A brittle star-like robot capable of immediately adapting to unexpected physical damage

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.

Back to life: Techniques for developing high-quality 3D reconstructions of plants and animals from digitized specimens

Expanded use of 3D imaging in organismal biology and paleontology has substantially enhanced the ability to visualize and analyze specimens. These techniques have improved our understanding of the anatomy of many taxa, and the integration of downstream computational tools applied to 3D datasets have broadened the range of analyses that can be performed (e.g., finite element analyses, geometric morphometrics, biomechanical modeling, physical modeling using 3D printing). However, morphological analyses inevitably present challenges, particularly in fossil taxa where taphonomic or preservational artifacts distort and reduce the fidelity of the original morphology through shearing, compression, and disarticulation, for example. Here, we present a compilation of techniques to build high-quality 3D digital models of extant and fossil taxa from 3D imaging data using freely available software for students and educators. Our case studies and associated step-by-step supplementary tutorials present instructions for working with reconstructions of plants and animals to directly address and resolve common issues with 3D imaging data. The strategies demonstrated here optimize scientific accuracy and computational efficiency and can be applied to a broad range of taxa.

Three-dimensional visualization as a tool for interpreting locomotion strategies in ophiuroids from the Devonian Hunsrück Slate

Living brittle stars (Echinodermata: Ophiuroidea) employ a very different locomotion strategy to that of any other metazoan: five or more arms coordinate powerful strides for rapid movement across the ocean floor. This mode of locomotion is reliant on the unique morphology and arrangement of multifaceted skeletal elements and associated muscles and other soft tissues. The skeleton of many Palaeozoic ophiuroids differs markedly from that in living forms, making it difficult to infer their mode of locomotion and, therefore, to resolve the evolutionary history of locomotion in the group. Here, we present three-dimensional digital renderings of specimens of six ophiuroid taxa from the Lower Devonian Hunsrück Slate: four displaying the arm structure typical of Palaeozoic taxa (Encrinaster roemeri, Euzonosoma tischbeinianum, Loriolaster mirabilis, Cheiropteraster giganteus) and two (Furcaster palaeozoicus, Ophiurina lymani) with morphologies more similar to those in living forms. The use of three-dimensional digital visualization allows the structure of the arms of specimens of these taxa to be visualized in situ in the round, to our knowledge for the first time. The lack of joint interfaces necessary for musculoskeletally-driven locomotion supports the interpretation that taxa with offset ambulacrals would not be able to conduct this form of locomotion, and probably used podial walking. This approach promises new insights into the phylogeny, functional morphology and ecological role of Palaeozoic brittle stars.

Decoding Decentralized Control Mechanism Underlying Adaptive and Versatile Locomotion of Snakes

Snakes have no limbs and can move in various environments using a simple elongated limbless body structure obtained through a long-term evolutionary process. Specifically, snakes have various locomotion patterns, which they change in response to conditions encountered. For example, on an unstructured terrain, snakes actively utilize the terrain's irregularities and move effectively by actively pushing their bodies against the "scaffolds" that they encounter. In a narrow aisle, snakes exhibit concertina locomotion, in which the tail part of the body is pulled forward with the head part anchored, and this is followed by the extension of the head part with the tail part anchored. Furthermore, snakes often exhibit three-dimensional (3-D) locomotion patterns wherein the points of ground contact change in a spatiotemporal manner, such as sidewinding and sinus-lifting locomotion. This ability is achieved possibly by a decentralized control mechanism, which is still mostly unknown. In this study, we address this aspect by employing a synthetic approach to understand locomotion mechanisms by developing mathematical models and robots. We propose a Tegotae-based decentralized control mechanism and use a 2-D snake-like robot to demonstrate that it can exhibit scaffold-based and concertina locomotion. Moreover, we extend the proposed mechanism to 3D and use a 3-D snake-like robot to demonstrate that it can exhibit sidewinding and sinus-lifting locomotion. We believe that our findings will form a basis for developing snake-like robots applicable to search-and-rescue operations as well as understanding the essential decentralized control mechanism underlying animal locomotion.

