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REVIEW 3 major objections 5 minor 31 references

Humanoid Loco-Manipulations Pattern Generation and Stabilization Control

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read By folding external manipulation forces into a single ext-ZMP variable, this paper extends the standard preview-control pattern generator and DCM-based stabilizer so a humanoid can plan and stabilize walking while sustained or alternating…

desk verdict A clean, useful extension of LIPM/DCM to external manipulation forces; the stabilizer's force-error compensation is solid for horizontal errors but rests on an unquantified constant-kappa assumption for vertical errors. read the letter →

arxiv 2505.24116 v1 pith:ICZLGKAE submitted 2025-05-30 cs.RO cs.SYeess.SY

Masaki Murooka , Kevin Chappellet , Arnaud Tanguy , Mehdi Benallegue , Iori Kumagai , Mitsuharu Morisawa , Fumio Kanehiro , Abderrahmane Kheddar This is my paper
classification cs.ROcs.SYeess.SY
keywords humanoidloco-manipulationdivergentcomponentofmotionlinearinvertedpendulummodeext-ZMPpatterngenerationstabilizationcontrolpreviewexternalmanipulationforces
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 a control strategy for humanoid robots that walk while manipulating objects, so that sustained hand forces act on the body. It re-derives the two standard models of bipedal walking, the linear inverted pendulum mode and the divergent component of motion, to include external manipulation forces instead of treating them as a small offset. From these formulas the authors build a pattern generator that plans center-of-mass motion from a reference ZMP and reference hand forces, and a stabilizer that explicitly corrects for differences between planned and actual hand forces. The claim is that this removes two approximations in prior loco-manipulation controllers: the vertical force effect on the ZMP scale is included exactly, and force errors are compensated in the stabilizer. If true, the payoff is a humanoid that can plan and maintain balance while pushing or rolling heavy objects.

What carries the argument

The central object is the ext-ZMP $\hat{z} = \kappa z - \gamma$, a single variable that absorbs horizontal and vertical hand forces into a modified ZMP. Here $\kappa = 1 - \sum_i f^{(i)}_{\mathrm{ex},z} / (m(\ddot{c}_z + g))$ is the scale factor produced by vertical external forces, and $\gamma$ collects the force and moment offsets. Substituting ext-ZMP into the preview-control pattern generator makes external-force reference tracking a drop-in extension, and the same definitions give the first- and second-order DCM error dynamics used to derive the stabilizer feedback law. The device carries the argument because all external-force effects are concentrated in one variable, so existing bipedal walking machinery survives intact.

What would settle it

Apply a humanoid to a pushing task while a sinusoidal vertical hand-force error of growing amplitude is commanded, and monitor the closed-loop DCM error or the ZMP fluctuation. If the $1/\kappa$ compensation terms in the stabilizer fail to keep the errors bounded beyond some force-error amplitude, the constant-$\kappa$ linearization is inadequate. A related calculation is to compare the closed-loop eigenvalues predicted by equation (23), which assume constant $\kappa$, with the response of the full nonlinear dynamics when $\kappa$ varies in time.

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Extended reading notes

Core claim

By reorganizing the Newton-Euler equations under the usual horizontal angular momentum assumptions, the paper shows that external manipulation forces enter the linear inverted pendulum mode only through a scale factor $\kappa$ and an offset $\gamma$, leaving the natural frequency $\omega$ unchanged. This yields the ext-ZMP $\hat{z} = \kappa z - \gamma$, so the conventional preview control can be reused directly. The divergent component of motion keeps its usual form, $\dot{\xi} = \omega(\xi - \kappa z + \gamma)$, so a DCM-based stabilizer can be extended without changing the unstable mode. The stabilizer separates the force-error offset into high-frequency and low-frequency components: fast errors are rejected by shifting the ZMP, slow errors by shifting the desired CoM, and the feedback gains are scaled by $1/\kappa$ to match the conventional closed-loop response. Experiments show the robot walking while rolling a bobbin and pushing a cart with changing friction.

Load-bearing premise

The stabilizer linearizes the DCM error dynamics by assuming that the scale factor $\kappa$ computed from planned and measured vertical hand forces is equal and constant, so that vertical force errors do not change how the ZMP is scaled into the DCM dynamics; the paper states this error is 'not so large' but gives no quantitative bound.

