  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 (e.g. 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 due 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.
