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REVIEW 2 major objections 5 minor 31 references

MOMAV: A highly symmetrical fully-actuated multirotor drone using optimizing control allocation

T0 review · 2 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper establishes that a six-rotor drone with arms at the vertices of an octahedron, each able to rotate continuously, can hover in any orientation while wasting little thrust, and that its SQP-based control allocation keeps tracking…

desk verdict A real flying octahedral rotating-arm drone with honest flight data and a citable geometry analysis, but the efficiency claims outrun the power measurements and the SQP equations carry a sign error. read the letter →

arxiv 2506.08868 v1 pith:APUNEGOF submitted 2025-06-10 cs.RO

Marco Ruggia This is my paper
classification cs.RO
keywords fullyactuatedmultirotoromnidirectionalflightcontrolallocationsequentialquadraticprogrammingoctahedronarmconfigurationslip-ringsrotatingdroneover-actuated
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 introduces MOMAV, a fully actuated multirotor drone whose six rotor arms point at the vertices of an octahedron and can each rotate continuously about their long axis. The author's central claim is that this highly symmetric rotating-arm geometry lets the drone control position and orientation independently, with flight efficiency that varies little with orientation. Compared to other fully actuated designs, the octahedron wastes less thrust fighting itself and needs less surplus total thrust for hover. Flight tests support the claim with mean position and orientation errors of a few millimeters and degrees during sweeping setpoints, and the paper argues that the slack from twelve actuators can be spent on efficiency rather than mere controllability.

What carries the argument

The central mechanism is the octahedral arm configuration with six rotating arms, each carrying a propeller whose thrust direction is a function of the arm angle. Two efficiency metrics, X1 and X2, are defined through an optimization that minimizes the sum of squared motor forces subject to the hover wrench; these metrics isolate the effect of arm geometry and show that the octahedron, tetrahedron, and cube are nearly equivalent and superior to planar rotating-arm and fixed-tilt designs. The second carrying element is a sequential quadratic programming (SQP) control allocation that minimizes squared throttles and arm-rotation velocity penalties while satisfying the desired force and torque, avoiding the arm-angle singularity that plagues pseudoinverse allocation. The slip-ring rotating-arm assembly is what makes continuous arm rotation physically possible without cable winding.

What would settle it

Measure the electrical power input to the six motors while MOMAV hovers in many fixed orientations, and compare measured power to the X1 and X2 predictions from the squared-throttle minimization: if power draw varies strongly with orientation even though X1 and X2 stay nearly flat, or if single-arm thrust at fixed throttle depends on arm angle and rotation history, the linear thrust model and the squared-force proxy fail.

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Extended reading notes

Core claim

The core discovery is that the combination of a three-dimensionally symmetric arm layout (octahedron, tetrahedron, or cube) with actively rotating arms yields the best efficiency across all orientations for fully actuated drones. For the octahedron, the paper defines and computes two efficiency metrics: X1, the fraction of thrust directed upward at hover, and X2, the fraction of total installed thrust usable for hover. It reports X1 between 0.82 and 1.00 and X2 between 0.67 and 0.82, meaning that at worst 18 percent of thrust is canceled by opposing motors and at worst a third of total thrust must be surplus. The paper further shows that MOMAV achieves independent position and orientation control in flight, with mean errors of 6.6 mm and 2.1 degrees during position sweeps and 11.8 mm and 3.3 degrees during orientation sweeps, and that replacing pseudoinverse allocation with the proposed SQP method reduces peak position errors during arm-angle singularities.

Load-bearing premise

The load-bearing premise is that each motor's force and torque are linear functions of throttle with constant coefficients, and that minimizing the sum of squared motor forces is a valid proxy for minimizing power; the author's own flight data suggest wake interactions and angle-dependent slip-ring losses already strain this premise.

