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Predicting center of mass position in non-cyclic activities: The influence of acceleration, prediction horizon, and ground reaction forces

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper shows that incorporating ground reaction forces into center-of-mass prediction, through constant or cubic acceleration profiles, cuts position error and improves direction accuracy at 125–250 ms horizons, and identifies 250 ms…

desk verdict Solid empirical comparison with an abstract that overstates one accuracy finding; the AE result holds, the ADA claim needs correction. read the letter →

arxiv 2411.16891 v1 pith:W4AGECZ5 submitted 2024-11-25 cs.RO

Mohsen Alizadeh Noghani , Edgar Bolívar-Nieto This is my paper · ORCID
classification cs.RO
keywords centerofmasspredictiongroundreactionforcesnon-cyclicactivitiesintentinferencewearablerobotsaccelerationprofilehorizondoubleintegrator
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 asks whether a wearable system can predict where the whole-body center of mass (CoM) will be a fraction of a second from now, using only the current state and a guessed future acceleration, and whether adding ground reaction forces (GRFs) helps. It analyzes data from 10 healthy adults performing 14 non-cyclic activities, comparing three acceleration forecasts—zero, constant, and a cubic that decays to zero—across horizons from 125 to 625 ms. The central result is that GRF-informed constant and cubic profiles clearly beat the zero-acceleration assumption at 125 and 250 ms horizons, in both position error and direction accuracy, and that 250 ms is the point where prediction quality starts to degrade sharply. A sympathetic reader would care because CoM position is a proxy for movement intent, and a 250 ms lookahead window is about the timescale on which exoskeletons and prostheses need to act.

What carries the argument

The load-bearing mechanism is a discrete-time double-integrator state-space model of the CoM, $\ddot{p}=u$, where the input $u$ is the GRF-derived acceleration (net external force divided by mass, with gravity removed). Given current position and velocity, the future position is computed by propagating the state with one of three assumed acceleration profiles over the horizon: zero, constant at the first sample, or a cubic that starts at the first sample and decays to zero with zero jerk at both ends. The cubic profile is motivated by minimum-jerk humanoid planning; the oracle profile uses the future GRFs directly and serves as a lower bound. Because the error formula (Appendix C) reduces to a double integral of the difference between assumed and true acceleration, a constant mismatch under the simplifying assumptions produces the observed quadratic error growth in horizon length.

What would settle it

Re-run the prediction pipeline with an instrumented chair or handrail that records contact forces during sit-to-stand and stand-to-sit, and compare ground-truth CoM acceleration from force plates plus contact forces against the whole-body marker estimate; if the zero-acceleration baseline then matches the GRF-based profiles at 125 and 250 ms, the reported benefit would be shown to depend on unmeasured external contacts.

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Extended reading notes

Core claim

The authors claim that future center-of-mass position over short horizons can be predicted by forward integration of a double-integrator model, and that the quality of that prediction is governed mainly by horizon length and by whether the assumed acceleration profile uses ground reaction forces. Using whole-body marker trajectories as ground truth, they find that position error grows quadratically with horizon (R² > 0.930 for all profiles) and direction accuracy falls linearly (R² > 0.615). At horizons of 125 and 250 ms, the constant and cubic-to-zero profiles—both seeded with the GRF-derived acceleration at the first sample—outperform the zero-acceleration baseline on average error and average direction accuracy, with statistically significant differences and large effect sizes; at longer horizons the advantage fades and sometimes reverses for worst-case error. The authors therefore treat 250 ms as a threshold for practical predictive intent inference.

Load-bearing premise

The comparisons assume that the whole-body marker-based OpenSim CoM estimate is an unbiased ground truth and that the measured ground reaction forces plus gravity are the only external forces acting on the body, so unmeasured chair or handrail contacts during activities like sit-to-stand and stand-to-sit would violate the acceleration input.

