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REVIEW 3 major objections 4 minor 28 references

Centroidal Trajectory Generation and Stabilization based on Preview Control for Humanoid Multi-contact Motion

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that preview control, not MPC, can generate and stabilize humanoid multi-contact motion at 0.1–0.4 ms per control cycle with a 2-second lookahead.

desk verdict Solid engineering: fast preview-control centroidal multi-contact stabilization that mostly delivers, but the angular momentum approximation is validated on only benign motions and the 'general multi-contact' claim outruns the evidence. read the letter →

arxiv 2505.23499 v1 pith:KSAULFIZ submitted 2025-05-29 cs.RO

Masaki Murooka , Mitsuharu Morisawa , Fumio Kanehiro This is my paper
classification cs.RO
keywords humanoidrobotsmulti-contactmotioncentroidaldynamicspreviewcontrolstabilizationwrenchdistributionrecedinghorizonwhole-body
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 claims that humanoid multi-contact motion—bipedal walking, climbing handrail stairs, climbing a vertical ladder, walking with hands on a wall, and balancing on moving floors and walls—can be planned and stabilized online from centroidal dynamics using preview control instead of full model predictive control. In simulation, the whole control update, including feedback stabilization and contact-wrench distribution, takes 0.1–0.4 ms while looking 400 samples (2 s) ahead, roughly one to two orders of magnitude faster than the MPC alternatives it compares against. That speed matters because the centroidal trajectory can be regenerated every control tick, which is what lets the robot absorb disturbances and follow contacts that move. The paper claims that the contact constraints omitted by preview control can be handled afterward by projecting the planned wrench onto the contact constraint manifold, and the simulations support that claim for a variety of motions.

What carries the argument

The load-bearing mechanism is the preview-control law for a triple-integrator plant, applied per axis to both the linear and angular centroidal dynamics. With state $x = (c, \dot c, \ddot c)$ and input $u = \dddot c$, the optimal input is $$u^*[k] = -K_{\mathrm{fb}} x[k] + \sum_{i=1}^{N_h} K_{\mathrm{ff}}[i] y_{\mathrm{ref}}[k+i],$$ where the gains depend only on the constant robot mass (and the approximated constant diagonal inertia for the angular part), so the runtime cost is one matrix multiplication regardless of the 400-sample horizon. The angular channel rests on the approximation $L \approx I\omega$ with constant diagonal $I$ and Euler-angle rates in place of true angular velocity. Around this core, a QP projects the planned wrench onto the contact wrench cone $w_i = G_i\lambda_i$, $\lambda_i \ge 0$, and damping control at each limb end tracks the distributed contact wrenches.

What would settle it

Run the controller on a motion with large joint swings and a fast base rotation—for example, a cartwheel or backflip—and compute, online or offline, the time series of $\|I_{\mathrm{all}}\dot{q} - I\omega\|$ (and $\|I\omega - I\dot{\alpha}\|$); if the error grows substantially beyond the 3.1 kg m²/s mean reported for the validated walking and stair motions, or if the simulated robot falls during execution, the central claim that this approximation supports general multi-contact motion is falsified.

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Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that a 6-degree-of-freedom centroidal trajectory—center of mass plus base orientation—can be generated online by solving, for each of the six axes, an independent preview-control problem, with the CoM and the resultant wrench (force and moment combined with gravity) as outputs instead of the ZMP used in classical bipedal preview control. For each axis the dynamics are a triple integrator: state (position, velocity, acceleration), input jerk, output (position, resultant wrench); the optimal input is a fixed state feedback plus a weighted sum of future reference outputs, so at runtime it is a single matrix multiplication. The planned wrench is then projected onto the contact constraint manifold, and a centroidal PD feedback law plus per-limb damping control turns it into stable whole-body motion. The paper further shows that the proposed feedback law contains DCM-based bipedal balance control as a special case, which gives a principled way to choose its gains.

Load-bearing premise

The load-bearing premise is that the robot's angular momentum can be modeled as a constant diagonal inertia times the base-link angular velocity, with joint motion and orientation-rate corrections ignored; if a motion involves large limb swings or fast orientation changes, the planned angular trajectory and wrench projection are built on a model that may be far off, and the robot can fall.

