Pith. sign in

REVIEW 3 major objections 5 minor 26 references

Adaptive MPC-based quadrupedal robot control under periodic disturbances

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Explicit periodic force compensation cuts quadruped tracking error

desk verdict The contribution is real but the paper omits its core algorithm and its own table contradicts the claim. read the letter →

arxiv 2505.12361 v1 pith:LQKIRKJX submitted 2025-05-18 cs.RO cs.AIcs.SYeess.SY

Elizaveta Pestova , Ilya Osokin , Danil Belov , Pavel Osinenko This is my paper · ORCID
classification cs.ROcs.AIcs.SYeess.SY
keywords quadrupedalrobotmodelpredictivecontrolperiodicdisturbanceadaptiveforceestimationreferencetrackingsimulationUnitreeA1
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

This paper proposes adding a lightweight disturbance estimator to a convex model-predictive controller for a quadrupedal robot, so that periodic external forces are modeled and compensated separately from static ones. The authors aim to show that explicitly estimating the amplitude and frequency of a sinusoidal disturbance reduces reference-tracking error compared to a baseline MPC and to an MPC that compensates only a static force estimate. This matters because quadrupedal robots working outdoors often meet cyclic loads such as swinging payloads, wind gusts, or rhythmic ground interactions, and standard adaptive MPC treats disturbances as constant. The paper evaluates the idea in simulation on a Unitree A1 under forces given by a static offset plus a sinusoid, reporting tracking mean-squared error for three controllers across several amplitudes and frequencies.

What carries the argument

The load-bearing mechanism is a regression-based disturbance estimator that separates the unknown external wrench into a stationary part and a non-stationary periodic part. Using the simplified floating-base dynamics with $\xi = (f_{\mathrm{unk}}, t_{\mathrm{unk}})$ entering the linear and angular momentum equations, the estimator solves a quadratic cost in closed form for the wrench that best explains the discrepancy between the predicted and measured next state. The periodic part is assumed to be a single sinusoid $A\sin(\omega t)$, so the estimator extracts the magnitude and frequency of the cyclic load and feeds them into the MPC dynamics, shrinking the model-prediction error over the horizon.

What would settle it

Reproduce the Table I experiment with the three controllers and compare the MSE columns: the claim is settled only if the periodic-compensation column is the smallest in rows with a non-zero periodic amplitude, which the printed numbers do not show (e.g., the first row lists 6.471 for periodic compensation against 2.690 for stationary compensation).

Watch

Extended reading notes

Core claim

The paper argues that a quadruped controlled by convex MPC tracks its commanded velocity with lower mean-squared error when the controller estimates and compensates the periodic part of an external disturbance in addition to the static part. The disturbance is modeled as $d(t) = d_{\mathrm{static}} + A\sin(\omega t)$, and the estimator reconstructs the unknown wrench $\xi = (f_{\mathrm{unk}}, t_{\mathrm{unk}})$ from the difference between predicted and measured robot states using a closed-form least-squares solve on the simplified floating-base dynamics. The estimated static and periodic components are fed back into the linearized MPC dynamics, so the optimizer can anticipate the sinusoidal force instead of treating it as constant. In Raisim simulations of a Unitree A1 across static balance, low-speed trot, and high-speed trot, the paper reports that the periodic compensation yields the lowest tracking error whenever the disturbance has a periodic component.

Load-bearing premise

The entire improvement rests on the disturbance being exactly a constant plus a single sinusoid of fixed frequency; if the load has multiple harmonics, a drifting frequency, or a random component, the periodic estimator has no guarantee and the paper states it should not be used.

Editorial extensions

If this is right

  • When a periodic component is present and matches the single-sinusoid model, explicitly compensating it lowers velocity-tracking MSE relative to both a non-adaptive baseline and a static-only compensator.
  • The estimator adds negligible computation to the control loop, since it is a closed-form least-squares solve on the simplified dynamics, keeping the MPC optimization convex and real-time compatible.
  • The same estimator structure is tested across static balance, low-speed trot, and high-speed trot, so the claimed benefit is not tied to one gait.
  • When no periodic disturbance is applied, the proposed method can be slightly worse than the baseline, so a practical controller would switch between periodic and non-periodic compensation based on the estimated amplitude.
  • Torque disturbances, stochastic loads, and abrupt frequency changes are explicitly out of scope and left for future work.

