Free-falling paper shapes exhibit rich, complex and varied behaviours that are extremely challenging to model analytically. Physical experimentation aids in system understanding, but is time-consuming, sensitive to initial conditions and reliant on subjective visual behavioural classification. In this study, robotics, computer vision and machine learning are used to autonomously fabricate, drop, analyse and classify the behaviours of hundreds of shapes. The system is validated by reproducing results for falling discs, which exhibit four falling styles: tumbling, chaotic, steady and periodic. A previously determined mapping from a non-dimensional parameter space to behaviour groups is shown to be consistent with these new experiments for tumbling and chaotic behaviours. However, steady or periodic behaviours are observed in previously unseen areas of the parameter space. More complex hexagon, square and cross shapes are investigated, showing that the non-dimensional parameter space generalizes to these shapes. The system highlights the potential of robotics for the investigation of complex physical systems, of which falling paper is one example, and provides a template for future investigation of such systems.
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Example data are available at https://github.com/th533/Falling-Paper.
Example code is available at https://github.com/th533/Falling-Paper.
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We acknowledge funding from EPSRC RG92738 and The Mathworks Ltd.
The authors declare no competing interests.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary material containing Supplementary Figs. 1–7 and Tables 1–4.
Demonstration of iterative physical experimentation system showing manufacture, picking, dropping and analysis of falling paper shapes.
Slow-motion representative examples of steady and periodic, chaotic and tumbling behaviours of circles, hexagons, squares and crosses.
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Howison, T., Hughes, J. & Iida, F. Large-scale automated investigation of free-falling paper shapes via iterative physical experimentation. Nat Mach Intell 2, 68–75 (2020). https://doi.org/10.1038/s42256-019-0135-z