Editorial extensions

If this is right

  • A single set of controller gains, except for a few hand-damping values, covers bipedal walking and the tested multi-contact motions, which means the method scales to new contact schedules without re-tuning the whole pipeline.
  • Because the gains are fixed as long as mass (and inertia) stay constant, the online computation does not grow with the preview horizon; looking 2 s ahead costs the same as looking 0.5 s ahead.
  • The feedback law's equivalence to DCM control for bipedal walking gives a closed-form way to convert a desired DCM gain into the centroidal feedback gains, transferring tuning intuition from bipedal walking to multi-contact motion.
  • Compared with constrained MPC on the same tasks, the planned and feedback-modified wrenches show projection errors of the same scale, so for motions that include feedback the two approaches are not significantly different despite the huge cost difference.

Reading between the lines

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

  • Beyond the paper, the preview-plus-projection recipe may transfer to other systems whose dynamics reduce to centroidal form, such as quadrupeds or manipulators in contact, wherever a rough reference and a constraint-projection layer are available.
  • The cartwheel results validate only trajectory generation, not execution; if whole-body tracking were added, the constant-inertia and Euler-angle-rate approximations would be the first place to look for failure, since the paper itself leaves execution out of scope.
  • The reference force is always set to zero in the paper, so an immediate testable extension is to feed nonzero reference forces (for example, when the robot must push or carry a load) and measure whether tracking degrades.
  • One could also replace the angular approximation with a better online inertia estimate and keep the same preview structure; the speed advantage would likely survive because only the gains would need updating.
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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 / 4 minor

Summary. The paper proposes a centroidal trajectory generation and stabilization framework for humanoid multi-contact motion. Instead of solving a constrained MPC problem at each step, the method uses linear preview control on the 6-DoF centroidal dynamics, approximating the centroidal angular momentum as L ≈ Iω with a constant diagonal inertia matrix and using Euler-angle rates as the angular velocity. The planned resultant wrench is projected onto the contact constraint manifold via a QP, and a centroidal PD feedback law together with per-limb damping control provides stabilization. The authors validate the approach in simulation on a HRP-5P model for bipedal walking and four multi-contact scenarios, report sub-millisecond computation times for a 2-s preview horizon, and show a planned cartwheel trajectory as a stress test for the angular model. The paper's central claim is that this combination achieves fast, general multi-contact motion control without the computational burden of constraint-enforcing MPC.

Significance. If the central claims are confirmed, the paper makes a useful contribution: it offers a computationally inexpensive alternative to MPC for centroidal multi-contact control, with a clear algorithmic structure and concrete simulation demonstrations. The derivation of the connection between the proposed feedback law and DCM-based bipedal control in the appendix is a nice theoretical bridge that could help practitioners tune gains. The paper also provides detailed parameter tables and simulation protocols, which makes the method reproducible in principle. However, the significance is tempered by gaps in the validation of the angular-momentum approximation, which is load-bearing for the claimed generality of the method, and by the fact that some controller parameters and reference trajectories are motion-specific, contradicting the stated parameter-free claim. These issues are addressable, but they need to be fixed before the broader claims can be accepted.