Editorial extensions

If this is right

  • Walking pattern generation can incorporate vertical hand forces exactly, without approximation, while keeping the same preview-control structure and constant gains.
  • The stabilizer can reject manipulation-force errors directly by adjusting ZMP for fast components and CoM for slow components, rather than relying only on conservative whole-body motion.
  • The proposed formulas run within 2 ms control cycles on the robot's embedded computer, so the added capability does not raise computational cost.
  • The same ext-ZMP substitution extends naturally to other pattern-generation methods such as linear MPC and DCM-based walking control.
  • Previous pushing controllers that only added an offset to the ZMP or CoM can be upgraded to include the full vertical-force scale effect.

Reading between the lines

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

  • The frequency-domain separation in the stabilizer suggests a practical tuning recipe: the cutoff frequency can be chosen so that the fast ZMP strategy stays within the sole region while the slower CoM strategy handles drift, a design trade-off not explicitly quantified in the paper.
  • The same ext-ZMP derivation should apply to other sustained contacts besides the hands, such as walking with a walker, carrying a heavy load on the torso, or pushing with the shoulder, wherever a known vertical force acts on the body.
  • If a quantitative bound on $\kappa$ error were established, the stabilizer could be made adaptive by estimating $\kappa$ online from measured vertical forces rather than assuming it equals the desired value.
  • Because the paper assumes the reference manipulation forces are given, coupling the controller with online force-prediction methods would extend it to tasks where the required object force is not known in advance.
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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 extends the standard LIPM/DCM framework for bipedal walking to humanoid loco-manipulation. It derives forced LIPM and DCM equations that include external manipulation forces, introduces an 'ext-ZMP' variable that absorbs scaling and offset effects of those forces, and reuses preview control for pattern generation. The stabilizer extends DCM feedback control by separating the error between actual and desired manipulation forces into a low-frequency component handled by a CoM strategy and a high-frequency component handled by a ZMP strategy, with feedforward compensation terms. The approach is evaluated in three simulation test cases and in real-robot experiments (HRP-5P bobbin rolling and HRP-2Kai cart pushing).

Significance. If the claims hold, this is a practical and computationally cheap extension of widely used humanoid walking controllers to tasks with sustained hand forces. The derivation from Newton-Euler to the forced LIPM/DCM is clean and internally consistent, the ext-ZMP formulation is elegant, and the frequency-domain separation of force errors is a useful engineering idea. The real-robot demonstrations on HRP-5P and HRP-2Kai are valuable and support the pattern-generation part of the paper. The main weakness is that the stabilizer's force-error compensation is derived under an unquantified assumption on the ZMP scaling factor kappa and is not validated in the regime where that assumption matters, namely errors in vertical manipulation forces.

major comments (3)
  1. [Section V-B1, Eqs. (13)-(14)] The linearized DCM error dynamics is derived under the assumption that kappa^a = kappa^d = kappa is constant. When vertical hand-force errors are present, this assumption fails: writing kappa^a = kappa + Delta_kappa introduces an additional term -omega Delta_kappa z^a in the DCM error dynamics, and the feedforward terms (1/kappa) gamma_bar^a_H and (1/(kappa rho)) dot_gamma_bar^a_H in Eqs. (22) and (26) then cancel only a fraction kappa^a/kappa^d of the actual disturbance, leaving a residual proportional to Delta_kappa/kappa. The only justification given, that the error of kappa is 'not so large', is not a quantitative statement. Because the explicit compensation of manipulation-force errors is a central contribution, this approximation is load-bearing. Please provide a quantitative bound on Delta_kappa in terms of the vertical force error, an analysis of the resulting residual disturbance and its effect on stability, or revise the claim to state that the force-error compensation applies to gamma while kappa errors are neglected.
  2. [Section VII and test-case 2] The claimed robustness to vertical manipulation-force errors is not experimentally validated. Test-case 2 applies vertical forces of 200 N per hand but the actual forces track the reference, so it validates the pattern generator's ext-ZMP formulation, not the stabilizer's response to a mismatch in vertical forces. The real-robot experiments (bobbin turning, cart pushing) involve predominantly horizontal hand forces, for which kappa remains close to 1; they do not exercise the regime in which kappa changes. A dedicated experiment or simulation with a step or ramp error in the vertical force component is needed to support the second central contribution.
  3. [Section V-B4, Eqs. (17)-(20)] The derivation of the CoM strategy assumes dot_gamma_bar^a_L is approximately zero (and consequently double-dot_gamma_bar^a_L is also zero) when the low-frequency force-error component is used to shift the desired CoM. The neglected terms double-dot_gamma_bar_L + rho dot_gamma_bar_L are not obviously small for components near the 1.0-s filter cutoff, and no bound or sensitivity study is provided. Please quantify this approximation or demonstrate that it has negligible effect on the closed-loop response.
minor comments (5)
  1. [Section V-B1] The barred variables, such as gamma_bar^a, are defined as the difference between actual and desired values, but this is only implicit; please state the definition explicitly for all barred symbols.
  2. [Section V-B2, Eq. (15)] The first-order lag is written directly for the error variable z_bar^a, which is valid only when the desired ZMP derivative dot_z^d is negligible; please state this assumption explicitly or include the dot_z^d term, since the desired ZMP changes during footstep transitions.
  3. [Section VI] The reported gain values (tilde_k_i = 0, tilde_k_p = 1.25, tilde_k_d = 0) are used with Eq. (22), but the value of kappa used to scale the conventional gains is not reported; please specify kappa for the simulation and experiments so the conventional gains can be recovered.
  4. [Section VII] The phrase 'papering' in the bobbin description should be corrected to 'paper' or 'paper products'.
  5. [References] Reference [26] is cited as 'in press'; please update it with the final publication details if available.

