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, oscillating vertical velocities precede oscillating horizontal velocities by 90 deg, as reflected by clockwise circular hodographs. Potential energy precedes horizontal kinetic energy by 9.6 deg and so they are nearly in phase. These phase relationships resemble terrestrial running gaits, except that podia are always on the ground. Kinetic and potential energy scale with body mass as Mb   1.1, 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 Mb-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.