major comments (3)
  1. [Section V-F and Section III-A4] The validation of the angular-momentum approximation (Eq. 6) is insufficient to support the claim of general multi-contact motion. The paper reports a mean error ||I_all qdot − Iω|| of 3.1 kg m^2/s even for bipedal walking and handrail stairs — two motions with relatively small base-link orientation changes — and the error is reduced to 0.011 only after adding an angular-momentum task to the whole-body IK, which is not part of the proposed controller. No error metrics are reported for the other demonstrated motions in Fig. 4(C), (D), and (E), which involve large hand forces, moving contacts, or different joint configurations, and the cartwheel stress test in Section V-D is planned but not executed. Because the preview controller and the wrench projection rely on this approximation, an unquantified model bias could be absorbed by the feedback stabilizer, making the success of the near-upright motions a weak witness for the model's validity. Please provide per-motion error statistics for all demonstrated motions and either execute the cartwheel or give a principled argument, with numerical evidence, for why the approximation holds in the large-orientation regime.
  2. [Section V-C, Tables II and III, and Contribution (ii)] The claim that the method handles bipedal walking and multi-contact motions 'without changing the parameters' is contradicted by the manuscript's own tables. Table II changes the hand damping gain Kd to 1000 for the wall-walking motion and to 50000 for the ladder motion, and Table III replaces the centroidal feedback gains KP and KD entirely for the ladder motion. In addition, the reference CoM trajectories are motion-specific: the stair motion uses a 50-mm inward offset and the ladder motion uses a 0.4-m offset with a 0.1-m forward adjustment, chosen per motion. Parameter tuning per motion is not inherently a flaw, but the claimed parameter invariance is a key selling point. Please either revise the claim to reflect the disclosed tuning, or demonstrate a single fixed parameter set that works across all presented motions, documenting how the reference offsets are generated from a common rule.
  3. [Section V-G] The comparison with constrained MPC is not sufficient to support the concluding statement that 'there is no significant difference between the two methods.' The comparison reports mean projection errors of the planned and desired wrenches, but these are not accompanied by statistical measures, tracking-error metrics, or stability-margin indicators. Moreover, the MPC baseline from reference [5] may include different feedback or posture tasks, making it unclear what exactly is being compared. Please either present a more quantitative comparison (e.g., CoM tracking RMSE, contact-force tracking error, or a robustness perturbation test) or soften the conclusion to a statement about comparable projection-error magnitudes in the specific tested scenarios.
minor comments (4)
  1. [Section V-F heading] The heading 'F . V alidation of Rotational Motion Approximation' contains stray spaces; it should be 'F. Validation of Rotational Motion Approximation'.
  2. [Figure 8(B)] The legend of Figure 8(B) lists 'planned force' twice; the second occurrence should likely be 'actual force' or another quantity, and the figure would be clearer if the legend entries were corrected.
  3. [Section V-B] The phrase 'the reference CoM trajectory is determined by a simple rule; the horizontal position is the center of the supporting foot...' is clear, but the sentence in Section V-C that says 'the reference CoM trajectories are represented by piecewise-constant functions' could be confusing because the actual reference trajectories shown in Figures 5-7 are step-like but not piecewise constant in the vertical direction; please clarify.
  4. [Section V-G] In the reporting of projection errors, it is not always clear which quantity the pair '(2.2 N and 4.4 Nm)' refers to — force and moment parts of the same vector norm or separate norms; please define the notation explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the preview-control derivation, wrench projection, and stabilization feedback are independent of the paper's own conclusions, and the disclosed parameter tuning is not fitted to the predicted outcomes.

full rationale

The paper's central derivation chain is self-contained and non-circular. The preview-control gains are obtained from standard LQ preview-control theory (Katayama et al. and Kajita et al.), with the novel output definition (CoM and resultant force instead of ZMP) explicitly stated as a design choice rather than derived from the claimed results. The wrench projection is a least-squares/QP projection onto contact constraints, and the stabilization feedback is a PD law on centroidal state error; neither is equivalent to the reference trajectories or to the performance claims. The DCM relationship in the appendix is presented as a consistency check and gain-estimation aid, not as an input that forces the control law. The angular-momentum approximation L ≈ Iω is admitted to be an approximation with stated assumptions and is validated post hoc on two motions; the cartwheel is explicitly out of scope for execution. Even where the validation is incomplete, that is a correctness/robustness concern, not circularity. The per-motion differences in damping and feedback gains are disclosed in Tables II and III as tuning choices made to avoid vibration for very different contact forces; they do not constitute fitting the prediction to the result. No load-bearing self-citation chain appears: citations to prior work by the authors' group are for the robot model, the broader receding-horizon context, or well-known centroidal-dynamics references, and none is used to justify the validity of the proposed controller in place of the presented simulations and derivations.

