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arxiv: 2605.14944 · v1 · pith:RR3UDZHVnew · submitted 2026-05-14 · 💻 cs.RO · cs.SY· eess.SY

Behavioral Data-Driven Optimal Trajectory Generation for Rotary Cranes

Iskandar Khemakhem , Manuel Zobel , Johannes Sch\"ule , Oliver Sawodny , Naoki Uchiyama , Abdallah Farrage This is my paper

Pith reviewed 2026-06-30 20:30 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY
keywords rotary cranestrajectory generationdata-driven controlload sway suppressionWillems fundamental lemmanonparametric modelingconvex optimizationunderactuated systems
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The pith

A behavioral data-driven approach generates optimal open-loop trajectories for rotary cranes that suppress load sway using limited input-output data.

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

The paper aims to show that a nonparametric method based on measured data can produce smooth, optimal slewing trajectories for rotary cranes without needing detailed dynamical models or large datasets. This matters because cranes in construction need to move loads quickly and safely, but traditional model-based methods require expert tuning and accurate models, while learning methods often need lots of data. By using generalizations of Willems' fundamental lemma, the approach identifies system behavior directly from limited experiments and solves a convex optimization problem for trajectories that reduce oscillations. Validation on a lab setup shows improvements over model-based methods. A practical workflow reduces the need for specialized knowledge.

Core claim

The central claim is that despite the underactuated nature of rotary crane dynamics, a nonparametric representation can be identified from limited measured input-output data using Willems' fundamental lemma, enabling the generation of smooth optimal trajectories via convex optimization that achieve better performance in reducing load sway, tracking error, and travel time compared to established model-based approaches.

What carries the argument

Willems' fundamental lemma and its generalizations, which allow constructing a nonparametric representation of the system behavior directly from input-output data to formulate trajectory optimization as a convex problem.

If this is right

  • Up to 35% reduction in load sway compared to model-based method.
  • Up to 43% reduction in tracking error.
  • Up to 50% reduction in travel time.
  • The method operates with limited data and no explicit modeling, making it more accessible.
  • Produces smooth trajectories suitable for open-loop control.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar data-driven methods could apply to other underactuated mechanical systems like pendulums or robots.
  • The approach might reduce reliance on precise parameter identification in industrial crane automation.
  • Extensions could incorporate real-time feedback by updating the data-based representation online.
  • Testing on full-scale cranes would be needed to confirm scalability beyond the laboratory setup.

Load-bearing premise

That Willems' fundamental lemma and its generalizations can be applied directly to the underactuated rotary crane system to create an accurate nonparametric representation from limited data without modeling.

What would settle it

An experiment where the data-driven trajectories produce more load sway or longer travel times than the model-based method on the same crane setup would falsify the performance claims.

Figures

Figures reproduced from arXiv: 2605.14944 by Abdallah Farrage, Iskandar Khemakhem, Johannes Sch\"ule, Manuel Zobel, Naoki Uchiyama, Oliver Sawodny.

Figure 1
Figure 1. Figure 1: Schematic model of a rotary crane with the crane coordinates and [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The laboratory rotary crane used in this work. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Schematic of the data-driven trajectory interpolation problem: On the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Experimental measurements compared with the trajectory predicted [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Changes in the objective function as one hyperparameter varies, with [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Optimal trajectory generation results. The predicted optimal trajec [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of the trajectories generated by the proposed data-driven [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
read the original abstract

With the growth of the construction industry and the global shortage of skilled labor, the automation of crane control has become increasingly important for safe and efficient operations. A central challenge in automatic crane control is the reduction of load oscillations during motion, which is primarily addressed through appropriate slewing trajectories. In this context, classical model-based control methods rely on accurate dynamical models and expert tuning, and often struggle to meet safety and precision requirements, while many learning-based approaches require large data sets and significant computational resources. This paper proposes a behavioral data-driven framework for generating open-loop slewing trajectories for rotary cranes that suppress load sway while reducing operation time and energy consumption. The approach builds on Willems' fundamental lemma and its generalizations, to bypass explicit system modeling and operate directly on measured input-output data. A practical workflow is presented in this paper to reduce the need for expert knowledge. Despite the underactuated nature of the crane dynamics, the method identifies a nonparametric representation of the system behavior and generates smooth, optimal trajectories using limited data and convex optimization. The proposed trajectory generation method is validated on a laboratory crane setup and compared against an established model-based approach, achieving up to 35% reduction in load sway, 43% reduction in tracking error, and 50% reduction in travel time.

