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REVIEW 5 major objections 3 minor 36 references

A 3-Step Optimization Framework with Hybrid Models for a Humanoid Robot's Jump Motion

T0 review · 5 major / 3 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that a 3-step trajectory optimization framework, using an SRMP model, joint-space QP mapping, and whole-body optimization, generates executable forward jumps of 1.0 m distance and 0.5 m height on a humanoid robot, with…

desk verdict A real robot doing 1m forward jumps is the bottom line; the paper is a credible engineering contribution with some under-specified validation. read the letter →

arxiv 2501.12594 v1 pith:SCLA2D2K submitted 2025-01-22 cs.RO

Haoxiang Qi , Zhangguo Yu , Xuechao Chen , Yaliang Liu , Chuanku Yi , Chencheng Dong , Fei Meng , Qiang Huang This is my paper · ORCID
classification cs.RO
keywords humanoidrobotforwardjumptrajectoryoptimizationreactionmasspenduluminertiashapingcentroidalangularmomentumcenterofpressurewhole-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 tries to show that a humanoid robot's forward jump can be planned by splitting the problem into three staged optimizations, each using a different dynamic model, so that the whole plan is computed in seconds rather than minutes. The first stage treats the robot as a pendulum whose inertia can change, jointly shaping momentum and body posture. The second maps that plan into joint motions. The third refines it on a whole-body planar model, and the result sends a 42 kg robot 1.0 m forward and 0.5 m high, in simulation and hardware. If right, this makes agile jumping a practical offline-planning routine rather than a heavy whole-body optimization.

What carries the argument

The central object is the SRMP (static reaction mass pendulum) model, a 2D pendulum whose center of mass is split into a barbell of two masses separated by a controllable radius $\varphi$, giving total rotational inertia $\rho = 2 m_p \varphi^2$. This scalar encodes the robot's body inertia, letting the optimizer shape inertia during flight while total angular momentum is conserved. The center-of-pressure constraint (Eq. 22) couples linear and angular momentum to the support region, and the flight-phase optimization treats the spatial inertia $\rho^R_{\text{total}}$ as the control variable to adjust the landing posture.

What would settle it

Use external motion capture to measure the robot's actual takeoff velocity and flight-phase pitch rotation during a forward jump: if the horizontal center-of-mass velocity at takeoff differs from the planned value by more than the landing controller can absorb, or if the robot's roll or yaw grows beyond a small threshold, the planar symmetry assumption behind the whole-body stage is violated and the claimed 1.0 m jump is not reproducible.

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Extended reading notes

Core claim

The central claim is that the coupling between body posture and centroidal angular momentum during launch, and the inertia shaping that controls rotation during flight, can be optimized together by a split-level approach. A static reaction mass pendulum (SRMP)—a pendulum whose endpoint mass is a barbell of adjustable radius—captures both the momentum and the rotational inertia of the robot, and its optimization produces reference trajectories for momentum, inertia, and center of pressure. The paper asserts that these references, after a joint-space mapping step and a final whole-body optimization on a planar 5-link model, yield a trajectory that the real robot can execute open-loop through launch and flight, landing with the feet placed for a stable touchdown.

Load-bearing premise

The final optimization runs on a planar 5-link model that merges the two legs into one, so the whole plan assumes the robot's left and right legs move identically and that roll and yaw dynamics are negligible; if the real robot breaks that symmetry, the planned center-of-pressure and landing postures are not dynamically consistent.

Editorial extensions

If this is right

  • Total optimization time under 10 seconds makes the framework feasible for online re-planning when jump targets change.
  • Inertia shaping during flight gives the robot control over landing orientation without breaking angular momentum conservation, so landing foot placement can be planned.
  • The center-of-pressure constraint links linear and angular momentum to the support region, so the optimized launch trajectory is executable without foot tipping.
  • The same split-level approach can be applied to other sagittal-plane jumps, such as backflips, by changing the target rotation.