Editorial extensions

If this is right

  • Fully actuated drones need not sacrifice efficiency for omnidirectionality; an octahedral rotating-arm layout keeps most thrust pointing upward at any hover orientation.
  • Using SQP with arm-angle velocity penalties removes the vertical-arm singularity problem that causes position errors in pseudoinverse-based controllers.
  • Slip-rings permit unlimited arm rotation, enabling maneuvers such as sustained multi-revolution rolls that would otherwise wind up motor cables.
  • The efficiency metrics X1 and X2 give a simple, mass-independent way to compare arm configurations of fully actuated drones before building them.
  • Future nonlinear or learned thrust models could further shrink the already small tracking errors by accounting for wake interactions and angle-dependent slip-ring losses.

Reading between the lines

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

  • The same efficiency analysis generalizes: any highly symmetric three-dimensional arrangement of rotating thrusters, such as a cube or tetrahedron, should show similarly flat efficiency across orientations, making the octahedron one instance of a broader design rule.
  • The slip-ring measurement, showing nearly 100 percent relative efficiency when placed between battery and motor driver, suggests a simple redesign of MOMAV would recover the roughly 10 percent of power currently lost.
  • Since the SQP objective is user-tunable, the same allocation framework could be extended to incorporate learned thrust models, propeller wake interactions, or per-arm temperature limits, turning the control allocation into a place where aerodynamic knowledge enters.
  • The reported position-error reduction near singularities is a statistical effect over 12 instances; a targeted experiment with repeated identical singularity passages could confirm it more directly.
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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. The paper presents MOMAV, a six-rotor fully actuated multirotor whose arms lie along octahedron vertices and can rotate continuously about their long axes by means of modified servos and slip rings. The authors propose two thrust-based metrics X1 and X2 to compare hover efficiency of arm configurations, document the mechanical design and single-arm slip-ring measurements, and introduce an SQP-based control allocation that distributes force/torque setpoints across throttles and arm angles. Flight tests with OptiTrack report mean position errors of 6.6 mm and orientation errors of 2.1° during position sweeps, and 11.8 mm and 3.3° during orientation sweeps, with a ten-revolution roll flight enabled by the slip rings.

Significance. The main strength is the demonstrated hardware capability: full decoupling of position and orientation, continuous arm rotation, quantitative tracking errors, and a statistical comparison showing that the SQP allocation reduces position peaks near arm-angle singularities relative to pseudoinverse allocation. The paper is unusually open, providing source code, 3D models, and raw test data. The claimed efficiency advantage is only weakly supported, however, because X1 and X2 are geometric thrust-utilization indices rather than measured power, and the paper's own slip-ring tests show a substantial hover power penalty. The printed SQP derivation also contains a sign error that would make the algorithm incorrect as written. These issues are local enough that the central hardware claims remain credible.

