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Large-scale automated investigation of free-falling paper shapes via iterative physical experimentation


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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Fig. 1: Schematic of the falling-paper system and proposed iterative physical experimentation approach.
Fig. 2: Diagram of the experimental set-up.
Fig. 3: Time-lapse images of the three falling behaviours observed in each shape.
Fig. 4: Trajectories and observable area profiles of falling shapes for different automatically classified behavioural groups.
Fig. 5: Variation in measured falling characteristics with respect to design parameters and automatically classified behaviour groups.
Fig. 6: Automatically classified falling behaviours in Reynolds number \(\mathrm{Re}\) and non-dimensional moment of inertia \({I}^{* }\) parameter space.

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Code availability

Example code is available at


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We acknowledge funding from EPSRC RG92738 and The Mathworks Ltd.

Author information




T.H., J.H. and F.I. conceived the study. T.H. designed the experimental set-up. T.H. and J.H. managed the experiments. T.H. and J.H. analysed the data. T.H., J.H. and F.I. wrote the manuscript.

Corresponding author

Correspondence to Toby Howison.

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The authors declare no competing interests.

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Supplementary information

Supplementary Material

Supplementary material containing Supplementary Figs. 1–7 and Tables 1–4.

Supplementary Video 1

Demonstration of iterative physical experimentation system showing manufacture, picking, dropping and analysis of falling paper shapes.

Supplementary Video 2

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).

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