Reading between the lines

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

  • Replacing the single-sinusoid model with a short Fourier series or an adaptive frequency tracker could extend the same closed-form estimator to multi-harmonic and chirp-like loads without changing the estimation framework.
  • A detector that disables the periodic term when the estimated amplitude drops below a noise floor would address the reported slight degradation in the no-periodic-disturbance case.
  • The static-versus-periodic separation principle transfers to other floating-base robots and even fixed-base systems with cyclic loads, since it depends only on simplified rigid-body dynamics and state feedback.
  • Using the estimated frequency to synchronize the gait cycle or the MPC horizon with the disturbance is a natural next step that the paper does not explore.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript proposes an adaptive MPC scheme for quadrupedal locomotion under periodic external disturbances. The scheme augments a convex force-level MPC with an external-force estimator; the stated contribution is the separation of disturbances into static and periodic components and compensation within the MPC model. Experiments in Raisim on a Unitree A1 under sinusoidal external forces are reported, with MSE tracking comparisons against a baseline MPC and a static-disturbance-compensated MPC. The central claim is that explicitly compensating for the periodic component reduces velocity-tracking MSE.

Significance. If substantiated, the contribution would be practically relevant: periodic disturbances are common in quadruped applications, and existing adaptive MPC methods largely treat disturbances as static. The use of a linearized convex MPC suggests the extension is computationally lightweight. However, as written, the manuscript does not specify the periodic estimator, the numerical evidence as printed contradicts the stated result, and the repository pointers are inconsistent. The claimed significance is therefore not currently established. Strengths of the paper are the clear problem framing and the simulation-based evaluation plan; no machine-checked proofs or parameter-free derivations are provided, and the missing algorithmic description is the central obstacle.

major comments (3)
  1. [Section III, Eq. (16)] The periodic disturbance estimation mechanism, the paper's central contribution, is not described anywhere in the manuscript. Section III derives only a static least-squares estimator for a constant vector ξ (Eq. 16). There is no regressor for the amplitude, frequency, or phase of d(t) = d_static + A sin(ωt), no update law that separates stationary from non-stationary components, and no statement of how a time-varying periodic estimate is inserted into the linearized dynamics (Eq. 10) or the MPC cost (Eq. 6). Consequently, the 'Periodic Compensation (Ours)' results in Section V.A cannot be reproduced or audited.
  2. [Section V.A and Table I] The numerical results as printed contradict the prose. In Table I, the first row (static 0 N, amplitude 15 N, frequency 0.33 Hz) lists MSE values 5.663, 2.690, and 6.471, with the largest value in the column labeled 'Periodic.' This pattern repeats in every periodic-disturbance row, e.g., 3.676 versus 1.895 and 15.468 versus 4.264. Section V.A states 'the proposed periodic compensation method (fourth column) yields the lowest tracking error,' which is the opposite of what the table shows under its stated column order. Furthermore, Section V.B states that with no periodic disturbance the proposed method is slightly worse than baseline, but the static-only row (-10 N, amplitude 0) shows Periodic MSE 1.222 versus Baseline MSE 1.261. These inconsistencies must be resolved before the experimental claim can be evaluated.
  3. [Abstract and Section I (repository URLs)] The reliability of the reported experiments is compromised by inconsistent source-code pointers: the abstract cites https://github.com/aidagroup/quad-periodic-mpc, while Section I cites https://github.com/LizaP9/Periodic_Adaptive_MPC. A reader cannot determine which repository contains the implemented algorithm. Combined with the absence of a periodic-estimator description in the text, this makes the central claim effectively unverifiable.
minor comments (5)
  1. [Throughout] There are several typographical errors, including 'compensaton' (Section V.A), 'allpicable' and 'mathods' (Section V.B), 'Stationar y' in the Table I header, and 'Figure 3 figure shows' in Section IV.A.
  2. [Eq. (18)] Equation (18) is described as a mean squared error, but the formula as printed is a sum over N terms without the factor 1/N; please add the normalization.
  3. [Eq. (17) and Section IV.B] The disturbance model is limited to a single sinusoid plus a static offset. The paper should state explicitly whether the frequency is assumed known and constant and should discuss the implications for multi-harmonic or chirped disturbances, which are acknowledged in the limitations only in passing.
  4. [Section IV.B and Section V.B] Equation (3) defines the estimator to include both force and torque disturbances, and Eq. (5) includes torque compensation, yet Section V.B states that only linear disturbances were tested. Please clarify whether torque disturbances were present in the simulations or entirely omitted.
  5. [References] Reference [17] appears malformed ('C. W. andNoel V . Csomay-Shanklin'); please check the author list.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the only derived estimator is a standard least-squares fit, and the unsupported periodic-compensation claim is a missing-evidence problem, not a circularity problem.

