. The reward in Eq. (9) penalizes foot drop velocity, but the paper reports no real-world measurements of foot contact velocity, ground reaction forces, or high-speed motion capture to show that MUTE actually reduces impact velocity. Because β=1 also scales down the speed reward, the relative contribution of the phase reward versus the speed trade-off to the measured noise reduction is not identifiable from the current data. An ablation that fixes actual speed (or reports contact velocity) would make the mechanism claim load-bearing.

minor comments (5)

[§III-D] The text states that on surfaces 'such as wood and tiles, MUTE exhibits the most significant reductions,' but Table II shows the largest absolute reduction versus DreamWaQ is on carpet (9.42 dBA), not wood (7.73 dBA) or tiles (6.19 dBA).
[Eq. (10)] Equation (10) defines unweighted SPL but labels it dBA; A-weighting is a frequency-domain correction and should be specified separately, including the filter or meter standard used.
[§III-E, Fig. 6] There are typos ('shows a increase') and the phrase 'suggesting a minor compromise' should be replaced with the reported velocity error value and its physical interpretation.
[§III-F] The statement that 68.25 dBA is below a '70 dBA threshold considered safe for human hearing' and that attenuation makes human-perceived noise lower assumes a particular human distance; please cite a standard and state the assumed distance.
[§III-A] The paper does not state whether the five trials per surface were conducted on different days, whether ambient noise was monitored and subtracted, or whether the sensor was calibrated before each session; please clarify.

Circularity Check

1 steps flagged · score 2.0 of 10

Core noise measurements are external and not fitted, so the comparison is not circular; however, the 8 dBA headline is partially a built-in speed concession from the quiet factor (Eq. 6), not fully independent discovery.

other [Sec. II-C (Eq. 6), Sec. I-D (Contribution 3), Sec. III-D (Table II), Fig. 6 caption]
"β = 1 emphasizes noise minimization at the cost of speed; ... For the experiments, k is set to 0.2; The velocity tracking squared error shows a increase as β approaches 1, indicating an active compromise in speed; ... the robot is instructed to traverse at a constant speed of 0.5 m/s; ... an average noise reduction of 8 dBA compared to baseline methods at equivalent locomotion speeds."

The quiet factor β is a design knob, not a fitted parameter, but it is constructed to sacrifice speed: Eq. (6) scales the velocity-tracking reward by (1−kβ)=0.8 at β=1, and the text confirms β=1 'emphasizes noise minimization at the cost of speed.' Fig. 6 then shows velocity tracking error grows as β→1, so the policy walks slower at a given command. The paper's own Fig. 4 establishes that MNL increases with actual speed. Since the headline 8 dBA average is taken from Table II at a common commanded 0.5 m/s without any per-method actual-speed reporting, part of the Table II margin is the definitional speed concession converted into measured noise reduction through the paper's own speed–noise relation, rather than a quieter gait discovered independently of the reward design.

full rationale

The central measurement (dBA sound pressure) is an external outcome that is never used to fit or train the policy: training is done in Isaac Gym without acoustic modeling, the paper stating that 'Given the constraints of acoustic modeling in physical simulations, this study addresses the problem by imposing constraints on the foot's velocity,' and the noise readings in Table II and Fig. 4 are independent physical measurements against external baselines (DreamWaQ and the built-in MPC). The reference list contains no self-citations by this paper's authors, so no load-bearing argument reduces to an author's own unverified prior work. The physics assumption that sound amplitude is proportional to foot contact velocity (derived from Ref. [19]) is an input proxy, not a fitted result, and the measured outcomes could have falsified it; the reward function itself contains no acoustic model, so the optimizer is not trained on the measured quantity. The one partially circular element is the 'equivalent locomotion speeds' claim: the quiet factor β=1 is defined to sacrifice speed, Eq. (6) down-weights velocity tracking by construction, Fig. 6 confirms the resulting speed compromise, and the paper's own Fig. 4 shows noise scales with actual speed. The headline 8 dBA figure, computed from Table II at a fixed commanded 0.5 m/s with no actual-speed data, therefore includes a noise margin that is a built-in speed concession rather than an independently discovered quieter gait. Independent content does remain: MUTE with β=0 (which does not sacrifice speed) is about 3.7 dBA quieter than DreamWaQ at the same command in Table II, and the matched-actual-speed experiment on wood (Fig. 4) shows MUTE β=1 quieter at equal actual speed. Because the core comparison is external, self-contained, and not fitted, the overall circularity is minor; score 2, reflecting that part of the headline gain reduces by construction to the reward's built-in speed trade-off rather than to a fully independent result.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The method introduces no physical entities beyond a scalar command input (beta). The central claim depends mainly on hand-tuned reward weights and domain assumptions about acoustic physics and sim-to-real transfer.