Editorial extensions

If this is right

  • At horizons up to 250 ms, GRF-informed constant and cubic profiles reduce average CoM position error and improve direction accuracy relative to zero-acceleration prediction, with the largest effects at 125 ms.
  • Prediction error grows quadratically and direction accuracy declines linearly with horizon for all profiles, so extending the prediction window beyond a few hundred milliseconds carries a steep accuracy cost.
  • The 250 ms horizon is proposed as a practical threshold for CoM-based intent prediction in applications such as lower-limb wearable robots.
  • At longer horizons, zero-acceleration can produce lower maximum errors than GRF-based profiles, because a single early acceleration sample becomes an unreliable forecast.
  • Even the oracle profile, which uses the true future GRFs, accumulates integration drift and loses direction accuracy, so no constant-profile method can fully escape horizon-dependent degradation.

Reading between the lines

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

  • Editorial inference: the one-sample advantage of GRF information suggests that even partially available GRFs in instrumented footwear or bionic limbs could improve short-horizon intent inference without a full motion-capture ground truth.
  • Editorial inference: because the quadratic error growth follows from double integration of a constant acceleration mismatch, the same scaling should appear whenever a point-mass CoM model is forward-integrated with a mismatched acceleration forecast; testing this in a different dataset (e.g., walking perturbations) would check the generality.
  • Editorial inference: chair contact forces during sit-to-stand and stand-to-sit are a plausible unmeasured external force; adding an instrumented chair or handrail would reveal whether the reported GRF benefit changes when contacts are not on the force plates.
  • Editorial inference: the near-oracle performance at 125 ms aligns with neuromuscular reaction time, suggesting that a control loop running at this timescale might be the natural operating point for balance-assist controllers.
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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

2 major / 5 minor

Summary. This manuscript studies short-horizon prediction of the whole-body center-of-mass (CoM) position during 14 non-cyclic activities performed by 10 healthy adults. The CoM is modeled as a double integrator driven by acceleration inputs derived from ground reaction forces, and four acceleration assumptions are compared: zero, constant, cubic-to-zero, and an oracle that uses future measured accelerations. For horizons of 125 to 625 ms, the authors report that average and maximum position errors grow quadratically with horizon length while direction accuracy decreases linearly, and that GRF-based constant and cubic profiles improve prediction at short horizons relative to the zero-acceleration baseline. The paper proposes 250 ms as a practical horizon threshold for intent inference in wearable robotics.

Significance. If the results hold, the paper provides a transparent, parameter-free baseline for CoM prediction and a concrete argument that even a single instantaneous GRF sample improves short-horizon prediction relative to a constant-velocity assumption. The statistical analysis is careful: Welch ANOVA, Bonferroni-corrected post-hoc tests, F-tests for trend degree, weighted least squares, confidence intervals, and reported effect sizes. The a priori definition of the acceleration profiles and the use of an oracle reference reduce circularity concerns, and the quadratic-error explanation in Appendix C is explicit and testable. The broad qualitative conclusions are likely robust, but the abstract overstates the direction-accuracy evidence for the constant profile, and the GRF-derived acceleration assumption is not satisfied for all analyzed activities due to unmeasured chair-contact forces.

