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REVIEW 3 major objections 6 minor 31 references

COM Adjustment Mechanism Control for Multi-Configuration Motion Stability of Unmanned Deformable Vehicle

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A sliding battery keeps a transforming robot stable in both modes.

desk verdict A real hardware steering result and a walking claim that needs a baseline before it is believed. read the letter →

arxiv 2505.20926 v1 pith:VYTZ4VBF submitted 2025-05-27 cs.RO cs.SYeess.SY

Jun Liu , Hongxun Liu , Cheng Zhang , Jiandang Xing , Shang Jiang , Ping Jiang This is my paper
classification cs.ROcs.SYeess.SY
keywords unmanneddeformablevehiclecenter-of-massadjustmentmechanismstabilityfactorzero-momentpointK-meansclusteringvariableuniversefuzzycontrolactivedisturbancerejectionhybridautomata
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 claims that one physical mechanism -- a two-axis slider that shifts the vehicle's center of mass -- can actively stabilize both motion configurations of a wheel-legged vehicle that transforms between a car and a biped. In the vehicular state, moving the X-slider changes the front and rear wheelbases, which changes the steering stability factor $K$; a Fuzzy-PID controller drives $K$ to the understeering target $0.0024$ from an uncontrolled $0.00097$. In the humanoid state, moving X- and Y-sliders keeps the zero-moment point (ZMP) on its desired trajectory; a K-means-graded variable-universe fuzzy controller with active disturbance rejection (VUFC-ADRC) keeps walking stability mostly at levels 1 and 2 in simulation and at level 2 in physical tests. The reason to care is that stability is achieved by a dedicated lightweight actuator, so the leg joints can keep executing the planned gait and the steering system does not have to interrupt its motion to recover from disturbances.

What carries the argument

The carrying object is the center-of-mass adjustment mechanism: a T-shaped pair of X- and Y-direction slides mounted on the body, with the battery itself serving as the movable mass, driven by a ball screw and modeled as the linear second-order electromechanical system $\ddot{y} = -\frac{B_z}{J}\dot{y} + \frac{K_a K_t r_g}{J}u$. The two identities that carry the argument are the steering stability factor $K = \frac{m}{L^2}\left(\frac{a}{k_2}-\frac{b}{k_1}\right)$ and the zero-moment point (ZMP); slider displacement enters both. The new coupling is K-means clustering on (ZMP error, ZMP error-rate) data, which turns the qualitative ZMP criterion into five discrete stability levels $L_1$-$L_5$, and a variable-universe fuzzy controller that expands or contracts its input universe according to the current level, followed by an ADRC that tracks the commanded slider displacement.

What would settle it

Freeze the COM sliders at their center positions and rerun the steady-state steering and walking tests under the same disturbances; if the stability factor still holds near $0.0024$ and the ZMP still stays at level 2, the mechanism is not doing the work. Sharper still: recompute the K-means cluster centers from hardware-measured (ZMP error, ZMP error-rate) samples during real walking and check whether they coincide with Table 1; mismatch would mean the stability-level labels that scale the fuzzy universe are miscalibrated.

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Extended reading notes

Core claim

The paper's central discovery is that center-of-mass adjustment alone is a sufficient control channel for both steady-state steering stability and walking stability. For steering, the problem is compressed into the stability factor identity $K = \frac{m}{L^2}\left(\frac{a}{k_2} - \frac{b}{k_1}\right)$: shifting the X-slider changes $a$ and $b$, and closed-loop Fuzzy-PID control converges $K$ to the desired value $0.0024$, improving overshoot from $14.99\%$ to $9.19\%$, rise time from $1.05\,\mathrm{s}$ to $0.35\,\mathrm{s}$, and settling time from $2.37\,\mathrm{s}$ to $1.52\,\mathrm{s}$ in simulation. For walking, the paper converts the qualitative ZMP stability criterion into a quantitative five-level scale by running K-means clustering on $10^5$ ADAMS-simulated ZMP deviation samples, then uses the stability level to scale the universe of a variable-universe fuzzy controller whose output is a desired slider displacement; an active disturbance rejection controller tracks that displacement. The reported results are a reduction in maximum ZMP tracking error from $0.037\,\mathrm{m}$ under PID to near the ideal trajectory, and, with K-means grading, a $14.86\%$ reduction in overshoot and $3.6\%$ reduction in steady-state error relative to VUFC-ADRC without grading.

Load-bearing premise

The walking-stability grading rests on the assumption that the real robot's ZMP deviations fall into the same clusters as the ADAMS simulation of the nominal gait, so the Table 1 cluster centers remain valid labels on hardware; the paper's own test already shows the real stability level running one level higher than simulation.

