Kinematics of sea star legged locomotion

Sea stars have slower crawling and faster bouncing gaits. Both speed and
oscillation amplitude increase during the transition from crawling to
oscillating. In the bouncy gait, vertical velocities precede horizontal
velocities by 98&[deg], as reflected by clockwise circular
hodographs. Potential energy precedes horizontal energy by
16&[deg] and so are nearly in phase. These phase relationships
resemble terrestrial running gaits, except that podia are always on the
ground. Kinetic and potential energy scale as mass1.1, with the change in
kinetic energy consistently two orders of magnitude less, indicating that
efficient exchange is not feasible. Frequency of the bouncy gait scales
with mass-0.14, which is similar to continuously running vertebrates and
indicates that gravitational forces are important. This scaling differs
from the Hill model, in which scaling of muscle forces determine
frequency. We propose a simple torque stabilized inverted pendulum (TS-IP)
model to conceptualize the dynamics of this gait. The TS-IP model
incorporates mathematics equivalent to an angular spring, but implemented
by a nearly constant upward force generated by the podia in each step.
That upward force is just larger than the force required to sustain the
underwater weight of the sea star. Even though the bouncy gait is the
rapid gait for these sea stars, the pace of movement is still very slow.
In fact, the observed Froude numbers (10-2 to 10-3) are much lower than
those typical of vertebrate locomotion and are as low or lower than those
reported for slow walking fruit flies, which are the lowest values for
pedestrian Froude numbers of which we are aware. --