Estimation of Aerodynamics Forces in Dynamic Morphing Wing Flight

Albert Park; Alireza Ramezani; Bibek Gupta; Eric Sihite; Koushil Sreenath; Mintae Kim

REVIEW 4 major objections 4 minor 25 references

Estimation of Aerodynamics Forces in Dynamic Morphing Wing Flight

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper claims that two force estimators—a conjugate momentum observer and an MLP regressor—recover aerodynamic forces on a morphing-wing robot within 0.04–0.13 N of load-cell measurements.

desk verdict First experimental validation of a momentum observer on a morphing-wing robot, but the load-cell ground truth needs an inertial baseline before the RMSE claims hold. read the letter →

arxiv 2508.02984 v1 pith:MQZFIJWR submitted 2025-08-05 cs.RO

Bibek Gupta , Mintae Kim , Albert Park , Eric Sihite , Koushil Sreenath , Alireza Ramezani This is my paper · ORCID

classification cs.RO

keywords aerodynamicforceestimationflapping-wingrobotconjugatemomentumobservermulti-layerperceptrontetheredflightmorphingwingHamiltonianmechanicsloadcellvalidation

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

Accurate aerodynamic force sensing is a missing ingredient for closed-loop control of flapping-wing robots whose wings morph during flight. This paper claims that two very different estimators can recover those forces on the Aerobat platform during tethered flight: a physics-based conjugate momentum observer built from Hamiltonian mechanics, and a data-driven multi-layer perceptron trained on joint kinematics and flapping frequency. Both are validated against a six-axis load cell, with RMSEs between 0.0401 N and 0.1322 N across the three force components. The values suggest that a model-based observer can match a learned regressor closely enough to serve as a training-free alternative for onboard force feedback.

What carries the argument

The two load-bearing tools are a conjugate momentum observer and a three-hidden-layer multi-layer perceptron. The observer exploits Hamiltonian structure: by filtering the conjugate momentum error between the modeled dynamics and the measured state, it produces an estimate of the external generalized force acting on the five-body armwing model. It requires only the mass-inertia matrix, Coriolis terms, gravity vector, and motor torque commands, so it is training-free. The MLP, with hidden layers of size 128×128×128, mean-squared-error loss, and the Adam optimizer, learns a nonlinear mapping from joint angles, velocities, flapping frequency, and environmental parameters to the three force components. A six-axis load cell sampled at 7 kHz provides the ground truth used both to train the regressor and to score both estimators.

What would settle it

Run the same flapping gait with the airflow fan off and subtract that baseline from the load-cell signal; if the resulting no-airflow force is comparable to or larger than the reported RMSE values, then the ground truth is contaminated by inertial reaction forces and the validation would not support the claimed accuracy.

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Extended reading notes

Core claim

The central claim is that external aerodynamic forces on a dynamically morphing flapping-wing robot can be estimated online by two distinct routes that agree with measured ground truth. The conjugate momentum observer derives from the system's reduced-order Hamiltonian model: it treats aerodynamic loads as an unknown external wrench and reconstructs it from joint state and motor torque without any training data. The MLP regressor instead learns the map from joint kinematics, flapping frequency, and environmental inputs to force outputs, and slightly outperforms the observer on all three axes (RMSE 0.0401 versus 0.0467 N on Fx, 0.0696 versus 0.1059 N on Fy, 0.1155 versus 0.1322 N on Fz). The reported agreement indicates that morphing-wing aerodynamics, despite unsteady fluid-structure interactions, are recoverable from body and joint motion plus actuation signals.

Load-bearing premise

The 6-axis load cell measures only aerodynamic forces, even though the wings accelerate each cycle and their inertia can push and pull on the mount.

Editorial extensions

If this is right

A training-free physics observer can supply aerodynamic force estimates during flapping flight, enabling force feedback without a labeled dataset.
The MLP's slightly lower RMSE shows that learned regressors can capture downstroke-to-upstroke transients that a rigid-body observer misses.
Both estimators reproduce the periodic force profile and directional asymmetries of morphing-wing flight, giving a benchmark for future control and gait design.
The approach can be repeated to generate ground-truth force datasets for offline aerodynamic model identification.
Force-aware control loops could use these estimates to regulate lift during hover and to transition toward untethered flight.

