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REVIEW 5 major objections 5 minor 73 references

System Identification of Thrust and Torque Characteristics for a Bipedal Robot with Integrated Propulsion

T0 review · 5 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The thesis shows that a fitted thrust equation predicts electric ducted fan thrust within 5.22% on average against CFD, and that torque-sensor measurement gives the joint motor a torque constant of $K_t = 0.0311\ \mathrm{N\,m/A}$.

desk verdict Torque-sensor Kt is solid hardware data; the thrust equation as printed has a unit bug that breaks reproducibility, and the validation is too weak to support the headline accuracy. read the letter →

arxiv 2504.20313 v1 pith:VNWIHJPC submitted 2025-04-28 cs.RO cs.SYeess.SY

Thomas Cahill This is my paper · ORCID
classification cs.ROcs.SYeess.SY
keywords systemidentificationelectricductedfanthrustmodelingtorqueconstantbipedalrobotimpedancecontrolCFDvalidationthruster-assistedlocomotion
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 thesis tries to establish that a simple closed-form thrust equation, fitted with two empirical constants, can predict the thrust of the electric ducted fans on the Harpy bipedal robot well enough for design and control, and that a direct torque-sensor measurement yields a trustworthy torque constant for the robot's joint motors. The practical motivation is that thrusters give a biped roll stabilization, obstacle clearance, and stumble recovery, but only if the propulsion and actuation hardware are well characterized. The paper reports the fitted equation agreeing with CFD to an average 5.22% error, and a torque constant of $K_t = 0.0311\ \mathrm{N\,m/A}$ that will be used for closed-loop force-based impedance control.

What carries the argument

The load-bearing object is a closed-form thrust equation, $F = 1.225 \cdot \pi (0.0254 d)^2/4 \cdot (\mathrm{RPM}\cdot 0.0254\cdot \mathrm{Pitch}/60)^2 \cdot (K_1 d/\mathrm{Pitch})^{K_2}$ with $K_1 \approx 0.30$ and $K_2 = 1.5$, where the first speed factor is the blade pitch speed and the parenthetical ratio is an empirically tuned loss term. It carries the thrust argument by predicting output from diameter, pitch, RPM, and air density without running CFD. The second mechanism is the torque-sensor testbed: a reaction torque sensor in the 0–2 N·m range, paired with a load-cell transmitter and its calibration curve, converts measured current into torque, and the slope of torque versus motor current supplies the $K_t$ used in the control law.

What would settle it

Mount the actual EDF on a thrust stand with a tachometer, sweep the throttle from minimum to maximum, and compare measured thrust with Eq. 3.9 at each measured RPM; systematic growth of error outside the fitted range, or residuals that trend with RPM, would falsify the pitch-speed-plus-loss-factor model. A locked-rotor test applying known currents and directly measuring torque would settle whether $K_t = 0.0311\ \mathrm{N\,m/A}$ holds at stall.

Watch

Extended reading notes

Core claim

The paper's central claim is that electric ducted fan thrust can be captured by a momentum-based equation in which the effective exit velocity is the pitch speed, RPM times blade pitch, and all remaining aerodynamic losses are absorbed by an empirically fitted factor. The constants $K_1 = 0.30$ and $K_2 = 1.5$ were selected by trial and error against 149 vendor data points, and the resulting equation reproduces CFD results across four diameter/pitch combinations with an average absolute error of 5.22%. For the selected EDF unit, the same equation predicts about 2.64 kgf of thrust, consistent with CFD and bench results near 2.4 kgf and the manufacturer's 2.75 kgf. On the motor side, the thesis claims that the KV380 motor's torque constant is most reliably obtained with a calibrated reaction torque sensor, giving $K_t = 0.0311\ \mathrm{N\,m/A}$, which becomes the conversion factor from motor current to joint torque for impedance control.

Load-bearing premise

The thrust equation assumes the air leaving the fan moves at pitch speed, RPM times blade pitch, and that every unmodeled effect is captured by the fitted factor $(K_1 d/\mathrm{Pitch})^{K_2}$ with $K_2 = 1.5$ chosen by trial and error; if the pitch-speed assumption or that functional form is wrong, the predicted thrust is wrong no matter how well $K_1$ was fitted.