major comments (2)
  1. [Section IV, Eqs. (11)-(14) and Algorithm 1] The Newton step for the KKT system has the wrong sign. Eq. (11) states Hδ + K = 0, so the correct solution is δ = -H^{-1}K, yet Eq. (14) and Algorithm 1 use H^{-1}K. Since K is the gradient of the Lagrangian, the printed step is an ascent direction for the minimization; as written the algorithm would not converge to a constrained minimum. Please correct Eq. (14) and Algorithm 1 (or explicitly solve Hδ = -K), and state whether the implemented code already uses the correct sign.
  2. [Abstract and Section II, Eqs. (1)-(3), with Sections III-B and V] The paper labels X1 and X2 as 'flight efficiency' and claims high efficiency largely unaffected by orientation, but these metrics are computed from a thrust-only optimization and are not measurements of electrical power. X1 is a thrust-direction utilization ratio and X2 is a static thrust-margin index; neither accounts for the motor/propeller power curve, wake interaction, or the angle-dependent slip-ring losses mentioned in Section V. Section III-B reports a relative thrust efficiency of 90% at hover thrust for the implemented slip-ring placement, which is a measured ~10% power penalty. Since no whole-vehicle power draw or hover endurance as a function of orientation is reported, the abstract's efficiency claims overstate the evidence. The same gap affects Section IV's statement that the objective O is chosen with the intention of minimizing power consumption: Eq. (5) penalizes squared throttles and arm velocities, which is a heuristic proxy, not a measured power model. Please add power measurements or restrict the claims to geometric thrust-utilization metrics.
minor comments (5)
  1. [Section IV, Eq. (6)] The notation in Eq. (6) is incomplete as printed; please define the quaternion rotation operation explicitly, for example n_i = q(a_i, x_i) z_i q(a_i, x_i)^{-1}, rather than relying on a parenthetical note that quaternions are multiplied with vectors.
  2. [Section III-B, marked thrust setpoints] The displayed expressions 'X2,min·mg/6 = 4.8 N' and 'X2,max·mg/6 = 5.9 N' do not evaluate to the stated values. The per-motor hover thrusts at the two orientations are mg/(6 X2,max) ≈ 4.8 N and mg/(6 X2,min) ≈ 5.9 N; please correct the formulas.
  3. [Section II, paragraph after Fig. 3] The phrase 'the ODAR configuration (Fig. 2C, like in [5])' appears to reference the wrong figure; ODAR is a fixed-tilt design and should be among the fixed-tilt configurations in Fig. 3.
  4. [Section V, SQP versus pseudoinverse comparison] Please state which hypothesis test was used for p = 0.0003 and whether the 12 instances are paired before/after comparisons.
  5. [Table I and Section IV] The symbol H is used both for the quaternion space in Table I and for the KKT matrix in Eqs. (11)-(12); rename one of these to avoid ambiguity.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the efficiency metrics and control allocation are derived from independent geometric optimization, and the flight-tracking errors are measured externally.

full rationale

The paper's central claims are supported by self-contained derivations and independent measurements, not by fitting parameters to the predicted outputs. The efficiency metrics X1 and X2 are defined by an optimization problem (Eq. 1) over thrust directions and arm geometry, and the paper explicitly notes that they depend only on thrust-direction constraints and motor locations, not on mass, gravity, or inertia. These metrics are then evaluated across orientations for several configurations as a static geometric comparison; they are not fitted to the subsequent flight results. The control allocation algorithm minimizes a stated objective (Eq. 5) subject to the force/torque constraint (Eq. 9), and the reported tracking errors come from OptiTrack ground-truth measurements during test flights. The motor constants mu and tau in Eqs. 7 and 8 are inputs adopted from the physical actuator/propeller setup, and they do not by themselves force the observed 6.6 mm and 2.1 degree errors. There are no load-bearing self-citations: the author cites only external prior hardware and algorithms, not a uniqueness theorem or prior result of the present author that would make the choice of octahedral geometry or SQP allocation forced by definition. The acknowledged limitations, such as the simplified linear thrust/torque model and the measured 10% slip-ring power loss, are honest empirical caveats rather than circular dependencies; they concern model accuracy and hardware efficiency, not a derivation that assumes its own conclusion. Therefore no step in the paper reduces, by construction or by self-citation, to its own inputs.

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

The central claims rest on a linear motor model with unstated constants, a hand-tuned PID loop, and a proxy efficiency metric that is not experimentally validated. No new physical entities are introduced. The free parameters are typical for a robotics paper, but the lack of reported values reduces reproducibility.

free parameters (3)
  • Motor thrust constant mu = not stated
    Used in Eq. 7 to map throttle to force; must be identified from motor/propeller tests. The paper does not report its value or identification procedure.
  • Motor torque constant tau = not stated
    Used in Eq. 8 to map throttle to torque. Same identification gap as mu.
  • PID controller gains = not stated
    Position and orientation PID gains are manually tuned (Section IV) and directly affect the reported tracking errors; values are not given.
assumptions (3)
  • domain assumption Linear thrust and torque model (Eqs. 7 and 8): motor force equals mu times throttle times direction, and motor torque is a linear combination of position cross force and spin torque, with constant mu and tau.
    Assumed in the control allocation; the paper's own flight data suggest wake interactions and slip-ring losses violate this linearity.
  • ad hoc to paper Hover efficiency metrics X1 and X2 are a valid proxy for power efficiency.
    The paper minimizes the sum of squared thrusts without demonstrating that this corresponds to electrical power consumption.
  • domain assumption In Eq. 1, for rotating-arm configurations, thrust directions can be freely chosen within the arm geometry, with no penalty on arm motion or actuator limits.
    Needed to compute the quoted X1 and X2 ranges; steady hover has zero arm velocity, so the velocity limits do not bind.