major comments (2)
  1. [Abstract and Section 3, Table 2] The abstract claims that "the constant and cubic profiles, which utilize the GRFs, outperform the zero-acceleration assumption in ... accuracy ... at horizons of 125 and 250 ms (p<0.034, d>1.44)." Table 2 shows that for ADA at T=250 ms the Zero-Const comparison has p=1.00 with no reported effect size, so the Constant profile does not significantly improve direction accuracy at 250 ms; only the Zero-Cubic comparison is significant there (p=0.034, d=1.44). The results text in Section 3 also states that differences were found between Zero-Const only at T=125 ms. The abstract and the corresponding sentence in Section 4.2 should be corrected to distinguish the Constant and Cubic profiles, e.g., Constant improving direction accuracy only at 125 ms and Cubic improving it at all tested horizons.
  2. [Section 2.1 and Appendix B, Eq. (B.1)] Equation (B.1) defines the acceleration input using ground reaction forces and gravity as the only external forces, but the protocol includes Sit to Stand, Stand to Sit, and Foot on Chair, during which the chair exerts reaction forces on the body that are not measured by the force plates. For samples in which the participant is still in contact with the chair, u[1] and the Oracle inputs are not the true CoM acceleration, so the error comparisons involving the Constant, Cubic, and Oracle profiles can be biased for those activities. The authors should either quantify the extent of chair-contact samples through a sensitivity analysis that excludes those activities or phases, or add an explicit limitation with evidence that the conclusions are unchanged; as written, the assumption in Eq. (B.1) is not satisfied for all analyzed data.
minor comments (5)
  1. [Abstract and Fig. 3b] The abstract reports R2>0.930 for the quadratic position-error fits, while Fig. 3b shows R2=0.918 for the Constant maximum-error fit; these numbers should be reconciled.
  2. [Section 4.2] The sentence "with the Zero having a significantly larger ADA than Cubic at all levels of T" appears to have the comparison reversed; Table 2 and Fig. 4a indicate that Cubic has significantly higher ADA than Zero, so the wording should be corrected.
  3. [Section 2.1] The manual labeling of force plate contact events is not described with any reliability measure; a brief statement on inter- or intra-rater consistency, or an automated rule-based alternative, would strengthen reproducibility.
  4. [Section 2.2] The choice of 125 ms as the minimum horizon is justified by a self-cited prior conference paper (Noghani and Bolivar-Nieto, 2024); restating the relevant evidence or providing an independent rationale would make the horizon grid self-contained.
  5. [Section 4.3] The statement that at T=250 ms the profiles achieved "AE <0.57 cm, ME <11.7 cm" should specify that these are mean values and should indicate whether the bounds apply to all profiles or only to the GRF-based profiles.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the acceleration profiles are defined a priori and predictions are compared against an independent marker-derived CoM estimate; the only minor self-citation is not load-bearing.

full rationale

The prediction pipeline is self-contained. The three acceleration profiles (Zero, Constant, Cubic-to-zero) are fixed functional forms specified in Section 2.2, with no parameters fitted to the error data; the only data-driven input is the instantaneous GRF-derived acceleration u[1], while the Oracle additionally uses future GRFs and is explicitly labeled as an ideal reference. Prediction errors (Eq. 2) and metrics (Eqs. 3-7) compare forward-integrated positions against the whole-body marker/OpenSim CoM estimate, which is an independent measurement chain (Section 2.1). The quadratic error growth is first established by F-tests on the measured errors (Section 3) and then rationalized post hoc in Appendix C under simplifying assumptions; the appendix is an explanation of the mechanism, not the source of the data. The only self-citation, Noghani and Bolívar-Nieto (2024), is used solely to justify the 125 ms minimum horizon ('The minimum length of 125 ms was determined by previous results...') and does not supply the comparative result that GRF-based profiles outperform zero acceleration; therefore it is not load-bearing. The abstract's joint claim about direction accuracy at 250 ms is somewhat overbroad relative to Table 2 (Zero-Const ADA p=1 at T=250 ms), but that is an internal reporting inconsistency, not a circular derivation. Limitations regarding unmeasured external forces and wearable deployment are acknowledged in Section 4.4 and affect external validity, not the internal derivation chain.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The prediction model itself has no fitted parameters: the zero, constant, and cubic acceleration profiles are defined a priori, and the statistical trend fits are descriptive outputs, not inputs to the predictor. The central claim depends on several domain assumptions, chiefly that the marker-based OpenSim CoM is ground truth and that GRFs plus gravity are the only external forces. Preprocessing choices, including filter cutoffs and manual contact labels, are hand-selected and could affect error magnitudes. No new physical entities are introduced.