Editorial extensions

If this is right

  • A designer can estimate EDF thrust from diameter, pitch, and RPM with a hand calculation, bypassing CFD, at an average error around 5% for the tested configurations.
  • The dual-EDF configuration on Harpy delivers roughly 2.4 kgf in simulation and on the bench, enough to support a thrust-to-weight ratio above one for the robot.
  • With the thrusters mounted about 0.2 m from the center of mass, maximum thrust produces roughly 0.5 kgf·m of roll moment, which the paper argues is sufficient for roll stabilization.
  • Using $K_t = 0.0311\ \mathrm{N\,m/A}$, joint torque can be commanded through motor current, enabling closed-loop force-based impedance control on the existing hardware.
  • Among the three torque-characterization methods, the torque-sensor approach gives the most consistent and precise values, while the back-EMF method is noisier.

Reading between the lines

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

  • The 5.22% error is reported against CFD, not against a dense set of direct thrust measurements on the actual EDF; a realistic next test is a full throttle sweep on a thrust stand to see whether the fitted form holds across the whole RPM range.
  • The fitting procedure could be extended to make air density and ducted-fan hub blockage explicit, which would likely improve fidelity at altitude or with the annular-area correction already noted in the thesis.
  • Using a single measured $K_t$ for all six joints assumes the motors are built alike; per-joint torque calibration would be a natural follow-up before relying on current-based torque commands in control.
  • With $K_t$ known, current feedback becomes torque feedback, so the same hardware could support contact-force estimation without adding joint torque sensors.
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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 / 5 minor

Summary. This MS thesis reports system-identification work for the Harpy thruster-assisted bipedal robot. It derives a semi-empirical thrust equation for electric ducted fans (EDFs) that relates thrust to fan diameter, blade pitch, RPM, air density, and ambient velocity through empirical coefficients K1 and K2, and it attempts to validate the model against ANSYS Fluent CFD and a limited load-cell measurement. The thesis also characterizes the KV380 joint motor's torque constant Kt by three methods: datasheet estimation, back-EMF measurement, and a calibrated reaction torque sensor, recommending Kt = 0.0311 Nm/A from the torque-sensor method for use in closed-loop force-based impedance control. In addition, the manuscript documents the EDF/ESC test platform, thruster mounting, and integration into Harpy.

Significance. The torque-sensor characterization is the strongest contribution: it is a direct calibrated measurement with 28 trials, and the reported value of 0.0311 Nm/A is plausible and useful for current-based joint torque control. The paper also provides a useful integration record for a thruster-assisted biped. However, the thrust-model contribution is not presently validated: K1 and K2 are fit to vendor data, the ANSYS model uses 200 nodes with a single-node thrust readout, the hardware comparison is a single maximum-thrust point without uncertainty, and Eq. (3.9) has a load-bearing units error. If the thrust model is reframed as a calibrated curve fit and the reproducibility errors are corrected, the thesis can be a useful engineering contribution; as written, the central thrust-model claim is not supported.

