Decentralized Control Mechanism for Determination of Moving Direction in Brittle Stars With Penta-Radially Symmetric Body

A methodological exploration to study 2D arm kinematics in Ophiuroidea (Echinodermata)

Brittle stars, unlike most other echinoderms, do not use their small tube feet for locomotion but instead use their flexible arms to produce a rowing or reverse rowing movement. They are among the fastest-moving echinoderms with the ability of complex locomotory behaviors. Considering the high species diversity and variability in morphotypes, a proper understanding of intra- and interspecies variation in arm flexibility and movement is lacking. This study focuses on the exploration of the methods to investigate the variability in brittle star locomotion and individual arm use. We performed a two-dimensional (2D) image processing on horizontal movement only. The result indicated that sinuosity, disc displacement and arm angle are important parameters to interpret ophiuroid locomotion. A dedicated Python script to calculate the studied movement parameters and visualize the results applicable to all 5-armed brittle stars was developed. These results can serve as the basis for further research in robotics inspired by brittle star locomotion.

Sea star inspired crawling and bouncing

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.

A general model of locomotion of brittle stars with a variable number of arms

Typical brittle stars have five radially symmetrical arms that coordinate to move the body in a certain direction. However, some species have a variable number of arms, which is a unique trait since intact animals normally have a fixed number of limbs. How does a single species manage different numbers of appendages for adaptive locomotion? We herein describe locomotion in Ophiactis brachyaspis with four, five, six and seven arms to propose a common rule for the movement of brittle stars with different numbers of arms. For this, we mechanically stimulated one arm of individuals to analyse escape direction and arm movement. By gathering quantitative indices and employing Bayesian statistical modelling, we noted a pattern: regardless of the total number of arms, an anterior position emerges at one of the second neighbouring arms to a mechanically stimulated arm, while arms adjacent to the anterior one synchronously work as left and right rowers. We propose a model in which an afferent signal runs clockwise or anticlockwise along the nerve ring while linearly counting how many arms it passes through. With this model, the question on how 'left and right' emerges in a radially symmetrical body via a decentralized system is answered.

Flexible Coordination of Flexible Limbs: Decentralized Control Scheme for Inter- and Intra-Limb Coordination in Brittle Stars' Locomotion

Conventional mobile robots have difficulties adapting to unpredictable environments or performing adequately after undergoing physical damages in realtime operation, unlike animals. We address this issue by focusing on brittle stars, an echinoderm related to starfish. Most brittle stars have five flexible arms, and they can coordinate among the arms (i.e., inter-arm coordination) as well as the many bodily degrees of freedom within each arm (i.e., intra-arm coordination). They can move in unpredictable environments while promptly adapting to those, and to their own physical damages (e.g., arm amputation). Our previous work focused on the inter-arm coordination by studying trimmed-arm brittle stars. Herein, we extend our previous work and propose a decentralized control mechanism that enables coupling between the inter-arm and intra-arm coordination. We demonstrate via simulations and real-world experiments with a brittle star-like robot that the behavior of brittle stars when they are intact and undergoing shortening or amputation of arms can be replicated.