free parameters (3)
  • Marker data low-pass filter cutoff = 6 Hz
    Set to 6 Hz in Motive for marker trajectories; affects the reference CoM and therefore the measured prediction errors.
  • GRF low-pass filter cutoff = 20 Hz
    Set to 20 Hz for force plate data; determines the acceleration input u[1] and the oracle.
  • Manual contact event labels = hand-labeled per trial
    Force plate contact onsets and offsets are manually labeled; this choice clips GRFs and could influence short-horizon predictions.
assumptions (4)
  • domain assumption Newton's second law: sum of external forces equals mass times CoM acceleration, with GRFs and gravity as the only external forces (Eq. B.1).
    The prediction model is a double integrator driven by u = GRF/m; any unmeasured external contact, such as a chair or handrail, would violate Eq. (B.1).
  • domain assumption Whole-body marker-based OpenSim CoM estimate is the ground truth reference.
    All prediction errors are computed against this reference (Section 2.1); marker artifacts, soft tissue motion, or model scaling errors propagate into reported errors.
  • domain assumption The future CoM acceleration is well approximated by one of three profiles: zero, constant, or cubic-to-zero with zero endpoint jerk.
    These profiles define the predictions (Section 2.2); they are motivated by time-series forecasting and minimum-jerk planning but are not validated against actual future accelerations except via the oracle.
  • standard math Statistical model assumptions: normality, variance handling via weighted least squares, and Bonferroni-corrected post-hoc tests.
    Section 2.3; with N=10 subjects per cell, normality checks are low-powered.

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Cite this review

Pith. "Pith review of Predicting center of mass position in non-cyclic activities: The influence of acceleration, prediction horizon, and ground reaction forces." pith.science (2026). https://pith.science/paper/W4AGECZ5

@misc{pith2026241116891,
  author       = {Pith},
  title        = {Pith review of: Predicting center of mass position in non-cyclic activities: The influence of acceleration, prediction horizon, and ground reaction forces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W4AGECZ5}},
  note         = {Machine review of arXiv:2411.16891}
}
abstract

The whole-body center of mass (CoM) plays an important role in quantifying human movement. Prediction of future CoM trajectory, modeled as a point mass under influence of external forces, can be a surrogate for inferring intent. Given the current CoM position and velocity, predicting the future CoM position by forward integration requires a forecast of CoM accelerations during the prediction horizon. However, it is unclear how assumptions about the acceleration, prediction horizon length, and information from ground reaction forces (GRFs), which provide the instantaneous acceleration, affect the prediction. We study these factors by analyzing data of 10 healthy young adults performing 14 non-cyclic activities. We assume that the acceleration during a horizon will be 1) zero, 2) remain constant, or 3) converge to zero as a cubic trajectory, and perform predictions for horizons of 125 to 625 milliseconds. We quantify the prediction performance by comparing the position error and accuracy of identifying the main direction of displacement against trajectories obtained from a whole-body marker set. For all the assumed accelerations profiles, position errors grow quadratically with horizon length ($R^2 > 0.930$) while the accuracy of the predicted direction decreases linearly ($R^2>0.615$). Post-hoc tests reveal that the constant and cubic profiles, which utilize the GRFs, outperform the zero-acceleration assumption in position error ($p<0.001$, Cohen's $d>3.23$) and accuracy ($p<0.034$, Cohen's $d>1.44)$ at horizons of 125 and 250$\,ms$. The results provide evidence for benefits of incorporating GRFs into predictions and point to 250$\,ms$ as a threshold for horizon length in predictive applications.

Figures

Figures reproduced from arXiv: 2411.16891 by the authors.

Figure 1
Figure 1. The activities and statistics of their durations, reported in milliseconds as mean (standard deviation) and minimum [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. (a) The framework for prediction of CoM position in a horizon, which works in two steps: 1) estimating the [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. The fitted curves for (a) the average error ( [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The fitted curves for (a) the average direction accuracy ( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

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Cited by 1 Pith paper

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.