Editorial extensions

If this is right

  • A conventional fixed-COM vehicle cannot change its stability factor; the mechanism gives the unmanned deformable vehicle an actively tunable understeering capability that can be re-targeted for different loading and speed conditions.
  • Because stability correction happens through the COM slider rather than through leg joints or steering, the planned gait and steering can continue undisturbed while the controller recovers stability.
  • The K-means five-level grading turns the ZMP criterion from a binary safe/unsafe check into a graded safety margin that can be monitored in real time and acted on before the ZMP leaves the support region.
  • The hybrid automata upper controller gives a formal way to switch the same physical actuator between the two configurations, so adding future motion modes only requires adding new discrete states rather than new hardware.

Reading between the lines

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

  • The one-level gap between simulated and hardware stability levels suggests a systematic calibration offset in the ZMP model; if the gap grows with terrain or gait, the cluster centers would need to be retrained per operating condition rather than once.
  • The constant target $K_d = 0.0024$ is a single operating point; a speed- or load-dependent target would be a natural extension and would test whether the slider authority is adequate at the characteristic speed of 75 km/h.
  • The mechanism's authority is bounded by slider travel, so for large disturbances the next step would be blending slider motion with leg or steering actuation; the hierarchical architecture already has the discrete states to host such a fallback.
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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 / 6 minor

Summary. This paper presents a center-of-mass (COM) adjustment mechanism for a reconfigurable wheel-legged robot and a hierarchical control strategy for two configurations. The upper-level hybrid automaton switches between a vehicular steady-state steering controller and a humanoid walking controller. The steering controller uses Fuzzy-PID to move an X-direction slider so that the vehicle stability factor K tracks a desired understeering value K_d = 0.0024, improving the simulated and measured K from 0.00097. The walking controller uses a variable-universe fuzzy controller combined with active disturbance rejection control (VUFC-ADRC), with a K-means clustering stage that grades the walking stability level from ZMP deviation and deviation rate. Simulation and hardware tests show the ZMP tracked near the planned reference and stability levels mostly at levels 1 and 2 in simulation and at level 2 in the hardware test; the paper also reports that hardware levels are one level higher than simulation. The central claim is that slider control significantly improves multi-configuration motion stability.

Significance. The idea of using a dedicated COM actuator for both vehicle steering and walking stability is useful, and the steering result is the strongest part: the stability factor is a standard objective, the before/after K values are external to the controller, and the hardware curves in Fig. 12 show a consistent understeering improvement. The walking control architecture is more speculative. The K-means-graded VUFC-ADRC is an interesting combination, but the hardware validation currently does not isolate the effect of the COM control from the gait planner, and the stability-level labels are not calibrated to a physical margin. The paper is transparent about the one-level discrepancy between simulation and test in Section 6.3, which is a useful limitation but also highlights the need for further validation. If the authors add a hardware baseline and validate the K-means labels against a physical ZMP margin, the contribution would be solid.