General Distributed Neural Control and Sensory Adaptation for Self-Organized Locomotion and Fast Adaptation to Damage of Walking Robots

Walking animals such as invertebrates can effectively perform self-organized and robust locomotion. They can also quickly adapt their gait to deal with injury or damage. Such a complex achievement is mainly performed via coordination between the legs, commonly known as interlimb coordination. Several components underlying the interlimb coordination process (like distributed neural control circuits, local sensory feedback, and body-environment interactions during movement) have been recently identified and applied to the control systems of walking robots. However, while the sensory pathways of biological systems are plastic and can be continuously readjusted (referred to as sensory adaptation), those implemented on robots are typically static. They first need to be manually adjusted or optimized offline to obtain stable locomotion. In this study, we introduce a fast learning mechanism for online sensory adaptation. It can continuously adjust the strength of sensory pathways, thereby introducing flexible plasticity into the connections between sensory feedback and neural control circuits. We combine the sensory adaptation mechanism with distributed neural control circuits to acquire the adaptive and robust interlimb coordination of walking robots. This novel approach is also general and flexible. It can automatically adapt to different walking robots and allow them to perform stable self-organized locomotion as well as quickly deal with damage within a few walking steps. The adaptation of plasticity after damage or injury is considered here as lesion-induced plasticity. We validated our adaptive interlimb coordination approach with continuous online sensory adaptation on simulated 4-, 6-, 8-, and 20-legged robots. This study not only proposes an adaptive neural control system for artificial walking systems but also offers a possibility of invertebrate nervous systems with flexible plasticity for locomotion and adaptation to injury.

The structural origins of brittle star arm kinematics: An integrated tomographic, additive manufacturing, and parametric modeling-based approach

Brittle stars are known for the high flexibility of their arms, a characteristic required for locomotion, food grasping, and for holding onto a great diversity of substrates. Their high agility is facilitated by the numerous discrete skeletal elements (ossicles) running through the center of each arm and embedded in the skin. While much has been learned regarding the structural diversity of these ossicles, which are important characters for taxonomic purposes, their impact on the arms' range of motion, by contrast, is poorly understood. In the present study, we set out to investigate how ossicle morphology and skeletal organization affect the flexibility of brittle star arms. Here, we present the results of an in-depth analysis of three brittle star species (Ophioplocus esmarki, Ophiopteris papillosa, and Ophiothrix spiculata), chosen for their different ranges of motion, as well as spine size and orientation. Using an integrated approach that combines behavioral studies with parametric modeling, additive manufacturing, micro-computed tomography, scanning electron microscopy, and finite element simulations, we present a high-throughput workflow that provides a fundamental understanding of 3D structure-kinematic relationships in brittle star skeletal 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.

Three-Legged Locomotion and the Constraints on Limb Number: Why Tripeds Don't Have a Leg to Stand On

Three-legged animals do not exist today and such an animal is not found in the fossil record. Which constraints operate to result in the lack of a triped phenotype? Consideration of animal locomotion and robotic studies suggests that physical constraints would not prevent a triped from being functional or advantageous. As is reviewed here, the strongest constraint on the evolution of a triped is phylogenetic: namely, the early genetic adoption of a bilaterally symmetrical body plan occurring before the advent of limbs. Presumably, this would greatly constrain any three-legged animal from ever evolving. Tripedalism is employed only by a few animals, but many use a tripod stance while engaged in a variety of activities. Because terms are often used interchangeably in the literature, a standardization of locomotion terminology is proposed. Understanding the constraints behind "forbidden" phenotypes forces us to confront gaps in our evolutionary understanding of which we may be unaware.

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

A brittle star, an echinoderm with penta-radially symmetric body, can make decisions about its moving direction and move adapting to various circumstances despite lacking a central nervous system and instead possessing a rather simple distributed nervous system. In this study, we aimed to elucidate the essential control mechanism underlying the determination of moving direction in brittle stars. Based on behavioral findings on brittle stars whose nervous systems were lesioned in various ways, we propose a phenomenological mathematical model. We demonstrate via simulations that the proposed model can well reproduce the behavioral findings. Our findings not only provide insights into the mechanism for the determination of moving direction in brittle stars, but also help understand the essential mechanism underlying autonomous behaviors of animals. Moreover, they will pave the way for developing fully autonomous robots that can make decisions by themselves and move adaptively under various circumstances.