Reading between the lines

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

  • The planar symmetry reduction suggests an obvious stress test: deliberately perturb the robot's initial posture in roll and yaw and see if the open-loop trajectory still lands stably; the paper does not report such a test.
  • The 10-second runtime depends on the QP mapping providing a good guess; this staged warm-start strategy could be reused in other whole-body optimal control problems, such as running takeoffs or stair hopping.
  • The paper's own admission that model error can be pre-compensated by biasing optimization goals hints that a sensitivity analysis—how much target bias per unit of model error—would turn the framework into a robust tuning tool.
  • If the inertia-shaping flight phase is the key new element, one could test it in isolation by executing only the flight-phase trajectory during a no-jump, in-place rotation maneuver.
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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

5 major / 3 minor

Summary. The paper proposes a three-stage offline trajectory optimization framework for generating forward jump motions on an adult-sized humanoid robot. Stage 1 uses a 2D SRMP model to optimize centroidal momentum, inertia, and CoP trajectories for the launching and flight phases; Stage 2 maps these trajectories into joint space via QP solvers on a 20-DOF full-body model; Stage 3 performs a whole-body optimization on a planar 5-link model whose leg mass and inertia are aggregated from the two legs, with the resulting trajectory mirrored to both legs. The optimized trajectory is executed open-loop in position mode during launching and flight, with a landing controller inherited from prior work. The central claims are that the three-stage framework generates agile forward jumps of about 1.0 m distance and 0.5 m height, that the whole optimization takes less than 10 seconds, and that inertia shaping during flight achieves favorable landing posture.

Significance. If fully validated, the framework would be a practical and fast trajectory-optimization pipeline for humanoid jumping, with a sensible hierarchical decomposition: SRMP-based momentum/inertia generation, QP-based joint-space mapping, and whole-body refinement. The physical robot experiments in Sec. VI-C show real forward jumps, which is nontrivial evidence that the optimized trajectories are executable, and the paper usefully identifies inertia shaping during flight as a key ingredient for landing posture. However, the validation is incomplete: there are no error bars, only selected trials are shown, the flight-phase CoM/CAM are not directly measured, bilateral ground-reaction data are absent, and admitted discrepancies between reference and actual performance are rationalized rather than quantified. The central methodological bridge from the planar symmetric whole-body model to the physical two-legged robot is therefore not yet demonstrated.

major comments (5)
  1. [Sec. II-C and Sec. V] The whole-body optimization uses a planar 5-link single-legged model whose leg mass and inertia are the sum of the two legs, and the resulting trajectory is mirrored to both legs. This assumes exact left-right symmetry and identical ground reactions during launch and landing. The paper never reports bilateral force/torque sensor data or CoP tracks from the experiments, so the dynamic consistency of the planned CoP constraint (Eq. 22) and the CAM trajectory with the real two-legged motion is not established. Please provide per-foot ground-reaction force and CoP measurements for the reported trials, or explicitly state the symmetry assumption and justify it with data.
  2. [Sec. VI-C, Fig. 14] The paper states that the robot does not reach the specified CoM height and that the actual CAM deviates from the reference, then suggests these discrepancies 'might be attributed to measurement errors' without supporting evidence. Because the flight-phase CoM and CAM are not measured (no external motion capture or state estimator), the claimed 1.0 m distance and 0.5 m height cannot be directly verified from the presented data. Please report multiple trials with error bars, measured takeoff velocity, measured flight-phase trajectories, or clearly limit the claim to selected successful trials.
  3. [Sec. VI-B] The simulation section says that model mismatch can be handled by 'adding bias to the optimization's goal,' but no definition, numerical value, or tuning procedure for this bias is given. This is a load-bearing detail for reproducibility, since the bias appears to be the mechanism by which the framework compensates for dynamic-model differences. Specify where the bias enters the optimization (objective or constraint), how it was selected, and whether it was tuned on the experimental trials.
  4. [Sec. I and Sec. VI] The paper claims that the whole optimization process takes less than 10 seconds, but no timing measurements, solver specifications, problem sizes, or hardware details are reported anywhere in the results. Since this is one of the stated contributions and is essential for the claimed online deployability, please provide quantitative timing data for each of the three optimization stages.
  5. [Sec. VI-B, Fig. 12] The simulation validation shows visible differences between reference and actual CoM position/velocity and CAM curves, attributed to dynamic model differences, but no quantitative error metric or acceptance threshold is given. Given that the simulation also uses modified dynamic parameters and open-loop execution, please quantify the tracking errors and show that the achieved jump distance and height match the targets within a defined tolerance.
minor comments (3)
  1. [Throughout] There are several typos and grammatical errors, including 'researches' and 'constracted' in Sec. I, 'the relationship the relationship' in Sec. IV-A, and 'cased' in Sec. VI-B. The paper would benefit from a careful language edit.
  2. [Fig. 12] The subplot captions in Fig. 12 are not self-contained; please specify in the caption which physical quantities are plotted and clarify the meaning of 'Ref' and 'Act'.
  3. [Sec. II-A and Sec. III-A] The symbol φ is used for the barbell radius in the SRMP configuration (Eq. 1) and also appears in derived quantities such as Eq. 4; the notation should be checked for consistency to avoid confusion between radius and other angular variables.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the 1.0 m / 0.5 m jump targets are optimization inputs, not fitted outputs, and the self-cited equations and controller from [2] are reused as standard dynamics and landing support rather than as the source of the claimed forward-jump derivation.