Assumptions & free parameters 6 free parameters · 8 assumptions · 0 invented entities

The central claim depends on the angular-momentum approximation, the given contact sequence, and hand-tuned reference trajectories and gains. The method itself is standard LQ preview control plus a least-squares projection, so the burden sits on the modeling assumptions rather than on new entities.

free parameters (6)
  • Linear preview control weights QL, RL = QL=diag(200, 5e-4), RL=diag(1e-8)
    Chosen by hand for the output and input costs in Eq. (4); no tuning procedure is given.
  • Angular preview control weights QA, RA = QA=diag(100, 5e-3), RA=diag(1e-8)
    Chosen by hand for the rotational output/input costs.
  • Discretization period dt and preview horizon Nh = dt=0.005 s, Nh=400
    Design choices for sampling and preview length; affect the gain matrices.
  • Damping control gains Kd, Ks, Kf = See Table II; hand Kd=1000 or 50000 per motion
    Tuned to be as compliant as possible within the range of non-vibration, with task-specific hand values.
  • Centroidal feedback gains KP, KD = See Table III; general and ladder-specific sets
    Chosen by hand; DCM relationship (Eq. 19) gives rough consistency for the linear part.
  • Per-motion reference CoM offsets = ladder: 0.4 m behind, +0.1 m forward; handrail: 50 mm inward
    Manually set to bias weight onto hands or reduce pitch moment, so the reference trajectory is task-dependent.
assumptions (8)
  • standard math Newton-Euler centroidal dynamics (Eq. 1)
    The centroidal dynamics are treated as exact for the rigid robot; standard mechanics.
  • standard math Preview control optimal solution (Eq. 5) from Katayama et al. [11]
    The paper uses the closed-form LQ preview gains without derivation.
  • domain assumption Angular momentum approximation L = I_all qdot ≈ I_base ω ≈ Iω with constant diagonal I (Eq. 6)
    Assumes joint momentum is negligible and I_base is pose-independent and diagonal; validated post hoc in Section V-F.
  • domain assumption Euler angle rate approximates base angular velocity (Eq. 7, K_Euler ignored)
    The state equation for orientation ignores the kinematic mapping K_Euler; validated post hoc in Section V-F.
  • domain assumption Reference force is set to zero and reference CoM is given by simple rules
    The reference trajectory is handcrafted per motion (Section V-C); the preview controller tracks these references rather than planning from scratch.
  • domain assumption Contact positions C_d are provided by a global planner or manually
    The method does not plan the contact sequence; it assumes one is given (Section II).
  • ad hoc to paper Task-specific reference offsets and some gains are tuned per motion
    Ladder and handrail offsets, hand Kd, and ladder KP/KD are chosen per task; this is disclosed but weakens the 'without changing parameters' contribution.
  • domain assumption Friction coefficient 0.6 in all environments
    Set for all simulations; contact polygon inner margins used in wrench distribution (Section V-B, Fig. 3 caption).

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Cite this review

Pith. "Pith review of Centroidal Trajectory Generation and Stabilization based on Preview Control for Humanoid Multi-contact Motion." pith.science (2026). https://pith.science/paper/KSAULFIZ

@misc{pith2026250523499,
  author       = {Pith},
  title        = {Pith review of: Centroidal Trajectory Generation and Stabilization based on Preview Control for Humanoid Multi-contact Motion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KSAULFIZ}},
  note         = {Machine review of arXiv:2505.23499}
}
read the original abstract

Multi-contact motion is important for humanoid robots to work in various environments. We propose a centroidal online trajectory generation and stabilization control for humanoid dynamic multi-contact motion. The proposed method features the drastic reduction of the computational cost by using preview control instead of the conventional model predictive control that considers the constraints of all sample times. By combining preview control with centroidal state feedback for robustness to disturbances and wrench distribution for satisfying contact constraints, we show that the robot can stably perform a variety of multi-contact motions through simulation experiments.

Figures

Figures reproduced from arXiv: 2505.23499 by the authors.

Figure 1
Figure 1. Overall components of the control system for humanoid multi-contact motion. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Contact constraints in wrench distribution. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Results of bipedal walking. (A) The reference, planned, and actual CoMs correspond to r ref , r p, and r a in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Simulation of multi-contact motion. The friction coefficient is set to 0.6 for all environments. (A) Stepping on scaffold boards with 25 degree incline while keeping the hand on a vertical wall. (B) Climbing four steps of 150 mm height with handrails. (C) Climbing a ve…
Figure 5
Figure 5. Figure 5: Results of walking with hands on the wall in Fig. 4 (A). [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Results of climbing handrail stairs in Fig. 4 (B). [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Results of climbing a vertical ladder in Fig. 4 (C). [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Centroidal trajectory generation of cartwheel motion. [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

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Reference graph

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