major comments (5)
  1. [§3.1, Eq. (3.9) and Table 3.2] Equation (3.9) is printed with 'kgf' as the output unit, but its right-hand side evaluates in Newtons: substituting d=8 in, Pitch=5 in, RPM=20,000, and vo=0 gives approximately 24.1 N, and Table 3.2 lists 2.455 kgf, which is exactly 24.1/9.81. The table can only be reproduced with an unprinted division by g. A reader implementing Eq. (3.9) verbatim while trusting the kgf label will overestimate thrust by roughly a factor of 9.8; this is a load-bearing reproducibility error in the central thrust-model claim.
  2. [§3.1, Eqs. (3.8)–(3.9)] The two printed forms of the thrust equation do not agree: Eq. (3.8) has K1=0.30 in (K1·d/Pitch)^K2, while Eq. (3.9) uses d/(3.29546·Pitch), i.e., a coefficient of approximately 0.30345, and the placement of the correction factor relative to the subtracted ambient-velocity term is ambiguous. The bracket structure in Eq. (3.9) is difficult to parse, and the text does not explain the change from 0.30 to 0.30345; this must be reconciled for the equation to be implementable.
  3. [§3.1 and §3.3] The validation is not independent: K1 was fitted to 149 vendor data points and K2 was set by trial and error in Section 3.1, and Section 3.3 then compares that same fitted model to ANSYS. The claimed average error of 5.22% therefore measures agreement of an empirical fit with one coarse simulation, not predictive accuracy on unseen conditions. The manuscript should either state that the model is a calibrated curve fit or validate it on held-out data and against direct thrust measurements.
  4. [§3.2, Table 3.1] The ANSYS model uses 200 nodes and reads thrust from a single node at the propeller output, with no mesh-convergence or domain-independence study reported. With this resolution, the 5.22% agreement cannot be distinguished from discretization error, so the CFD comparison does not provide quantitative validation of the thrust equation. A mesh-convergence study and thrust integration over the outlet or rotor surface are required.
  5. [§3.3, Table 3.3] The hardware comparison is a single maximum-thrust point (2.4 kgf) without RPM measurement, error bars, or a stated number of repeated trials, and the load-cell plot in Fig. 3.5 appears to come from a separate tabletop test. This is insufficient to support the thesis's 'less than 6% error' claim; a sweep over PWM/RPM with repeated trials and reported uncertainty is needed.
minor comments (5)
  1. [§3.1, Eq. (3.7)] Equation (3.7) gives pitch speed in mph (RPM·Pitch/1056), while Eq. (3.8) uses RPM·Pitch·0.0254/60 in m/s; the two expressions are inconsistent, and Eq. (3.7) is not used in the subsequent derivation.
  2. [§4.3] The sentence 'using the maximum thrust of the EDF, which is 2.7 kgf (approximately 27 N), applied at a distance of 0.2 m... the resulting moment is slightly over 0.5 kgf·m' mixes kgf and N; the moment should be expressed in N·m for consistency.
  3. [Figures 3.4 and 3.5, Table 3.2] The symbols 'KGF' and 'kgf' are used inconsistently; the manuscript should standardize on either kgf or N throughout.
  4. [§5.2] The statement that 'all three methods fall within five sigma of the Back EMF method' is not supported because the sigma values for the three methods are not reported; the distributions should be given numerically.
  5. [Throughout] There are numerous typos and grammar issues, including 'coeficients', 'radio' for 'ratio', and 'menuvers'; a careful proofread is needed before publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the thrust model is empirically calibrated but validated against external CFD; the motor torque constant is a direct sensor measurement.

full rationale

The central thrust equation (Eq. 3.9) is not a first-principles prediction: Sec. 3.1 states K2 = 1.5 was chosen by trial and error and K1 = 0.30 by minimizing error against 149 vendor data points, and the paper itself notes the analytical basis for K2 is unclear. That is an honest description of an empirically fitted model, not a circular reduction. The claimed validation is external to the fitted data: Table 3.2 and Fig. 3.6 compare Eq. 3.9 against ANSYS Fluent CFD for four diameter/pitch combinations, and the quoted 5.22% average error is an out-of-sample check, albeit a limited one given the 200-node mesh and single-node thrust readout described in Sec. 3.2. The motor-torque result adopted for control, Kt = 0.0311 Nm/A, comes from 28 direct torque-sensor trials (Sec. 5.1.3 and 5.2), an independent physical measurement, not from the datasheet or back-EMF estimates. The many Harpy/Husky self-citations in Chapter 2 are background context and are not used as evidence for the thrust or torque derivations; no uniqueness theorem or forced ansatz is imported from the authors' prior work. The kgf/Newton inconsistency in Eq. 3.9 and Table 3.2 is a unit-correctness defect, not circularity. Under the rule that only actual reductions-to-input count, no circular step is present.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central thrust claim rests on two fitted constants (K1, K2), a pitch-speed exit velocity assumption, and a very coarse CFD reference. The motor torque claim rests on manufacturer calibration and current logs. No new entities are introduced.