full rationale

The derivation chain starts from externally selected jump height h and distance l. Section III-A3 imposes these as hard constraints: Eq. (17) requires 2*p_end_c0x + v_end_c0x*t_f = l, and Eq. (18) requires v_end_c0z = sqrt(2*g*h). The validation targets therefore enter as inputs, not as quantities recovered from the experimental outcome. Each subsequent stage propagates these targets through independent dynamics models (SRMP, full-DOF QP, and 5-link whole-body optimization), and the paper reports open-loop execution with visible tracking errors rather than claiming that the model reproduced measured data. The reused equations from the authors' prior vertical-jump paper [2]—centroidal dynamics, tiptoe constraints, and the landing controller—are standard contact/centroidal relations and a previously demonstrated landing controller; they are not used to force the forward-jump distance or height, and the paper invokes no uniqueness theorem to forbid alternatives. The vague 'bias to the optimization's goal' in Sec. VI-B is an admitted compensation knob, but no value or fitted parameter is specified, so it cannot be identified as a fitted input renamed as a prediction on the quoted evidence. The planar single-legged symmetry reduction in Sec. II-C is a correctness and robustness risk rather than a circularity: it is an approximation stated before the optimization and is falsifiable against the reported simulation and experiment errors.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The framework relies on several manually chosen weights, bounds, and model reductions. The central targets of 1.0 m distance and 0.5 m height are user-set inputs rather than derived outputs. No new physical entity or conserved quantity is introduced.

free parameters (5)
  • Cost weight matrices = not reported
    All weight matrices in Sections III to V (W_sl_u, W_sl_v, W_sl_L, W_sl_pl, W_sl_t, W_sf_I, W_sf_u, W_jl, W_jf, W_wl, W_wf) are hand-tuned. No values are given and no sensitivity analysis is provided.
  • State and control bounds = not reported
    Boundary constraints for ssl, usl, Fsr, swl, uwl, swf, and uwf are manually designed without numerical values. The paper states these bounds need not be precise, but they still affect the feasible trajectory.
  • Inertia and momentum limits = rho_min_sr, rho_max_sr, Lmin, Lmax not reported
    The inertia and angular momentum ranges in Eq. 23 and the end constraints in Eq. 19 are chosen by hand to match the physical robot, but the actual values are not disclosed.
  • CoP support limits = X_min_CoP, X_max_CoP not reported
    The support region constraints in Sec. III-A5 are manually set to keep the CoP inside the foot, but no numerical values are given.
  • Model-compensation bias = not reported
    Sec. VI-B states that model mismatch errors are solved by adding bias to the optimization's goal, but the bias values and procedure are not described.
assumptions (6)
  • domain assumption The jump can be split into launching and flight phases with the landing angle symmetric to the launching angle (Sec. III, Eq. 17 and Eq. 27).
    This symmetry lets the planner count the lean distance twice in Eq. 17 and makes the landing posture mirror takeoff. If the robot cannot achieve this posture, the distance constraint and landing stability are not guaranteed.
  • domain assumption The two legs move identically, so the 5-link single-legged model with aggregated leg mass and inertia represents the full robot (Sec. II-C).
    The whole-body optimization solves the single-legged model and applies the result symmetrically to both legs, ignoring roll and yaw asymmetries and unequal ground reactions.
  • domain assumption During flight, angular momentum and horizontal linear momentum are exactly conserved, so inertia shaping is the only control of posture (Sec. III-B, Eq. 26).
    Air resistance, actuation lag, and asymmetric contact are neglected. The planned landing posture depends on this conservation.
  • domain assumption The fixed-base SRMP model with unlimited support force and torque, plus CoP bounds, is a valid surrogate for the contact dynamics of the launching phase (Sec. III-A5, Eq. 22).
    The SRMP model has no actuation limits. CoP constraints are added to make the momentum trajectory executable, but the mapping to the full robot is only verified indirectly through the later optimizations and experiments.
  • standard math Lagrangian equations of motion for the three models (Eqs. 2, 6, 8) describe the robot's dynamics accurately.
    The paper relies on standard rigid-body dynamics. No formal verification of these derivations is given.
  • ad hoc to paper The manually set cost weights and state and control bounds can be chosen so the optimum is feasible on the physical robot (Secs. III to V).
    No values, no tuning procedure, and no sensitivity analysis are reported. The reported experiment required adding bias to compensate model mismatch (Sec. VI-B).