Reading between the lines

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

If load-cell inertial contamination is confirmed, the apparent advantage of the MLP over the observer may shrink or reverse, because the regressor could be learning the wing's inertial signature rather than true aerodynamics.
The same observer recipe should transfer to other morphing-wing robots, since it needs only the reduced-order model and motor commands, while the MLP would require retraining for each new platform.
A hybrid estimator that feeds the momentum observer's output into the MLP as an additional feature could combine the observer's physical consistency with the regressor's peak-tracking ability, though the paper does not test this.
With reliable force estimates, wing-gait optimization could target the observed upstroke negative-force phase to reduce drag and improve hover efficiency.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is the first experimental application of a conjugate momentum observer to aerodynamic force estimation on a dynamically morphing flapping-wing robot (Aerobat), paired with an MLP regression baseline. The comparison is useful and the RMSE numbers are plausibly in the right ballpark. The weak spot is the ground truth: the 6-axis load cell measures the total reaction at the mount, which includes the inertial reaction forces from the wings (each ~0.4 g, flapping at 100 ms cycle). The text never describes a no-airflow baseline or any subtraction step, so both estimators may be validated against aerodynamic-plus-inertial force. The stress-test concern holds up on reading.

What's genuinely new: momentum observers have a long history in legged locomotion, but this paper brings them to flapping flight, on a platform designed to have significant wing inertia—the exact regime where momentum-based methods are relevant. The MLP is a standard regression, but the side-by-side comparison on the same hardware is useful for the community. The paper also describes the testbed (Kinova arm, ATI Nano17, 7 kHz sampling) and gives concrete RMSE values.

Where it gets soft: besides the missing inertial baseline, the version we inspected omits Section IV (the observer derivation) and most of Section V (training details, data processing). I can't check whether the dynamics model correctly compensates for wing inertia internally, or whether the MLP train/test split is clean. The RMSE values are reported without error bars or trial-to-trial spread, even though the conclusion mentions 'multiple trials.' These are fixable, but they're part of the validation story.

Overall: the idea is sound, the platform is genuinely interesting, and the first validation of a momentum observer on a morphing wing is a legitimate contribution. The inertial contamination of the load cell is a load-bearing validity issue that needs to be addressed—either by demonstrating that wing inertial reaction forces are negligible at the mount or by adding a baseline subtraction. That's a revision, not a desk reject.

Recommendation: I'd send this to peer review. It's the kind of paper a serious referee can push into shape. If the authors add the missing derivation, show a no-airflow baseline, and give proper train/test and trial-to-trial statistics, this could become a solid reference for force estimation in morphing-wing robots.

For your reading group: it's narrow, but if anyone works on flapping-wing control or force feedback, it's worth a look. I'd cite it if I were in the subfield; the platform plus the first momentum-observer comparison is citable.

Referee Report

4 major / 4 minor

Summary. This paper addresses estimation of aerodynamic forces in the bat-inspired flapping-wing robot Aerobat. Two estimators are presented and compared experimentally: a conjugate momentum observer derived from Hamiltonian mechanics, which requires no training data, and a multilayer perceptron (MLP) regression model trained on joint kinematics and experimental parameters. Both are validated against a 6-axis ATI Nano17 load cell mounted between the robot and a Kinova arm during tethered flapping with axial fan airflow. The paper reports RMSE values from 0.0401 N to 0.1322 N across Fx, Fy, and Fz, with the MLP generally more accurate than the observer. The conclusion states that both methods robustly reproduce the measured force profiles, and the authors propose integrating the estimators for closed-loop control.