Circularity Check

0 steps flagged · score 0.0 of 10

Derivation is self-contained; no circular step found. The ext-ZMP is a change of variables, and the stabilizer feedback uses measured force errors; the constant-kappa approximation is a robustness limitation, not circularity.

full rationale

The paper's central derivation (Section III) starts from the Newton-Euler centroidal equation (1) and algebraically derives the forced LIPM (4) and DCM dynamics (8) with no fitted parameters. The ext-ZMP (9) is a linear re-parametrization (zhat = kappa z - gamma) of the forced dynamics into conventional form, not a quantity fitted to outcome data; preview control then tracks this transformed quantity. The stabilizer (Section V) computes gamma^a from measured actual manipulation forces and adds feedforward compensation terms in (22)/(26); this is feedback using sensor measurements, not a prediction forced by construction. Self-citations ([2], [4]) are to standard DCM stabilizer implementations that the paper re-derives explicitly; they do not carry the mathematical argument, and the cited software is open source. The constant-kappa assumption in V-B1 is an explicit linearization whose residual effect is unquantified; that is a correctness/robustness concern, not a circularity: Eq (14) would contain an extra term if kappa^a != kappa^d, but that does not make any equation equivalent to its input by definition. Experimental comparisons against a kappa=1 baseline and with/without ST compensation provide external falsifiability. Therefore no circular step is present.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central control design rests on standard LIPM/DCM modeling assumptions plus two paper-specific simplifications that are stated but not quantitatively justified: constant kappa and negligible low-frequency gamma_L rate. The free numerical parameters are rho (unspecified), preview weights, DCM gains, and the filter cutoff. No new physical entities are introduced.

free parameters (4)
  • rho (ZMP first-order lag parameter)
    Appears in the ZMP delay model (15) and in the feedback and command laws (22), (26). No numerical value is given, so the stabilizer cannot be exactly reproduced.
  • Preview control weights Q and R = Q=1, R=1e-8
    Weights in the objective function (11), chosen by hand. They shape how aggressively the CoM tracks the reference ext-ZMP.
  • DCM feedback gains = k~i=0, k~p=1.25, k~d=0
    Chosen in Section VI by pole placement or experiment. The proposed gains scale the conventional gains by 1/kappa as in (25).
  • Low-pass filter cutoff period = 1.0 s
    Separates the force-error offset into high-frequency (ZMP strategy) and low-frequency (CoM strategy) components. No sensitivity analysis is reported.
assumptions (6)
  • domain assumption Horizontal components of angular momentum rate around the CoM are zero (Ldot_c,x = Ldot_c,y = 0)
    Used to derive LIPM (3a)-(3b) from (2) in Section III-B. This is the standard LIPM assumption, but external hand forces and arm motions can excite angular momentum.
  • domain assumption Vertical CoM height and ZMP height are constant, so omega is constant
    Invoked in Section III-B before (4). Required for the linear time-invariant LIPM/DCM forms used by the pattern generator and stabilizer.
  • standard math ZMP is defined so n_Z,x = n_Z,y = 0
    Used in Section III-B to drop the horizontal moment components. This follows from the definition of ZMP.
  • ad hoc to paper kappa = kappa^a = kappa^d is constant in the stabilizer
    Section V-B1, needed to linearize the DCM error dynamics in (14). The paper states the error is not so large but gives no bound or stability analysis.
  • domain assumption Low-frequency component gamma_L has negligible rate (dot gamma_L^a is approximately 0)
    Section V-B4, before (19a). Justifies replacing the desired CoM with c'_d = c_d - gamma_L^a. Its validity depends on the filter design and disturbance spectrum.
  • domain assumption Actual ZMP follows command ZMP through a first-order lag with parameter rho
    Equation (15), borrowed from [28] and [2]. Used to derive the second-order DCM error dynamics in (16c).

