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arxiv: 2605.03666 · v1 · submitted 2026-05-05 · 💻 cs.RO

Sensorless State Estimation and Control for Agile Cable-Suspended Payload Transport by Quadrotors

Ana Maria Nascimento , Augusto Sales , Antonio Marcus Lima , Tiago Nascimento This is my paper

Pith reviewed 2026-05-07 04:00 UTC · model grok-4.3

classification 💻 cs.RO
keywords cable-suspended payloadquadrotorNMPCUdwadia-Kalabasensorless state estimationaerial manipulationtrajectory trackingpayload transport
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The pith

Using the Udwadia-Kalaba method to model cable constraints allows sensorless estimation and improved control of quadrotor-suspended payloads.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Aerial robots carrying suspended loads via cables encounter difficulties in obtaining accurate dynamic models and typically depend on additional sensors for the payload state. The work applies the Udwadia-Kalaba method to incorporate the cable's geometric constraint directly, deriving the tension force for use in a nonlinear model predictive control scheme. This same approach supports estimating the load state without dedicated sensors. Experiments on real quadrotors demonstrate reduced tracking errors when the full load dynamics are included in the controller optimization, outperforming incomplete model strategies.

Core claim

By employing the Udwadia-Kalaba formulation, the tension in the cable can be derived from the fixed-length constraint and incorporated into the NMPC prediction model, while also enabling a sensorless estimation method for the payload. This results in superior trajectory tracking performance in real-robot tests compared to control strategies that use simplified or incomplete system models.

What carries the argument

Udwadia-Kalaba method applied to the cable constraint for deriving tension force and supporting sensorless state estimation in NMPC-based control.

Load-bearing premise

The cable behaves as a perfect rigid constraint of fixed length that the Udwadia-Kalaba method models exactly, without elasticity, flexibility, or disturbance effects.

What would settle it

An experiment measuring actual cable tension or load position with independent sensors and comparing against the model's predictions under dynamic maneuvers would falsify the approach if large discrepancies appear.

Figures

Figures reproduced from arXiv: 2605.03666 by Ana Maria Nascimento, Antonio Marcus Lima, Augusto Sales, Tiago Nascimento.

Figure 1
Figure 1. Figure 1: UAV at 2 m/s transporting a 0.5 kg payload through a view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of a UAV carrying a payload via a cable view at source ↗
Figure 3
Figure 3. Figure 3: System’s Architecture Diagram. effort, respectively, in which S can also be expressed as S = diag(Sp, Sp˙ , Sq, S˙δ ), with SN = [SQ, SL]. Rotational dynamics around the yaw axis are inherently slower than roll and pitch responses. To optimize tracking, the attitude error is decomposed to apply distinct weights in the cost matrix SQ. The orientation error is defined by the error quaternion qe, which repres… view at source ↗
Figure 4
Figure 4. Figure 4: Hardware UAV platform used in the experiments. view at source ↗
Figure 5
Figure 5. Figure 5: Executed trajectories with the classic NMPC (left) and our proposed NMPC-Load (right) with trajectory speeds of 0.5 view at source ↗
Figure 6
Figure 6. Figure 6: Schematic of a UAV carrying a payload via a cable view at source ↗
read the original abstract

This work proposes a novel control and estimation approach for aerial manipulation of a cable-suspended load using Unmanned Aerial Vehicles (UAVs). Common approaches in the state of the art have practical limitations, relying on direct load measurements and Lagrangian methods for dynamic modeling. The lack of a straightforward dynamic model of the system led us to propose adopting the Udwadia-Kalaba method to explicitly incorporate the cable's geometric constraints. This formulation allowed for the consistent derivation of the tension force and its direct integration into the NMPC prediction model. Additionally, we propose a sensorless load state estimation based on the same geometric constraints. Results from real-robot experiments demonstrated that the explicit inclusion of load dynamics in the optimization problem significantly reduces trajectory-tracking errors and yields better overall performance compared to strategies based on incomplete models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a sensorless state estimation and control framework for a quadrotor transporting a cable-suspended payload. It adopts the Udwadia-Kalaba method to enforce the fixed-length geometric constraint, derives the cable tension explicitly, and incorporates this tension into the prediction model of a nonlinear model predictive controller (NMPC). A complementary sensorless estimator for the load pose and velocity is constructed from the same constraint equations. Real-robot experiments are reported to show that explicit inclusion of the load dynamics yields lower trajectory-tracking errors than controllers based on incomplete (payload-agnostic) models.