free parameters (4)

Phase reward weights w_d and w_r = -0.05 and 0.01
Hand-chosen in Table I; these directly determine the strength of the foot-impact penalty that produces quieter gait.
Speed trade-off coefficient k = 0.2
Set in Section II-C in Eq. (6); controls how much beta reduces the velocity-tracking reward.
Loss weights lambda_fwd and lambda_phi = not reported
From Eq. (2); balance forward-model and phase-estimation losses, but their values are not given.
PD gains Kp and Kd = 20 and 0.5
Section II-D, action space; chosen controller gains that affect foot impact dynamics.

assumptions (4)

domain assumption Sound amplitude is proportional to the square root of impact energy, making foot contact velocity the key noise driver.
Section II opening; cites [19] for generic physical shapes, not validated for the Go1's feet or the measured dBA.
domain assumption Motor and joint noise is relatively minor compared with foot-ground impact noise.
Section I-C states this and excludes hardware changes from scope.
domain assumption The phase estimator trained in simulation transfers to the real robot without tuning.
Section III-A2 states direct sim-to-real transfer with proprioceptive sensors only; no real-world phase ground truth is available.
domain assumption A-weighting and the 30 cm onboard microphone position provide a meaningful measure of human-perceived indoor noise.
Section III-A2 and III-B; no independent calibration or listener study is reported.

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Cite this review

Pith. "Pith review of Minimizing Acoustic Noise: Enhancing Quiet Locomotion for Quadruped Robots in Indoor Applications." pith.science (2026). https://pith.science/paper/UX6WMSBY

@misc{pith2026250623114,
  author       = {Pith},
  title        = {Pith review of: Minimizing Acoustic Noise: Enhancing Quiet Locomotion for Quadruped Robots in Indoor Applications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UX6WMSBY}},
  note         = {Machine review of arXiv:2506.23114}
}

read the original abstract

Recent advancements in quadruped robot research have significantly improved their ability to traverse complex and unstructured outdoor environments. However, the issue of noise generated during locomotion is generally overlooked, which is critically important in noise-sensitive indoor environments, such as service and healthcare settings, where maintaining low noise levels is essential. This study aims to optimize the acoustic noise generated by quadruped robots during locomotion through the development of advanced motion control algorithms. To achieve this, we propose a novel approach that minimizes noise emissions by integrating optimized gait design with tailored control strategies. This method achieves an average noise reduction of approximately 8 dBA during movement, thereby enhancing the suitability of quadruped robots for deployment in noise-sensitive indoor environments. Experimental results demonstrate the effectiveness of this approach across various indoor settings, highlighting the potential of quadruped robots for quiet operation in noise-sensitive environments.

Figures

Figures reproduced from arXiv: 2506.23114 by the authors.

**Figure 1.** Noise-sensitive indoor scenarios. Quadruped robots operating in noise-sensitive environments, such as hospitals, offices, and residential spaces, must minimize noise levels to maintain a comfortable atmosphere. especially in indoor spaces or environments with specific noise constraints, the noise they produce becomes a critical concern. Noise pollution may result in inconvenience, give rise to unexpected disturbance… view at source ↗

**Figure 2.** Proposed Controller Structure. The controller features a Long Short-Term Memory (LSTM) encoder-decoder network for phase estimation and latent variable representation. The quiet factor β serves as an input to the policy network, which is trained to balance noise reduction and speed. The gray area indicates the training phase conducted in simulation, while the green area highlights the transition to real-world implem… view at source ↗

