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Automating Box Folding: Sequence Extraction and Ranking Methodologies

Giuseppe Fabio Preziosa, Davide Ferloni, Andrea Maria Zanchettin, Marco Faroni, Paolo Rocco

TL;DR

Addresses automated box folding by bridging folding-sequence extraction with hardware-aware ranking. The authors present a three-phase framework: (i) box modeling with a joint-angle vector $\boldsymbol{\theta}$ and connectivity matrix $C$, (ii) folding-sequence identification via backtracking on action vectors $\boldsymbol{u_t}$ under collision constraint $CC$, and (iii) hardware-aware ranking using costs $C_{\text{vol}}$, $C_{\text{dim}}$, and $C_{\text{aerial}}$. The main contributions are a hardware-independent folding-sequence extractor and three ranking indices that favor collision-free, compact, and fabrication-friendly sequences, illustrated through a Unity simulation and an ABB GoFa robot case study where a feasible sequence is implemented. The results demonstrate practical feasibility and provide a blueprint for scalable deployment across carton designs, enabling more flexible and cost-effective packaging automation.

Abstract

Box folding represents a crucial challenge for automated packaging systems. This work bridges the gap between existing methods for folding sequence extraction and approaches focused on the adaptability of automated systems to specific box types. An innovative method is proposed to identify and rank folding sequences, enabling the transformation of a box from an initial state to a desired final configuration. The system evaluates and ranks these sequences based on their feasibility and compatibility with available hardware, providing recommendations for real-world implementations. Finally, an illustrative use case is presented, where a robot performs the folding of a box.

Automating Box Folding: Sequence Extraction and Ranking Methodologies

TL;DR

Addresses automated box folding by bridging folding-sequence extraction with hardware-aware ranking. The authors present a three-phase framework: (i) box modeling with a joint-angle vector and connectivity matrix , (ii) folding-sequence identification via backtracking on action vectors under collision constraint , and (iii) hardware-aware ranking using costs , , and . The main contributions are a hardware-independent folding-sequence extractor and three ranking indices that favor collision-free, compact, and fabrication-friendly sequences, illustrated through a Unity simulation and an ABB GoFa robot case study where a feasible sequence is implemented. The results demonstrate practical feasibility and provide a blueprint for scalable deployment across carton designs, enabling more flexible and cost-effective packaging automation.

Abstract

Box folding represents a crucial challenge for automated packaging systems. This work bridges the gap between existing methods for folding sequence extraction and approaches focused on the adaptability of automated systems to specific box types. An innovative method is proposed to identify and rank folding sequences, enabling the transformation of a box from an initial state to a desired final configuration. The system evaluates and ranks these sequences based on their feasibility and compatibility with available hardware, providing recommendations for real-world implementations. Finally, an illustrative use case is presented, where a robot performs the folding of a box.
Paper Structure (19 sections, 15 equations, 5 figures, 1 table)

This paper contains 19 sections, 15 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Works
  3. Box Representation and Kinematic Modeling
  4. Robotics for Box Handling
  5. Contributions
  6. Proposed Approach
  7. Box Modeling and Connectivity Matrix Generation
  8. Folding Sequence Identification
  9. Evaluation Metrics for Ranking Folding Sequences
  10. Bounding Box Volume Criterion
  11. Bounding Box Maximum Dimension Criterion
  12. Number of Aerial Foldings Criterion
  13. Implementation Overview and Case Study
  14. Simulation Carton Modeling
  15. Case Study
  16. ...and 4 more sections

Figures (5)

  • Figure 1: Folding steps of the implemented sequence extracted by the proposed algorithm.
  • Figure 2: Simplified structure of a three-panel decision tree. On the left, the first five iterations of the backtracking process are shown, highlighting excluded paths and intermediate states. On the right, the completed search is depicted, with the valid sequences reaching the final states $S_f$ highlighted in orange.
  • Figure 3: On the left, an example of Aerial Folding is shown. On the right, the folding process involves a panel taken from the workbench, which does not classify as Aerial Folding
  • Figure 4: Hardware setup used in our case study
  • Figure 5: Representation of the box model used in the use case, including all necessary parameters