full rationale

I walked the paper's derivation chain and found no step in which a claimed prediction or first-principles result reduces, by the paper's own equations or by self-citation, to its own inputs. The only estimator actually derived is Eq. (16), the closed-form least-squares solution to Eq. (15); it estimates the constant vector xi from the one-step prediction residual and is not defined in terms of the tracking error or of the claimed periodic-compensation advantage. No parameter is fitted to the Table I MSE values and then renamed as a prediction: the prose claims the periodic method performs best, but the periodic estimator itself is never specified in Section III, and Table I as printed shows the Periodic column with the highest MSE in every periodic-disturbance row. That is an under-specification and an internal inconsistency, not circularity. The references to prior adaptive MPC and disturbance-estimation work are background and none is load-bearing in a self-citation chain. The limitation statements in Section V.B honestly restrict the method to periodic, non-stochastic, simulation-only settings, but they do not smuggle in the target conclusion. Therefore the honest finding is no significant circularity.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central contribution (periodic compensation) rests on a disturbance model and a regressor whose behavior is not shown. The free parameters are many unstated tuning knobs. No new physical entities are introduced.

free parameters (3)
  • MPC cost weights P, R, S = not reported
    Equations (6) and (15) define quadratic costs with weight matrices P, R, S. No values are given, yet tracking MSE depends on these tuning choices.
  • Estimation window length = not reported
    The regressor in Eq. (16) estimates forces from a state trajectory; the time window over which the estimate is computed is not specified, but it controls the trade-off between responsiveness and noise.
  • Periodic fit hyperparameters = not reported
    The paper claims to extract magnitude and frequency of the periodic disturbance, but the fitting procedure, initial conditions, and any learning rates or forgetting factors are not described in the text.
assumptions (3)
  • domain assumption The external disturbance is exactly a sum of a constant and a single sinusoid: d(t) = d_static + A sin(ωt).
    Equation (17) in Section IV.B restricts disturbances to this form; if the physical disturbance has multiple harmonics or is non-periodic, the proposed separation and compensation are not justified. The authors' own limitations concede stochastic disturbances are out of scope.
  • domain assumption Simplified floating-base dynamics with small angles, diagonal inertia, and neglected cross-coupling are adequate for force estimation and control.
    Section II.C lists the linearization assumptions used to build the convex MPC (Eq. 10). These are standard in quadruped MPC but are unverified in this work against the full nonlinear model.
  • standard math The least-squares estimator (Eq. 16) provides an unbiased estimate of the unknown force ξ from state prediction errors.
    The closed-form solution follows from quadratic minimization; however, its statistical properties depend on the noise model, which is not specified.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Adaptive MPC-based quadrupedal robot control under periodic disturbances." pith.science (2026). https://pith.science/paper/LQKIRKJX

@misc{pith2026250512361,
  author       = {Pith},
  title        = {Pith review of: Adaptive MPC-based quadrupedal robot control under periodic disturbances},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LQKIRKJX}},
  note         = {Machine review of arXiv:2505.12361}
}
read the original abstract

Recent advancements in adaptive control for reference trajectory tracking enable quadrupedal robots to perform locomotion tasks under challenging conditions. There are methods enabling the estimation of the external disturbances in terms of forces and torques. However, a specific case of disturbances that are periodic was not explicitly tackled in application to quadrupeds. This work is devoted to the estimation of the periodic disturbances with a lightweight regressor using simplified robot dynamics and extracting the disturbance properties in terms of the magnitude and frequency. Experimental evidence suggests performance improvement over the baseline static disturbance compensation. All source files, including simulation setups, code, and calculation scripts, are available on GitHub at https://github.com/aidagroup/quad-periodic-mpc.

Figures

Figures reproduced from arXiv: 2505.12361 by the authors.