Significance. The topic is relevant to flapping-wing robot control, where online force estimation is a known bottleneck. The paper's positive features are the use of an external 6-axis load cell as a reference, quantitative RMSE metrics, and a comparison between a physically interpretable observer and a learned regressor. The MLP architecture and hyperparameters are explicitly stated, which aids reproducibility. If the ground-truth measurement issue is resolved, the study would provide useful evidence that a parameter-free momentum observer can compete with a data-driven model in this high-DOF morphing-wing platform. However, because the validation signal may contain unmodeled inertial components, the current contribution is not yet established.

major comments (4)

[Section II-B] The load cell is treated as a pure aerodynamic force ground truth, but no no-airflow baseline or inertial compensation is described. The Aerobat's wings each have mass of approximately 0.4 g and undergo a 100 ms flapping cycle; the reaction forces from these accelerations propagate to the mount and are included in the measured signal. The manuscript itself attributes part of the upstroke force signature to "possible inertial effects arising from rapid wing retraction" (Section V, discussion of Fig. 8), which is inconsistent with treating the load-cell output as purely aerodynamic. Since both estimators are validated against this mixed signal, the reported RMSE values (0.0401-0.1322 N) may reflect agreement with total mount force, not aerodynamic force. Please provide a no-airflow control experiment or a model-based subtraction to separate aerodynamic from inertial contributions.
[Section IV (referenced)] The central physics-based estimator, the conjugate momentum observer, is never derived. The text says the observer is "based on the conjugate momentum observer detailed in Section IV" (Section V, first paragraph), but Section IV is absent from the manuscript and no explicit observer equation, filter gain, or external-force extraction law is given. Without the observer equations and a statement of the assumptions (e.g., known mass-inertia matrix, no modeling error, availability of joint acceleration measurements), the claim that the observer is physics-based and parameter-free cannot be verified. Please include the full derivation and the exact algorithm used in the experiments.
[Section V] The MLP regression results are reported as single RMSE values with no indication of the number of trials, standard deviation, or train/test split. It is also not stated whether the test data were used for hyperparameter tuning; the text says hyperparameters were "tuned empirically based on validation performance," which suggests a possible selection bias. For a fair comparison with the observer, which has no free parameters, please report per-trial errors, cross-validation, and the size of the training set; also state whether any test datapoints were used in tuning.
[Section IV/V] The MLP inputs are described as "joint kinematics, flapping frequency, and environmental parameters," but the only environmental parameter described in the hardware section is the fan wind speed measured at one location. It is unclear what environmental variables were actually used, how many distinct operating conditions are represented in the dataset, and whether the model was tested across conditions. This matters because the abstract claims agreement across three force components and the concluding section claims a "diverse dataset incorporating flapping frequency, joint kinematics, and environmental variables." Please specify the actual inputs and the experimental conditions covered.

minor comments (4)

[Section V] The RMSE values are printed with placeholder characters (e.g., "0�0401") and without units; please use consistent decimal notation and state that the errors are in Newtons.
[Section II] The introduction states that the goal is to estimate forces "during hovering," but the experiments are tethered with an axial fan. Please clarify how the tethered configuration with forced airflow relates to the hovering condition.
[Figures 6-8] The figure captions and the text mention "two consecutive flapping cycles" and shaded downstroke/upstroke regions, but the phase alignment, the filtering of the load-cell signal, and the synchronization between load-cell and encoder data are not described. Please add these details.
[Section III] Equation (1) introduces coordinate-frame notation, but the notation is not used consistently later because the observer derivation is missing. Please ensure that all symbols in the observer equations are defined when that derivation is added.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the conjugate momentum observer is an independent physics-based estimator and the MLP is a supervised regression validated against an external load cell; the reported concerns about test-split and load-cell purity are reporting or validity issues, not reductions of the estimates to their inputs.