free parameters (2)
  • K1 (thrust coefficient constant) = 0.30
    Fitted by goal-seeking to minimize error between predicted and measured thrust across 149 vendor data points; used in Eq. 3.8 and 3.9.
  • K2 (thrust power constant) = 1.5
    Chosen by trial and error; the paper states its precise analytical basis is unclear; used in Eq. 3.8 and 3.9.
assumptions (5)
  • standard math Thrust equals rate of change of air momentum, F = mdot * (v_e - v_ac) (Newton's second law).
    Used to derive Eq. 3.2 through 3.6.
  • domain assumption Propeller exit velocity is approximated by the pitch speed, v_e = RPM * pitch (converted to m/s).
    Invoked in Eq. 3.8 and 3.9; no induced-velocity or efficiency correction is derived.
  • ad hoc to paper The correction factor (K1 * d / Pitch)^K2 captures all remaining propeller losses and geometry effects.
    Introduced in Eq. 3.8 with K1 and K2 fitted to vendor data; the functional form is not derived.
  • domain assumption ANSYS Fluent with a 200-node mesh and single-node thrust readout provides a valid reference for thrust validation.
    Assumed in Section 3.2 and 3.3; the mesh resolution is extremely coarse for propeller CFD and the thrust is read at one node.
  • domain assumption The torque sensor calibration curve from the manufacturer (ATO) is accurate and the Elmo Studio current logs are correct.
    Used in Section 5.1.3 to convert measured current and torque into Kt.

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Cite this review

Pith. "Pith review of System Identification of Thrust and Torque Characteristics for a Bipedal Robot with Integrated Propulsion." pith.science (2026). https://pith.science/paper/VNWIHJPC

@misc{pith2026250420313,
  author       = {Pith},
  title        = {Pith review of: System Identification of Thrust and Torque Characteristics for a Bipedal Robot with Integrated Propulsion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VNWIHJPC}},
  note         = {Machine review of arXiv:2504.20313}
}
read the original abstract

Bipedal robots represent a remarkable and sophisticated class of robotics, designed to emulate human form and movement. Their development marks a significant milestone in the field. However, even the most advanced bipedal robots face challenges related to terrain variation, obstacle negotiation, payload management, weight distribution, and recovering from stumbles. These challenges can be mitigated by incorporating thrusters, which enhance stability on uneven terrain, facilitate obstacle avoidance, and improve recovery after stumbling. Harpy is a bipedal robot equipped with six joints and two thrusters, serving as a hardware platform for implementing and testing advanced control algorithms. This thesis focuses on characterizing Harpy's hardware to improve the system's overall robustness, controllability, and predictability. It also examines simulation results for predicting thrust in propeller-based mechanisms, the integration of thrusters into the Harpy platform and associated testing, as well as an exploration of motor torque characterization methods and their application to hardware in relation to closed-loop force-based impedance control.

Figures

Figures reproduced from arXiv: 2504.20313 by the authors.