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Cite this review

Pith. "Pith review of Humanoid Loco-Manipulations Pattern Generation and Stabilization Control." pith.science (2026). https://pith.science/paper/ICZLGKAE

@misc{pith2026250524116,
  author       = {Pith},
  title        = {Pith review of: Humanoid Loco-Manipulations Pattern Generation and Stabilization Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ICZLGKAE}},
  note         = {Machine review of arXiv:2505.24116}
}
read the original abstract

In order for a humanoid robot to perform loco-manipulation such as moving an object while walking, it is necessary to account for sustained or alternating external forces other than ground-feet reaction, resulting from humanoid-object contact interactions. In this letter, we propose a bipedal control strategy for humanoid loco-manipulation that can cope with such external forces. First, the basic formulas of the bipedal dynamics, i.e., linear inverted pendulum mode and divergent component of motion, are derived, taking into account the effects of external manipulation forces. Then, we propose a pattern generator to plan center of mass trajectories consistent with the reference trajectory of the manipulation forces, and a stabilizer to compensate for the error between desired and actual manipulation forces. The effectiveness of our controller is assessed both in simulation and loco-manipulation experiments with real humanoid robots.

Figures

Figures reproduced from arXiv: 2505.24116 by the authors.

Figure 1
Figure 1. Overall components for humanoid loco-manipulation. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Calculation procedure of the stabilizer. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Strategy for dealing with external force error in stabilizer. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Calculation procedure of DCM feedback control. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: Test-cases 1 and 3. 0 5 10 15 20 time [s] −40 −20 0 20 40 hand force in X-axis [N] desired left/right actual left/right 0 5 10 15 20 time [s] −0.05 0.00 0.05 0.10 CoM and ZMP in X-axis [m] reference ext-ZMP desired ext-ZMP desired CoM 0 5 10 15 20 time [s] −0.05 0.00 0…
Figure 8
Figure 8. Figure 8: Test-case 2. 0 5 10 15 20 25 time [s] −200 −100 0 100 200 hand force in Z-axis [N] desired left/right actual left/right 0 5 10 15 20 25 time [s] −0.2 −0.1 0.0 0.1 0.2 CoM and ZMP in Y-axis [m] command ZMP command CoM actual ZMP actual CoM 0 5 10 15 20 25 time [s] −0.2 …
Figure 10
Figure 10. Figure 10: Results of test-case 3, where the ST compensates for the external force disturbances on the X-axis. [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 11
Figure 11. Figure 11: Bobbin rolling operation by HRP-5P. 0 5 10 15 20 25 time [s] −70 −60 −50 −40 −30 −20 −10 0 hand force in X-axis [N] desired left desired right actual left actual right 0 5 10 15 20 25 time [s] −0.10 −0.08 −0.06 −0.04 −0.02 0.00 0.02 0.04 0.06 CoM and ZMP offset in X-a…
Figure 12
Figure 12. Figure 12: Cart pushing operation by HRP-2Kai. (A) Floor with ununiform friction (B) Uneven floor [PITH_FULL_IMAGE:figures/full_fig_p008_12.png]
Figure 13
Figure 13. Figure 13: Pushing operation on the floor with model error. [PITH_FULL_IMAGE:figures/full_fig_p008_13.png]

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    K. Kaneko, H. Kaminaga, T. Sakaguchi, S. Kajita, M. Morisawa, I. Kumagai, and F. Kanehiro, “Humanoid Robot HRP-5P: An electrically actuated humanoid robot with high-power and wide-range joints,”IEEE Robotics and Automation Letters, vol. 4, no. 2, pp. 1431–1438, 2019

    2019

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.