Kinematics of sea star legged locomotion

Gearing in a hydrostatic skeleton: the tube feet of juvenile sea stars (Leptasterias sp.)

Hydrostatic skeletons, such as an elephant trunk or a squid tentacle, permit the transmission of mechanical work through a soft body. Despite the ubiquity of these structures among animals, we generally do not understand how differences in their morphology affect their ability to transmit muscular work. Therefore, the present study used mathematical modeling, morphometrics, and kinematics to understand the transmission of force and displacement in the tube feet of the juvenile six-rayed star (Leptasterias sp.). An inverse-dynamic analysis revealed that the forces generated by the feet during crawling primarily serve to overcome the submerged weight of the body. These forces were disproportionately generated by the feet at more proximal positions along each ray, which were used more frequently for crawling. Owing to a combination of mechanical advantage and muscle mass, these proximal feet exhibited a greater capacity for force generation than the distal feet. However, the higher displacement advantage of the more elongated distal feet offer a superior ability to extend the feet into the environment. Therefore, the morphology of tube feet demonstrates a gradient in gearing along each ray that compliments their role in behavior.

Limb coordination: Coming together to bounce along

Experimental, modeling, and robotic research shows that switching of sea stars from crawling to bouncing gaits does not require centralized neural control. Bouncing can instead arise cooperatively, with synchronization of sea star tube feet occurring by locally acting mechanisms alone.

Cooperative transport in sea star locomotion

It is unclear how animals with radial symmetry control locomotion without a brain. Using a combination of experiments, mathematical modeling, and robotics, we tested the extent to which this control emerges in sea stars (Protoreaster nodosus) from the local control of their hundreds of feet and their mechanical interactions with the body. We discovered that these animals compensate for an experimental increase in their submerged weight by recruiting more feet that synchronize in the power stroke of the locomotor cycle during their bouncing gait. Mathematical modeling of the mechanics of a sea star replicated this response to loading without a central controller. A robotic sea star was found to similarly recruit more actuators under higher loads through purely decentralized control. These results suggest that an array of biological or engineered actuators are capable of cooperative transport where the actuators are dynamically recruited by the mechanics of the body. In particular, the body's vertical oscillations serve to recruit feet in greater numbers to overcome the weight to propel the body forward. This form of distributed control contrasts the conventional view of animal locomotion as governed by the central nervous system and offers inspiration for the design of engineered devices with arrays of actuators.

Soft skeletons transmit force with variable gearing

A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human's tongue, an octopus' arm and a nematode's body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore modeled the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA×DA) or, equivalently, the ratio of output to input work. The transmission efficiency changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance.