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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., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2024 Elsevier Inc. All rights reserved.)

The oral surface of sea stars is lined with arrays of tube feet that enable them to achieve highly controlled locomotion on various terrains. The activity of the tube feet is orchestrated by a nervous system that is distributed throughout the body without a central brain. How such a distributed nervous system produces a coordinated locomotion is yet to be understood. We develop mathematical models of the biomechanics of the tube feet and the sea star body. In the model, the feet are coupled mechanically through their structural connection to a rigid body. We formulate hierarchical control laws that capture salient features of the sea star nervous system. Namely, at the tube foot level, the power and recovery strokes follow a state-dependent feedback controller. At the system level, a directionality command is communicated through the nervous system to all tube feet. We study the locomotion gaits afforded by this hierarchical control model. We find that these minimally coupled tube feet coordinate to generate robust forward locomotion, reminiscent of the crawling motion of sea stars, on various terrains and for heterogeneous tube feet parameters and initial conditions. Our model also predicts a transition from crawling to bouncing consistently with recent experiments. We conclude by commenting on the implications of these findings for understanding the neuromechanics of sea stars and their potential application to autonomous robotic systems.

Many fish species span two or three orders of magnitude in length during the growth from larvae to adults, and this change may have dramatic consequences for locomotor performance. We measured how the performance of coasting changes over the life history of zebrafish (Danio rerio) and examined the scaling of mechanics underlying this change. Adult zebrafish coast disproportionately further and faster and maintain their speed for a longer duration than do larvae and juveniles. Measurements of drag on tethered dead fish suggest that adult fish operate in an inertial regime by coasting at relatively high Reynolds numbers (Re > 1000), and in vivo drag measurements showed adults to operate with a drag coefficient (Cinert approximately 0.024) that was consistent with previously published estimates. However, drag scaled differently at lower Re values than those assumed in previous studies. We found a viscous regime at Re < 300, which corresponds to the routine coasting of larvae and juveniles. Despite these changes in hydrodynamics over growth, a mathematical model of coasting mechanics suggests that the disproportionately longer coasting of adults is caused primarily by their large body mass and high speed at the beginning of coasting. We therefore propose that changes in coasting performance with growth are dictated primarily by the scaling of momentum rather than resulting from hydrodynamic changes. These results provide an opportunity for new interpretations of function in the growth and evolution of fish.

Understanding how the shape and motion of an aquatic animal affects the performance of swimming requires knowledge of the fluid forces that generate thrust and drag. These forces are poorly understood for the large diversity of animals that swim at Reynolds numbers (Re) between 10(0) and 10(2). We experimentally tested quasi-steady and unsteady blade-element models of the hydrodynamics of undulatory swimming in the larvae of the ascidian Botrylloides sp. by comparing the forces predicted by these models with measured forces generated by tethered larvae and by comparing the swimming speeds predicted with measurements of the speed of freely swimming larvae. Although both models predicted mean forces that were statistically indistinguishable from measurements, the quasi-steady model predicted the timing of force production and mean swimming speed more accurately than the unsteady model. This suggests that unsteady force (i.e. the acceleration reaction) does not play a role in the dynamics of steady undulatory swimming at Re approximately 10(2). We explored the relative contribution of viscous and inertial force to the generation of thrust and drag at 10(0)10(2)) and low (<10(0)) Re, the fluid forces that generate thrust cannot be assumed to be the same as those that generate drag at intermediate Re.