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Cite this review

Pith. "Pith review of MOMAV: A highly symmetrical fully-actuated multirotor drone using optimizing control allocation." pith.science (2026). https://pith.science/paper/APUNEGOF

@misc{pith2026250608868,
  author       = {Pith},
  title        = {Pith review of: MOMAV: A highly symmetrical fully-actuated multirotor drone using optimizing control allocation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/APUNEGOF}},
  note         = {Machine review of arXiv:2506.08868}
}
read the original abstract

MOMAV (Marco's Omnidirectional Micro Aerial Vehicle) is a multirotor drone that is fully actuated, meaning it can control its orientation independently of its position. MOMAV is also highly symmetrical, making its flight efficiency largely unaffected by its current orientation. These characteristics are achieved by a novel drone design where six rotor arms align with the vertices of an octahedron, and where each arm can actively rotate along its long axis. Various standout features of MOMAV are presented: The high flight efficiency compared to arm configuration of other fully-actuated drones, the design of an original rotating arm assembly featuring slip-rings used to enable continuous arm rotation, and a novel control allocation algorithm based on sequential quadratic programming (SQP) used to calculate throttle and arm-angle setpoints in flight. Flight tests have shown that MOMAV is able to achieve remarkably low mean position/orientation errors of 6.6mm, 2.1{\deg} ({\sigma}: 3.0mm, 1.0{\deg}) when sweeping position setpoints, and 11.8mm, 3.3{\deg} ({\sigma}: 8.6mm, 2.0{\deg}) when sweeping orientation setpoints.

Figures

Figures reproduced from arXiv: 2506.08868 by the authors.

Figure 1
Figure 1. Prototype drone MOMAV continuous arm rotation using slip-rings. It serves to simplify the constraints placed on the control allocation. Not doing so would require a more sophisticated solution to prevent the cables powering the propeller motors from winding up around the arms after multiple rotations. II. ARM CONFIGURATION Many arm configurations for fully-actuated drones featuring ingenious mechanical solutions hav… view at source ↗
Figure 2
Figure 2. Flight efficiency X1, X2 depending on orientation for a selection of drones with rotating arms Two metrics are calculated to compare flight efficiencies of various arm configurations. X1 is the fraction of thrust directed upwards during hovering flight (Eq. 2). The remainder (1 − X1) is thrust, that is wasted by motors having to push against each other instead of upwards. X2 on the other hand is the fraction of tota… view at source ↗
Figure 3
Figure 3. Flight efficiency X1, X2 depending on orientation for a selection of drones with fixed-tilt arms never shown to be capable of flying in arbitrary orientations. As expected, designs using fixed-tilt arms (Fig. 3A–3D, like in [3–6]) show significantly worse X1 and X2 efficiencies across all orientations. Notably, the ODAR configuration (Fig. 2C, like in [5]), which was optimized for wrench generation across orientatio… view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Views of the octahedral body implementation showing [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 6
Figure 6. Figure 6: Arm actuator step responses (A) and frequency re [PITH_FULL_IMAGE:figures/full_fig_p004_6.png]
Figure 5
Figure 5. Figure 5: Rotating arm assembly with a section view showing [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 7
Figure 7. Figure 7: Slip-ring efficiency analysis performed on a single a [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]
Figure 8
Figure 8. Figure 8: Penalty functions used in optimization objective [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 9
Figure 9. Figure 9: Test flight sweeping through orientations and keepin [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: Test flight with a trajectory like in Fig. 9, but using [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 11
Figure 11. Figure 11: Test flight with ten revolutions in roll while mainta [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 12
Figure 12. Figure 12: Test flight sweeping through positions and keeping t [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]

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