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 behavioral data-driven framework for open-loop slewing trajectory generation in rotary cranes. It applies Willems' fundamental lemma and generalizations to identify a nonparametric system representation directly from limited measured input-output data, then solves a convex optimization problem to generate smooth trajectories that suppress load sway while reducing travel time and energy use. The method is presented as bypassing explicit dynamical modeling and expert tuning; laboratory validation on a rotary crane setup reports up to 35% reduction in load sway, 43% in tracking error, and 50% in travel time relative to an established model-based approach.

Significance. If the central assumption that Willems' lemma extends to this nonlinear underactuated system holds and the data satisfy the required rank conditions, the approach would provide a practical, low-data alternative to model-based crane control that reduces reliance on accurate pendulum models and manual tuning. The reported laboratory gains and use of convex optimization on measured data would constitute a concrete demonstration of data-driven trajectory optimization for an underactuated mechanical system.

major comments (2)
  1. [Section describing the theoretical foundation and application of Willems' lemma (referenced in the abstract as operating] The manuscript invokes Willems' fundamental lemma (and generalizations) to obtain a nonparametric behavioral representation from measured I/O data, yet provides no derivation or explicit verification that the persistency-of-excitation rank condition or the behavioral representation itself is preserved under the nonlinear pendulum dynamics and underactuation of the rotary crane. This assumption is load-bearing for the central claim that limited data alone suffice for convex optimal trajectory generation.
  2. [Validation and experimental results section] Laboratory performance numbers (35% sway reduction, 43% tracking error, 50% travel time) are stated without reported data access, error bars, statistical tests, exclusion criteria, or explicit confirmation that the collected trajectories satisfy the algebraic requirements of the cited lemma; this prevents independent verification of the nonparametric representation's validity.
minor comments (2)
  1. [Abstract and practical workflow description] The abstract and workflow description would benefit from a concise statement of the precise data length and excitation conditions used to construct the Hankel matrices.
  2. [Method formulation] Notation for the behavioral representation and the convex program should be introduced with explicit dimension statements to clarify how the underactuated output (load angle) is handled in the data matrices.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address the two major comments point by point below, offering clarifications and committing to revisions where appropriate to strengthen the presentation of the behavioral framework and experimental results.

read point-by-point responses

  1. Referee: The manuscript invokes Willems' fundamental lemma (and generalizations) to obtain a nonparametric behavioral representation from measured I/O data, yet provides no derivation or explicit verification that the persistency-of-excitation rank condition or the behavioral representation itself is preserved under the nonlinear pendulum dynamics and underactuation of the rotary crane. This assumption is load-bearing for the central claim that limited data alone suffice for convex optimal trajectory generation.

    Authors: We acknowledge that the manuscript does not contain an explicit derivation showing preservation of the rank condition under the crane's nonlinear underactuated dynamics. The approach relies on the behavioral representation and cited generalizations of Willems' lemma, with validity demonstrated through successful experimental application on the physical system. We agree that additional discussion would improve clarity. In revision we will add a brief subsection referencing relevant extensions of the lemma to nonlinear mechanical systems and stating the data collection assumptions used to satisfy persistency of excitation. revision: yes

  2. Referee: Laboratory performance numbers (35% sway reduction, 43% tracking error, 50% travel time) are stated without reported data access, error bars, statistical tests, exclusion criteria, or explicit confirmation that the collected trajectories satisfy the algebraic requirements of the cited lemma; this prevents independent verification of the nonparametric representation's validity.

    Authors: We agree that the validation section would benefit from greater detail on reproducibility. We will add error bars, statistical summaries, and explicit statements confirming that the collected input trajectories meet the persistency-of-excitation rank conditions. Processed experimental data and code will be made available in a public repository; full raw sensor logs will be provided upon reasonable request subject to laboratory access policies. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external lemma applied to measured data

full rationale

The paper's central workflow identifies a nonparametric behavioral representation directly from measured input-output data via Willems' fundamental lemma and generalizations, then solves a convex optimization problem for trajectories. No equations or steps reduce by construction to fitted parameters renamed as predictions, self-definitional loops, or load-bearing self-citations whose content is unverified within the paper. Laboratory validation provides an independent empirical check against a model-based baseline. The applicability of the lemma to nonlinear underactuated dynamics is an external assumption (correctness risk) rather than a circular reduction internal to the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of Willems' fundamental lemma to underactuated crane dynamics from limited data; no free parameters or invented entities are mentioned.

axioms (1)
  • domain assumption Willems' fundamental lemma and its generalizations can be applied to identify a nonparametric representation of underactuated rotary crane behavior directly from measured input-output data.
    Invoked to bypass explicit system modeling and enable data-driven trajectory generation.

pith-pipeline@v0.9.1-grok · 5780 in / 1413 out tokens · 41112 ms · 2026-06-30T20:30:07.625010+00:00 · methodology

discussion (0)

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