Figure 1
Figure 1. A quadrupedal robot under periodic disturbances [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Block diagram of the adaptive MPC-based control system [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Simulation setup in Raisim [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Comparison of commanded (dashed red) and measured linear [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

26 extracted references · 24 canonical work pages

  1. [1]

    Dynamic locomotion in the mit cheetah 3 through convex model-predictive control,

    J. D. Carlo, P. M. Wensing, B. Katz, G. Bledt, , and S. Kim, “Dynamic locomotion in the mit cheetah 3 through convex model-predictive control,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1–9, Jan. 2018

    work page 2018

  2. [2]

    Adaptive clf-mpc with application to quadrupedal robots,

    M. V . Minniti, R. Grandia, F. Farshidian, and M. Hutter, “Adaptive clf-mpc with application to quadrupedal robots,” IEEE Robotics and Automation Letters, vol. 7, no. 1, pp. 565–572, Jan. 2022

    work page 2022

  3. [3]

    Control lyapunov functions for adaptive nonlinear stabilization,

    M. Krsti ´c and P. V . Kokotovi ´c, “Control lyapunov functions for adaptive nonlinear stabilization,” Systems & Control Letters , vol. 26, no. 1, pp. 17–23, 1995

    work page 1995

  4. [4]

    J.-J. E. Slotine and W. Li, Applied Nonlinear Control . Englewood Cliffs, NJ, USA: Prentice-Hall, 1991, vol. 199, no. 1

    work page 1991

  5. [5]

    On the adaptive control of robot manipula- tors,

    J.-J. Slotine and W. Li, “On the adaptive control of robot manipula- tors,” International Journal of Robotics Research , vol. 6, no. 3, pp. 49–59, 1987

    work page 1987

  6. [6]

    Adaptive- control oriented meta-learning for nonlinear systems,

    S. Richards, N. Azizan, J.-J. E. Slotine, and M. Pavone, “Adaptive- control oriented meta-learning for nonlinear systems,” in Proceedings of Robotics: Science and Systems (RSS) , jul 2021

    work page 2021

  7. [7]

    Adaptive safety with control barrier functions,

    A. J. Taylor and A. D. Ames, “Adaptive safety with control barrier functions,” in Proceedings of the American Control Conference (ACC) , 2020, pp. 1399–1405

    work page 2020

  8. [8]

    Bayesian learning-based adaptive control for safety critical systems,

    D. D. Fan, J. Nguyen, R. Thakker, N. Alatur, A. a. Agha-mohammadi, and E. A. Theodorou, “Bayesian learning-based adaptive control for safety critical systems,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) , 2020, pp. 4093– 4099

    work page 2020

Show all 26 references
  1. [9]

    Highly dynamic quadruped locomotion via whole-body impulse control and model predictive control,

    D. Kim, J. D. Carlo, B. Katz, G. Bledt, and S. Kim, “Highly dynamic quadruped locomotion via whole-body impulse control and model predictive control,” IEEE Robotics and Automation Letters (RA-L) , vol. 36, no. 6, pp. 1623–1641, Sept. 2019

    2019

  2. [10]

    Real-time model predictive control for versatile dynamic motions in quadrupedal robots,

    Y . Ding, A. Pandala, and H.-W. Park, “Real-time model predictive control for versatile dynamic motions in quadrupedal robots,” in Pro- ceedings of the International Conference on Robotics and Automation (ICRA), 2019, pp. 8484–8490

    2019

  3. [11]

    Nonlinear model predictive control of robotic systems with control lyapunov functions,

    R. Grandia, A. J. Taylor, A. Singletary, M. Hutter, and A. D. Ames, “Nonlinear model predictive control of robotic systems with control lyapunov functions,” in Proceedings of Robotics: Science and Systems (RSS), Jul 2020

    2020

  4. [12]

    Whole-body nonlinear model predictive control through contacts for quadrupeds,

    M. Neunert, M. St ¨auble, M. Giftthaler, C. D. Bellicoso, J. Carius, and C. Gehring, “Whole-body nonlinear model predictive control through contacts for quadrupeds,” IEEE Robotics and Automation Letters , vol. 3, no. 3, pp. 1458–1465, July 2018

    2018

  5. [13]

    Guided constrained policy optimization for dynamic quadrupedal robot locomotion,

    S. Gangapurwala, A. Mitchell, and I. Havoutis, “Guided constrained policy optimization for dynamic quadrupedal robot locomotion,” IEEE Robotics and Automation Letters , vol. 5, no. 2, pp. 3642–3649, 2020