Figure 1.1
Figure 1.1. Harpy v2 designed and developed at Northeastern University [PITH_FULL_IMAGE:figures/full_fig_p011_1_1.png] view at source ↗
Figure 1.2
Figure 1.2. Bipedal robots with thrusters designed by Haldane et al. [1], X. Zeng et al. [2], N. [PITH_FULL_IMAGE:figures/full_fig_p013_1_2.png] view at source ↗
Figure 2.1
Figure 2.1. A visual breakdown of Harpy primary subsystems [PITH_FULL_IMAGE:figures/full_fig_p031_2_1.png] view at source ↗
Figures from the paper (23 more)
Figure 2.2
Figure 2.2. Figure 2.2: Harpy’s Actuator Sectional View Legged robot joint actuators in general must be extremely power dense with high trans￾parency, high efficiency, and minimal backlash. The importance of the joint lies in its fundamental role in enabling robots to mimic the bio-inspired…
Figure 2.3
Figure 2.3. Figure 2.3: Harpy Thruster EDF ESC 6S LIPO Battery Assembly [PITH_FULL_IMAGE:figures/full_fig_p033_2_3.png]
Figure 2.4
Figure 2.4. Figure 2.4: Schuebeler DS-30 AXI HDS [74] Parameter(s) Value Max. Thrust 27 N Max. Exhaust speed 87.3 m/s Duct weight 100 g Motor weight 300 g Duct diameter 70 mm Duct length 60 mm [PITH_FULL_IMAGE:figures/full_fig_p035_2_4.png]
Figure 2.5
Figure 2.5. Figure 2.5: Motor Propeller Thrust Relationship EDFs were chosen as the ideal thruster option, primarily due to their ability to deliver high thrust in compact volumes while also housing the blades. The Schuebeler HDS series, specifically the DS-30-AXI HDS model ( [PITH_FULL_IM…
Figure 3.1
Figure 3.1. Figure 3.1: Illustration of data while solving for pitch-diameter coefficient [PITH_FULL_IMAGE:figures/full_fig_p042_3_1.png]
Figure 3.2
Figure 3.2. Figure 3.2: Head on ANSYS CFD Dual-Prop Simulation In the simulation shown below, the flow dynamics can be observed with the inlet velocity 35 [PITH_FULL_IMAGE:figures/full_fig_p044_3_2.png]
Figure 3.3
Figure 3.3. Figure 3.3: Isometric View of ANSYS Propeller Thrust Simulation [PITH_FULL_IMAGE:figures/full_fig_p045_3_3.png]
Figure 3.4
Figure 3.4. Figure 3.4: Harpy ANSYS Thrust Output at Observed Node [PITH_FULL_IMAGE:figures/full_fig_p046_3_4.png]
Figure 3.5
Figure 3.5. Figure 3.5: Loadcell measurements PWM signal and the resulting thrust. The data was plotted, typically with the PWM signal in mi￾croseconds on the x-axis and thrust output in grams or Newtons on the y-axis. Additional plots could be generated to compare power consumption versus …
Figure 3.6
Figure 3.6. Figure 3.6: Comparison of ANSYS Fluent and hand-derived theoretical thrust calculations. [PITH_FULL_IMAGE:figures/full_fig_p048_3_6.png]
Figure 4.1
Figure 4.1. Figure 4.1: EDF Test Platform Schematic The schematic shown in [PITH_FULL_IMAGE:figures/full_fig_p053_4_1.png]
Figure 4.2
Figure 4.2. Figure 4.2: ESC-EDF Harpy Integration Schematic 4.3 Thruster Mounts The EDFs are rigidly mounted, as shown in [PITH_FULL_IMAGE:figures/full_fig_p054_4_2.png]
Figure 4.3
Figure 4.3. Figure 4.3: Illustration of EDF fixation onto the torso structure. [PITH_FULL_IMAGE:figures/full_fig_p055_4_3.png]
Figure 4.4
Figure 4.4. Figure 4.4: Moment vs. EDF Location from Harpy Center of Mass [PITH_FULL_IMAGE:figures/full_fig_p056_4_4.png]
Figure 5.1
Figure 5.1. Figure 5.1: Back EMF motor constant evaluation setup: Physical testbed (top) and CAD represen [PITH_FULL_IMAGE:figures/full_fig_p063_5_1.png]
Figure 5.2
Figure 5.2. Figure 5.2: Three Phase Motor Oscilloscope Observation. [PITH_FULL_IMAGE:figures/full_fig_p064_5_2.png]
Figure 5.3
Figure 5.3. Figure 5.3: Back EMF Torque Constant Plot The plot, along with the summary of the Back EMF proportional trials in relation to the torque constant, will be discussed in more detail in the results Section 5.2, where the findings and their implications will be further elaborated an…
Figure 5.4
Figure 5.4. Figure 5.4: Torque coefficient testing setup: Actual hardware (top) and Schematic (bottom). [PITH_FULL_IMAGE:figures/full_fig_p067_5_4.png]
Figure 5.5
Figure 5.5. Figure 5.5: Overview of Torque Sensor Setup and Power Supply Inputs. [PITH_FULL_IMAGE:figures/full_fig_p068_5_5.png]
Figure 5.6
Figure 5.6. Figure 5.6: Torque Sensor Motor Characterization Schematic [PITH_FULL_IMAGE:figures/full_fig_p069_5_6.png]
Figure 5.7
Figure 5.7. Figure 5.7: Torque Sensor Calibration Curve Once the torque was back-calculated for each trial of the 28 trials of input currents and output torques, the plot below was created for each trial, where the input motor current can be see on the x-axis and the output torque in n*m fr…
Figure 5.8
Figure 5.8. Figure 5.8: Torque Sensor Data (Coefficient investigation Method 3) [PITH_FULL_IMAGE:figures/full_fig_p071_5_8.png]
Figure 5.9
Figure 5.9. Figure 5.9: Torque Constant Investigation Methods Comparison [PITH_FULL_IMAGE:figures/full_fig_p072_5_9.png]

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.