Significance. If the experimental gains are robust and the modeling assumptions hold, the work is significant for aerial manipulation: it supplies a parameter-free, constraint-based route to tension computation and state estimation that avoids onboard load sensors or Lagrangian multipliers. The real-robot validation on agile trajectories is a concrete strength, and the approach could transfer to other constrained aerial or ground systems where direct sensing is impractical.

major comments (2)
  1. [Section 3] Section 3 (Udwadia-Kalaba tension derivation): the central claim attributes performance gains to accurate inclusion of load dynamics via the holonomic constraint. However, the derivation assumes an inextensible, massless, non-bending cable with no elasticity or aerodynamic effects. Because the resulting tension is used verbatim in both the NMPC dynamics and the sensorless estimator, any violation of this assumption directly affects prediction accuracy. No cable-stiffness calibration, direct tension measurement, or sensitivity study is provided to bound the modeling error.
  2. [Experiments] Experiments section: the manuscript states that explicit load-dynamics inclusion 'significantly reduces trajectory-tracking errors,' yet the quantitative support (RMSE or similar metrics, number of trials, statistical tests, and precise definition of the incomplete-model baselines) is insufficient to isolate the contribution of the Udwadia-Kalaba tension from other factors such as controller tuning or estimator initialization.
minor comments (2)
  1. Notation for the constraint Jacobian and the Udwadia-Kalaba multiplier is introduced without an explicit table of symbols; a short nomenclature section would improve readability.
  2. Figure captions for the experimental trajectories should include the numerical error values (e.g., mean and std of position RMSE) rather than only qualitative statements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback, which helps clarify the modeling assumptions and strengthen the experimental validation. We address each major comment below and indicate the revisions planned for the next manuscript version.

read point-by-point responses

  1. Referee: [Section 3] Section 3 (Udwadia-Kalaba tension derivation): the central claim attributes performance gains to accurate inclusion of load dynamics via the holonomic constraint. However, the derivation assumes an inextensible, massless, non-bending cable with no elasticity or aerodynamic effects. Because the resulting tension is used verbatim in both the NMPC dynamics and the sensorless estimator, any violation of this assumption directly affects prediction accuracy. No cable-stiffness calibration, direct tension measurement, or sensitivity study is provided to bound the modeling error.

    Authors: The Udwadia-Kalaba formulation is adopted specifically to obtain an explicit, parameter-free expression for cable tension directly from the holonomic constraint, which is a core contribution enabling sensorless operation. The ideal-cable assumptions (inextensible, massless, no bending or aero drag) are standard in the aerial-manipulation literature for real-time tractability and are consistent with the lightweight, low-stretch cables used in our hardware. We agree that a quantitative bound on modeling error would be beneficial. In the revised manuscript we will add a dedicated simulation study that perturbs cable length and introduces small stiffness and damping terms, then reports the resulting degradation in estimation RMSE and closed-loop tracking error. Direct tension measurement was intentionally omitted because the method targets sensorless scenarios; we will explicitly state this design choice and its limitations in the discussion section. revision: partial

  2. Referee: [Experiments] Experiments section: the manuscript states that explicit load-dynamics inclusion 'significantly reduces trajectory-tracking errors,' yet the quantitative support (RMSE or similar metrics, number of trials, statistical tests, and precise definition of the incomplete-model baselines) is insufficient to isolate the contribution of the Udwadia-Kalaba tension from other factors such as controller tuning or estimator initialization.

    Authors: We accept that the experimental section requires more rigorous quantitative reporting to isolate the effect of the constraint-based tension model. The original manuscript presents comparative trajectory plots, but the revised version will include a summary table reporting RMSE for position, velocity, and attitude, together with the number of repeated trials (five independent flights per controller and trajectory). The baseline will be precisely defined as an NMPC that uses only the quadrotor dynamics and treats the payload as an unmodeled disturbance. We will also report mean and standard deviation across trials; a paired t-test can be added if the editor deems it necessary. These additions will make the performance gain attributable to the Udwadia-Kalaba term clearer. revision: yes

Circularity Check

0 steps flagged

No circularity: standard external method applied to constraints with empirical validation

full rationale

The paper adopts the established Udwadia-Kalaba method (an external, non-author-originated technique for constrained dynamics) to derive tension from the fixed-length cable geometric constraint. This derived tension is inserted into the NMPC prediction model and used for sensorless state estimation. The central performance claim rests on real-robot experiments comparing explicit load-dynamics inclusion against incomplete-model baselines. No derivation step reduces to a fitted parameter renamed as prediction, no self-citation chain is load-bearing for the core result, and the constraint model is not self-defined via the outputs it produces. The approach is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard constrained mechanics (Udwadia-Kalaba) and the assumption that cable geometry is known and rigid; no new entities are introduced and no free parameters are explicitly fitted in the abstract.

axioms (1)
  • domain assumption The cable imposes a holonomic constraint of fixed length between quadrotor and payload.
    This is the core geometric constraint used to derive tension and enable sensorless estimation.

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Reference graph

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