    2020

  6. [14]

    Variational contact-implicit tra- jectory optimization,

    Z. Manchester and S. Kuindersma, “Variational contact-implicit tra- jectory optimization,” in Robotics Research. Springer, 2020, pp. 985– 1000

    2020

  7. [15]

    Learning fast adapta- tion with meta strategy optimization,

    W. Yu, J. Tan, Y . Bai, E. Coumans, and S. Ha, “Learning fast adapta- tion with meta strategy optimization,” IEEE Robotics and Automation Letters, vol. 5, no. 2, pp. 2950–2957, 2020

    2020

  8. [16]

    Learning a contact-adaptive controller for robust, efficient legged locomotion,

    X. Da, Z. Xie, D. Hoeller, B. Boots, A. Anandkumar, Y . Zhu, B. Babich, and A. Garg, “Learning a contact-adaptive controller for robust, efficient legged locomotion,” 4th Conference on Robot Learning (CoRL 2020) , vol. -, no. -, pp. –, Nov. 2020

    2020

  9. [17]

    Online learning of unknown dynamics for model-based controllers in legged locomotion,

    Y . Sun, W. L. Ubellacker, W.-L. M. andXiang Zhang, and C. W. andNoel V . Csomay-Shanklin, “Online learning of unknown dynamics for model-based controllers in legged locomotion,” IEEE Robotics and Automation Letters, vol. 6, no. 4, pp. 8442–8449, Oct 2021

    2021

  10. [18]

    Imitation learning from mpc for quadrupedal multi-gait control,

    A. Reske, J. Carius, Y . Ma, F. Farshidian, and M. Hutter, “Imitation learning from mpc for quadrupedal multi-gait control,” IEEE Interna- tional Conference on Robotics & Automation (ICRA) , Mar. 2021

    2021

  11. [19]

    Asynchronous deep model reference adaptive control,

    G. Joshi, J. Virdi, and G. Chowdhary, “Asynchronous deep model reference adaptive control,” in Proceedings of the Conference on Robot Learning, 2020, pp. 984–1000

    2020

  12. [20]

    Hierarchical reinforcement learning for quadrupedal locomotion,

    D. Jain, A. Iscen, and K. Caluwaerts, “Hierarchical reinforcement learning for quadrupedal locomotion,” IEEE/RSJ International Con- ference on Intelligent Robots and Systems (IROS) , Nov. 2019

    2019

  13. [21]

    L1 adaptive control for bipedal robots with control lyapunov function based quadratic programs,

    Q. Nguyen and K. Sreenath, “L1 adaptive control for bipedal robots with control lyapunov function based quadratic programs,” in Pro- ceedings of the American Control Conference , 2015, pp. 862–867

    2015

  14. [22]

    Adaptive force-based control for legged robots,

    Y . Chen and Q. Nguyen, “Adaptive force-based control for legged robots,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2021

    2021

  15. [23]

    Parameters es- timation via dynamic regressor extension and mixing,

    S. Aranovskiy, A. Bobtsov, R. Ortega, and A. Pyrkin, “Parameters es- timation via dynamic regressor extension and mixing,” 2016 American Control Conference (ACC) , July 2016

    2016

  16. [24]

    New results on parameter estimation via dynamic regressor extension and mixing,

    R. Ortega, S. Aranovskiy, A. A. Pyrkin, A. Astolfi, and A. A. Bobtsov, “New results on parameter estimation via dynamic regressor extension and mixing,” IEEE Transactions on Automatic Control , vol. 66, no. 5, pp. 2265–2272, Jan. 2020

    2020

  17. [25]

    Implicit regularization and mo- mentum algorithms in nonlinearly parameterized adaptive control and prediction,

    N. M. Boffi and J.-J. E. Slotine, “Implicit regularization and mo- mentum algorithms in nonlinearly parameterized adaptive control and prediction,” Neural Computation , vol. 33, no. 3, pp. 590–673, 2021

    2021

  18. [26]

    Composite adaptive disturbance rejection in robotics via instrumental variables based drem,

    A. Glushchenko and K. Lastochkin, “Composite adaptive disturbance rejection in robotics via instrumental variables based drem,” arXiv preprint 2406.19838, 2024

    2024 arXiv

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.