full rationale

The paper's two estimators do not reduce to their own outputs by construction. The conjugate momentum observer is a physics-based residual estimator: it uses the reduced-order rigid-body dynamics, motor torque commands, and real-time joint kinematics to infer external aerodynamic forces without training data, as the abstract states: 'This observer builds on the system's reduced-order dynamic model and utilizes real-time sensor data to estimate forces without requiring training data.' This provides an independent estimate whose agreement with the load cell is an empirical finding rather than a tautology. The MLP is a supervised regressor that learns a mapping from 'joint kinematics, flapping frequency, and environmental parameters to aerodynamic force outputs' and is evaluated against an external 6-axis load cell whose data, per Section II, 'serves as ground truth to validate the performance of our estimators.' Fitting a regressor to sensor data and reporting RMSE is not circular in itself, because the load cell is an outside measurement source rather than a function of the fitted parameters. The absence of an explicitly stated train/test split is a reporting gap, not a demonstrated circularity; the text only says hyperparameters were 'tuned empirically based on validation performance,' which does not establish that the reported RMSE is an in-sample training score. Similarly, the load cell may include inertial reaction forces from the flapping appendages, and the paper itself acknowledges 'possible inertial effects arising from rapid wing retraction,' but this contaminates the ground-truth signal rather than making either estimator equal to its input by construction. The self-citations document the Aerobat platform and prior momentum-observer applications, but they are not invoked as a uniqueness theorem or as the sole justification for the central force-estimation claim. Therefore, no specific circular step is exhibited, and the appropriate score is mild.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central claim rests on the sensor ground truth representing pure aerodynamic forces and on the accuracy of the rigid-body model for the physics-based observer. The MLP contributes no new entities but introduces many fitted parameters.

free parameters (2)

MLP network weights (3 hidden layers of 128 units) = unknown (learned from training data)
The MLP regression model's predictions depend on these fitted weights; no trained model is released.
MLP hyperparameters (layer sizes, learning rate, optimizer settings) = layer sizes: 128; others tuned empirically
Hyperparameters were tuned based on validation performance, as stated in Section V.

assumptions (3)

domain assumption The load cell measurements represent the aerodynamic forces on the robot.
The paper calls the load cell data 'aerodynamic force contributions' and uses it as ground truth without describing how inertial forces from flapping wings are removed. If this assumption is false, the validation is invalid.
domain assumption The five-rigid-body model accurately captures the robot's inertial dynamics.
The conjugate momentum observer relies on the reduced-order dynamic model to compute expected momentum changes; model errors directly affect force estimates.
standard math Standard Hamiltonian mechanics applies to the rigid-body system.
The observer derivation relies on the conjugate momentum principle from classical mechanics.

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Cite this review

Pith. "Pith review of Estimation of Aerodynamics Forces in Dynamic Morphing Wing Flight." pith.science (2026). https://pith.science/paper/MQZFIJWR

@misc{pith2026250802984,
  author       = {Pith},
  title        = {Pith review of: Estimation of Aerodynamics Forces in Dynamic Morphing Wing Flight},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MQZFIJWR}},
  note         = {Machine review of arXiv:2508.02984}
}

read the original abstract

Accurate estimation of aerodynamic forces is essential for advancing the control, modeling, and design of flapping-wing aerial robots with dynamic morphing capabilities. In this paper, we investigate two distinct methodologies for force estimation on Aerobat, a bio-inspired flapping-wing platform designed to emulate the inertial and aerodynamic behaviors observed in bat flight. Our goal is to quantify aerodynamic force contributions during tethered flight, a crucial step toward closed-loop flight control. The first method is a physics-based observer derived from Hamiltonian mechanics that leverages the concept of conjugate momentum to infer external aerodynamic forces acting on the robot. This observer builds on the system's reduced-order dynamic model and utilizes real-time sensor data to estimate forces without requiring training data. The second method employs a neural network-based regression model, specifically a multi-layer perceptron (MLP), to learn a mapping from joint kinematics, flapping frequency, and environmental parameters to aerodynamic force outputs. We evaluate both estimators using a 6-axis load cell in a high-frequency data acquisition setup that enables fine-grained force measurements during periodic wingbeats. The conjugate momentum observer and the regression model demonstrate strong agreement across three force components (Fx, Fy, Fz).

Discussion (0). Continue with ORCID to comment.

Reference graph

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Reviewed August 6, 2026 · model on record in the stance chip above.

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