major comments (3)
  1. [6.3 and Fig. 13] The central walking-stability improvement claim is not supported on hardware: no no-control or alternative-controller baseline is reported for the walking test. The hardware evidence in Figs. 13(a)-(b) is that the controlled ZMP tracks the ideal trajectory, and Figs. 13(c)-(d) show the resulting stability levels. Tracking a planned reference does not by itself demonstrate that the COM controller improves stability; the comparison against the PID in the simulation of Section 5.2 is not an experimental baseline. Please add a hardware baseline with the COM slider fixed, or with PID-only control, or otherwise restrict the hardware claim to 'stability is maintained' rather than 'significantly improved.'
  2. [4.2, Table 1, 6.3] The K-means cluster centers in Table 1 are trained exclusively on ADAMS simulation data for the nominal gait, yet they are applied to real-robot COP measurements in Section 6.3 to label the stability level. The paper itself reports that the hardware stability levels are systematically one level higher than the simulation results (Section 6.3), demonstrating a simulation-to-hardware calibration gap. Consequently, the reported 'level 2' result is a cluster index with unvalidated physical meaning; if the real COP distribution differs beyond the observed shift, the variable-universe scaling factors will be triggered by mislabeled levels and the claimed walking improvement may not transfer. Furthermore, the level is defined from the same ZMP error signal that the controller minimizes, so the level improvement is partly self-referential unless calibrated to a physical stability margin. Please validate the cluster labels against a physical margin (e.g., distance from ZMP to the support-polygon boundary) on hardware, or retrain/calibrate the clusters with hardware data and show that the labels remain consistent.
  3. [3.2, Eq. (9)] The homogeneous transformation matrix in Eq. (9) is not a valid transformation matrix as printed: entries such as 'cosθ_iz cosθ_ix - cosθ_iz cosθ_ix' and the placement of squared cosine terms are internally inconsistent, and the matrix does not have the standard rigid-body form. Since Eqs. (11)-(15) compute COM and ZMP from this transformation, the kinematic model used for the walking controller and simulation should be corrected or replaced with a correctly rendered version, or the derivation should be referenced to a reliable source.
minor comments (6)
  1. [3.1] Equation (6) appears twice verbatim in the text; one duplicate should be removed.
  2. [4.2, Eq. (17)] Equation (17) states '105' actual ZMP samples, but the surrounding text says 10,000 steps with 10 samples per step, which is 100,000 samples; the exponent formatting should be corrected and the notation made explicit.
  3. [6.1, 6.2] Reference [28] is cited for the ZMP/COP approximation and reference [29] for the fixed front wheel steering angle method, but the reference list identifies [28] as an automobile handling test standard and [29] as a trajectory optimization paper; the citations should be remapped.
  4. [4.2 c)] Equation (25) places the observer poles at -ω0 while Eq. (26) and the simulation parameters in Section 5.2 use ω_e; unify the notation for the observer bandwidth.
  5. [5.2] The simulation claims 'anti-disturbance ability' but does not specify what external disturbance was applied. Please state the disturbance model and magnitude, otherwise the comparison between the VUFC-ADRC variants is not reproducible.
  6. [4.2, Eq. (18)] The weighted distance in Eq. (18) uses fixed weights 0.7/0.3. A brief justification of these weights, or a sensitivity study of the resulting cluster centers to them, would strengthen the K-means grading stage.

Circularity Check

1 steps flagged · score 4.0 of 10

Walking-stability grading is a self-referential transform of the controlled ZMP error; the vehicular stability claim is independent and externally anchored.

  1. self definitional [Section 4.2 (walking stability control steps 1–4), Eqs. (17)–(18), Table 1, Figs. 10(c,d) and 13(c,d).]
    "Based on the K-means clustering algorithm, the walking stability grade is quantitatively evaluated according to the deviation ZMP_e and deviation change rate ZMP_ec between the expected ZMP_d and the actual ZMP. (2) The evaluation result L_i is input into the variable universe fuzzy controller... The basis fuzzy controller then outputs the desired slider displacement y_d to the ADRC after fuzzy operation based on the optimized universe, deviation ZMP_e, and deviation change rate ZMP_ec."

    The walking stability level L_i is defined as the nearest-cluster-center label of the vector (ZMP_e, ZMP_ec) (Eq. 17, Eq. 18, Table 1), and the very same two signals are the inputs to the basis fuzzy controller that generates the corrective slider command. Therefore, reporting that VUFC-ADRC keeps the stability level at 1–2 is a discretized restatement of the tracking-error vector the controller is designed to minimize; it is not an independent stability margin such as distance to the support-polygon boundary.

full rationale

The vehicular steady-state steering claim is not circular: the desired stability factor K_d = 0.0024 is taken from an external reference [27], the stability factor K is computed from the standard bicycle model (Eqs. 7–8), and the Fuzzy-PID controller is assessed by its ability to track this external target against a no-control baseline (K = 0.00097). No fitted parameter is renamed as a prediction in that loop. The walking claim is more problematic. The K-means 'stability levels' in Table 1 are cluster labels trained on the same ZMP deviation and deviation-rate signals that form the controller's inputs. Saying the controller 'basically remained at levels 1 and 2' is therefore equivalent to saying the controller kept the ZMP error small relative to simulation-derived cluster thresholds; the grading does not measure an independent physical safety margin. This is a genuine but partial self-referentiality: the controller's ZMP-tracking comparison against PID is still a meaningful control result, and the paper does not rely on a uniqueness theorem or on load-bearing self-citations to make its main control-design choices. The self-citations [1]–[6] are background for the robot platform and are not used to forbid alternatives. A no-control hardware walking baseline is not reported, and the simulation-to-reality one-level offset is a calibration weakness, but those are correctness risks rather than circularity. Overall, the central vehicular claim is self-contained, while the walking-stability grading partially reduces by construction, giving a moderate circularity score of 4.

