  Compared to agile legged animals, wheeled and tracked vehicles often suffer
large performance loss on granular surfaces like sand and gravel. Understanding
the mechanics of legged locomotion on granular media can aid the development of
legged robots with improved mobility on granular surfaces; however, no general
force model yet exists for granular media to predict ground reaction forces
during complex limb intrusions. Inspired by a recent study of sand-swimming, we
develop a resistive force model in the vertical plane for legged locomotion on
granular media. We divide an intruder of complex morphology and kinematics,
e.g., a bio-inspired robot L-leg rotated through uniform granular media
(loosely packed ~ 1 mm diameter poppy seeds), into small segments, and measure
stresses as a function of depth, orientation, and direction of motion using a
model leg segment. Summation of segmental forces over the intruder predicts the
net forces on both an L-leg and a reversed L-leg rotated through granular media
with better accuracy than using simple one-dimensional penetration and drag
force models. A multi-body dynamic simulation using the resistive force model
predicts the speeds of a small legged robot (15 cm, 150 g) moving on granular
media using both L-legs and reversed L-legs.