**Figure 3.** Experimental Setup for Simulation and RealWorld Transfer. The left panel depicts the simulation environment used for training in Isaac Gym, while the right panel presents the real robot setup, equipped with a sound pressure sensor for noise measurement in actual environments. The sensor updates at a frequency of 20 Hz to capture real-time noise levels during robot locomotion. B. Evaluation Metrics To assess the no… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Noise levels on wooden flooring at different actual speeds. The solid lines represent the MNL, while the lightcolored bands indicate the PNL. The x-axis denotes the robot’s actual speed, calculated using EKF [31], [32], rather than the commanded speed. MUTE consistent…

**Figure 5.** Figure 5: Noise levels during long-distance walking on mixed surfaces. The colored line represents the robot’s path, with color variations indicating noise levels at different points. Dotted lines divide the various surface types. The total path is approximately 91.7 meters, wit…

**Figure 6.** Figure 6: Noise levels on wooden flooring at 0.8 m/s command for different β values. The red line represents the MNL, the light-colored bands indicate the PNL, and the blue line denotes the velocity tracking squared error. Noise levels decrease as β increases, with the MNL drop…

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G. Bledt, M. J. Powell, B. Katz, J. Di Carlo, P. M. Wensing, and S. Kim, “Mit cheetah 3: Design and control of a robust, dynamic quadruped robot,” in 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) , 2018, pp. 2245–2252

2018
[33]

What is a safe noise level for the public?

D. J. Fink, “What is a safe noise level for the public?” pp. 44–45, 2017

2017

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Learning agile and dynamic motor skills for legged robots,

J. Hwangbo, J. Lee, A. Dosovitskiy, D. Bellicoso, V . Tsounis, V . Koltun, and M. Hutter, “Learning agile and dynamic motor skills for legged robots,” Science Robotics, vol. 4, no. 26, p. eaau5872, 2019

2019

[2] [2]

Learning quadrupedal locomotion over challenging terrain,

J. Lee, J. Hwangbo, L. Wellhausen, V . Koltun, and M. Hutter, “Learning quadrupedal locomotion over challenging terrain,” Science robotics, vol. 5, no. 47, p. eabc5986, 2020

2020

[3] [3]

Learning robust perceptive locomotion for quadrupedal robots in the wild,

T. Miki, J. Lee, J. Hwangbo, L. Wellhausen, V . Koltun, and M. Hutter, “Learning robust perceptive locomotion for quadrupedal robots in the wild,” Science robotics, vol. 7, no. 62, p. eabk2822, 2022

2022

[4] [4]

Anymal parkour: Learning agile navigation for quadrupedal robots,

D. Hoeller, N. Rudin, D. Sako, and M. Hutter, “Anymal parkour: Learning agile navigation for quadrupedal robots,” Science Robotics , vol. 9, no. 88, p. eadi7566, 2024

2024

[5] [5]

Extreme parkour with legged robots,

X. Cheng, K. Shi, A. Agarwal, and D. Pathak, “Extreme parkour with legged robots,” in 2024 IEEE International Conference on Robotics and Automation (ICRA) . IEEE, 2024, pp. 11 443–11 450

2024

[6] [6]

Rma: Rapid motor adaptation for legged robots,

A. Kumar, Z. Fu, D. Pathak, and J. Malik, “Rma: Rapid motor adaptation for legged robots,” arXiv preprint arXiv:2107.04034 , 2021

arXiv 2021

[7] [7]

Walk these ways: Tuning robot control for generalization with multiplicity of behavior,

G. B. Margolis and P. Agrawal, “Walk these ways: Tuning robot control for generalization with multiplicity of behavior,” in Conference on Robot Learning . PMLR, 2023, pp. 22–31

2023

[8] [8]

Fabrication and testing of the rescue quadruped robot for post-disaster search and rescue operations,

N. Li, J. Cao, and Y . Huang, “Fabrication and testing of the rescue quadruped robot for post-disaster search and rescue operations,” in 2023 IEEE 3rd International Conference on Electronic Technology, Communication and Information (ICETCI) . IEEE, 2023, pp. 723– 729

work page 2023