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

The central results depend on several unverified modeling assumptions: the linear electromechanical model of the COM mechanism, the ADAMS simulation as a source of stability labels, the ZMP/COP approximation, and manually tuned controller parameters. The paper does not identify physical parameters or provide sensitivity analysis, so these assumptions are largely unvalidated.

free parameters (8)
  • Desired stability factor K_d = 0.0024
    Control target for steady-state steering, taken from reference [27] rather than derived for this vehicle; the paper calls it optimal but does not justify it for this robot.
  • ADRC lumped input gain b0 = 0.08
    Set to 0.08 in simulation for both X and Y axes; it is the lumped gain K_a K_t r_g / J in Eq. (4) and should be identified from hardware, but no identification procedure is reported.
  • ADRC observer bandwidth omega_e = 200 (X), 250 (Y)
    Chosen by the authors; controls extended-state-observer pole locations in Eq. (25) and thus disturbance estimation speed.
  • ADRC controller/tracking parameters omega_0 = 1000 (X), 1200 (Y)
    Used in the tracking differentiator and state error feedback; no tuning rule is given beyond manual selection.
  • Fuzzy-PID initial gains = kp0=15, ki0=0.8, kd0=9
    Selected after 'several debugging processes', i.e., hand-tuned for the simulated plant.
  • K-means weighted distance weights = 0.7 and 0.3
    Weights in Eq. (18) between ZMP error and error-rate; chosen arbitrarily, not justified by data or theory.
  • Number of stability clusters = 5
    The authors chose to divide ZMP error space into five levels (Table 1); no criterion for the number of clusters is given.
  • Variable universe scaling factor range = scaling factors in [0.5, 1.5]
    Membership functions and universe ranges for the scaling-factor fuzzy controller are hand-set design choices.
assumptions (6)
  • domain assumption Linear 2-DOF bicycle model with constant cornering stiffness and small slip angle is valid for steady-state steering.
    Used to derive the stability factor K in Eqs. (5)-(8); the paper itself notes nonlinear tire behavior above 0.3g, so the model is scoped to low lateral acceleration.
  • domain assumption ZMP criterion is a valid stability measure and ZMP can be approximated by COP measured by foot pressure sensors.
    Standard assumption in legged robotics, cited [28]; the paper uses COP as ZMP in the walking test (Section 6.1).
  • domain assumption The ADAMS simulation model of the robot is an accurate representation of the real robot for ZMP statistics.
    The K-means stability clusters are trained on this simulation (Section 4.2); if the simulation differs from hardware, the stability labels are invalid.
  • domain assumption The electromechanical model of the center-of-mass adjustment mechanism is linear second-order with constant coefficients and known b0.
    Eq. (4) and the ADRC design assume this; friction, backlash, and cross-coupling between X and Y slides are ignored.
  • standard math Disturbance f in Eq. (19) is differentiable so that the linear extended state observer converges.
    Standard ADRC assumption; ensures e converges to 0 given negative-real-part observer poles.
  • ad hoc to paper The fuzzy rule tables (Tables 2-4) correctly encode the desired control policy for stability factor and ZMP tracking.
    The rules are manually constructed and not derived from any optimization or stability proof; the paper provides no justification for specific entries.

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Cite this review

Pith. "Pith review of COM Adjustment Mechanism Control for Multi-Configuration Motion Stability of Unmanned Deformable Vehicle." pith.science (2026). https://pith.science/paper/VYTZ4VBF

@misc{pith2026250520926,
  author       = {Pith},
  title        = {Pith review of: COM Adjustment Mechanism Control for Multi-Configuration Motion Stability of Unmanned Deformable Vehicle},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VYTZ4VBF}},
  note         = {Machine review of arXiv:2505.20926}
}
read the original abstract

An unmanned deformable vehicle is a wheel-legged robot transforming between two configurations: vehicular and humanoid states, with different motion modes and stability characteristics. To address motion stability in multiple configurations, a center-of-mass adjustment mechanism was designed. Further, a motion stability hierarchical control algorithm was proposed, and an electromechanical model based on a two-degree-of-freedom center-of-mass adjustment mechanism was established. An unmanned-deformable-vehicle vehicular-state steady-state steering dynamics model and a gait planning kinematic model of humanoid state walking were established. A stability hierarchical control strategy was designed to realize the stability control. The results showed that the steady-state steering stability in vehicular state and the walking stability in humanoid state could be significantly improved by controlling the slider motion.

Figures

Figures reproduced from arXiv: 2505.20926 by the authors.

Figure 1
Figure 1. Components and motion modes of unmanned deformable vehicle. Components Walking in humanoid state Front body Steer-by-wire Suspension system Rear body EHB Hub motor COM adjustment mechanism Joint motor Leg mixer mechanism Parallel linkage Horizontal lifting parallel mechanism Lift motor Electric actuators Unmanned deformable vehicle Steering driving in vehicular state [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

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Pith tools

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