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Robophysical study of jumping dynamics on granular media


Characterizing forces on deformable objects intruding into sand and soil requires understanding the solid- and fluid-like responses of such substrates and their effect on the state of the object. The most detailed studies of intrusion in dry granular media have revealed that interactions of fixed-shape objects during free impact (for example, cannonballs) and forced slow penetration can be described by hydrostatic- and hydrodynamic-like forces. Here we investigate a new class of granular interactions: rapid intrusions by objects that change shape (self-deform) through passive and active means. Systematic studies of a simple spring-mass robot jumping on dry granular media reveal that jumping performance is explained by an interplay of nonlinear frictional and hydrodynamic drag as well as induced added mass (unaccounted by traditional intrusion models) characterized by a rapidly solidified region of grains accelerated by the foot. A model incorporating these dynamics reveals that added mass degrades the performance of certain self-deformations owing to a shift in optimal timing during push-off. Our systematic robophysical experiment reveals both new soft-matter physics and principles for robotic self-deformation and control, which together provide principles of movement in deformable terrestrial environments.

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Figure 1: An actively and passively self-deforming robot jumping on granular media.
Figure 2: Jump heights for various self-deformations.
Figure 3: Measurements of force versus intrusion depth.
Figure 4: Particle image velocimetry (PIV) measurement of granular flow kinematics.
Figure 5: Quasistatic and inertial properties of a jamming granular cone.
Figure 6: Simulation of coupled added-mass and robot jumping dynamics.


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This work was supported by NSF Physics of Living Systems, Burroughs Wellcome Fund, and the Army Research Office. We thank A. Karsai for assistance in simulation work and P. Umbanhowar and L. London for insightful comments and discussion.

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J.A. and D.I.G. conceived the study and wrote the paper. J.A. performed the experimental work, designed and ran the simulation models, and analysed the results.

Corresponding authors

Correspondence to Jeffrey Aguilar or Daniel I. Goldman.

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The authors declare no competing financial interests.

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Aguilar, J., Goldman, D. Robophysical study of jumping dynamics on granular media. Nature Phys 12, 278–283 (2016).

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