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Cite this review

Pith. "Pith review of A 3-Step Optimization Framework with Hybrid Models for a Humanoid Robot's Jump Motion." pith.science (2026). https://pith.science/paper/SCLA2D2K

@misc{pith2026250112594,
  author       = {Pith},
  title        = {Pith review of: A 3-Step Optimization Framework with Hybrid Models for a Humanoid Robot's Jump Motion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SCLA2D2K}},
  note         = {Machine review of arXiv:2501.12594}
}
read the original abstract

High dynamic jump motions are challenging tasks for humanoid robots to achieve environment adaptation and obstacle crossing. The trajectory optimization is a practical method to achieve high-dynamic and explosive jumping. This paper proposes a 3-step trajectory optimization framework for generating a jump motion for a humanoid robot. To improve iteration speed and achieve ideal performance, the framework comprises three sub-optimizations. The first optimization incorporates momentum, inertia, and center of pressure (CoP), treating the robot as a static reaction momentum pendulum (SRMP) model to generate corresponding trajectories. The second optimization maps these trajectories to joint space using effective Quadratic Programming (QP) solvers. Finally, the third optimization generates whole-body joint trajectories utilizing trajectories generated by previous parts. With the combined consideration of momentum and inertia, the robot achieves agile forward jump motions. A simulation and experiments (Fig. \ref{Fig First page fig}) of forward jump with a distance of 1.0 m and 0.5 m height are presented in this paper, validating the applicability of the proposed framework.

Figures

Figures reproduced from arXiv: 2501.12594 by the authors.

Figure 1
Figure 1. Illustration of a forward jump experiment. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Overview of the framework in this paper were explored, and yet the harmonious control of the posture and the CAM is still worth digging. On the other hand, large￾scale nonlinear optimization solvers have been widely utilized in the trajectory generation of humanoid robot. Researchers constracted the solver with whole body model and designed complex cost function and constraints to obtain ideal trajecto￾ries [12], [1… view at source ↗
Figure 3
Figure 3. The robot platform used in this paper: (a) actual [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Diagram of the reaction mass pendulum (RMP) model. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 6
Figure 6. Figure 6: Illustration of the optimized SRMP trajectory during [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: Illustration of the optimized body trajectory from Sec. [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 8
Figure 8. Figure 8: The optimized joint trajectories of Sec. V. Each column [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 9
Figure 9. Figure 9: The optimized inertia and momentum trajectories of [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]
Figure 10
Figure 10. Figure 10: Illustration of the optimized results of Sec. V [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 11
Figure 11. Figure 11: Snapshot of a forward jump simulation [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 12
Figure 12. Figure 12: The momentum results of the simulation. Similar to [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]
Figure 13
Figure 13. Figure 13: Snapshots of jump experiments, which are numbered by “A, B, C” [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]
Figure 12
Figure 12. Figure 12: In the figures of the CoM’s position and veloc [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 14
Figure 14. Figure 14: CoM position and CAM results during the launching [PITH_FULL_IMAGE:figures/full_fig_p010_14.png]

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    2013

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.