Different Synchrony in Rhythmic Movement Caused by Morphological Difference between Five- and Six-armed Brittle Stars

Physiological experiments and mathematical models have supported that neuronal activity is crucial for coordinating rhythmic movements in animals. On the other hand, robotics studies have suggested the importance of physical properties made by body structure, i.e. morphology. However, it remains unclear how morphology affects movement coordination in animals, independent of neuronal activity. To begin to understand this issue, our study reports a rhythmic movement in the green brittle star Ophiarachna incrassata. We found this animal moved five radially symmetric parts in a well-ordered unsynchronized pattern. We built a phenomenological model where internal fluid flows between the five body parts to explain the coordinated pattern without considering neuronal activity. Changing the number of the body parts from five to six, we simulated a synchronized pattern, which was demonstrated also by an individual with six symmetric parts. Our model suggests a different number in morphology makes a different fluid flow, leading to a different synchronization pattern in the animal.

Planarian regeneration as a model of anatomical homeostasis: Recent progress in biophysical and computational approaches

Planarian behavior, physiology, and pattern control offer profound lessons for regenerative medicine, evolutionary biology, morphogenetic engineering, robotics, and unconventional computation. Despite recent advances in the molecular genetics of stem cell differentiation, this model organism's remarkable anatomical homeostasis provokes us with truly fundamental puzzles about the origin of large-scale shape and its relationship to the genome. In this review article, we first highlight several deep mysteries about planarian regeneration in the context of the current paradigm in this field. We then review recent progress in understanding of the physiological control of an endogenous, bioelectric pattern memory that guides regeneration, and how modulating this memory can permanently alter the flatworm's target morphology. Finally, we focus on computational approaches that complement reductive pathway analysis with synthetic, systems-level understanding of morphological decision-making. We analyze existing models of planarian pattern control and highlight recent successes and remaining knowledge gaps in this interdisciplinary frontier field.

Integrating morphology and in vivo skeletal mobility with digital models to infer function in brittle star arms

Brittle stars (Phylum Echinodermata, Class Ophiuroidea) have evolved rapid locomotion employing muscle and skeletal elements within their (usually) five arms to apply forces in a manner analogous to that of vertebrates. Inferring the inner workings of the arm has been difficult as the skeleton is internal and many of the ossicles are sub-millimeter in size. Advances in 3D visualization and technology have made the study of movement in ophiuroids possible. We developed six virtual 3D skeletal models to demonstrate the potential range of motion of the main arm ossicles, known as vertebrae, and six virtual 3D skeletal models of non-vertebral ossicles. These models revealed the joint center and relative position of the arm ossicles during near-maximal range of motion. The models also provide a platform for the comparative evaluation of functional capabilities between disparate ophiuroid arm morphologies. We made observations on specimens of Ophioderma brevispina and Ophiothrix angulata. As these two taxa exemplify two major morphological categories of ophiuroid vertebrae, they provide a basis for an initial assessment of the functional consequences of these disparate vertebral morphologies. These models suggest potential differences in the structure of the intervertebral articulations in these two species, implying disparities in arm flexion mechanics. We also evaluated the differences in the range of motion between segments in the proximal and distal halves of the arm length in a specimen of O. brevispina, and found that the morphology of vertebrae in the distal portion of the arm allows for higher mobility than in the proximal portion. Our models of non-vertebral ossicles show that they rotate further in the direction of movement than the vertebrae themselves in order to accommodate arm flexion. These findings raise doubts over previous hypotheses regarding the functional consequences of ophiuroid arm disparity. Our study demonstrates the value of integrating experimental data and visualization of articulated structures when making functional interpretations instead of relying on observations of vertebral or segmental morphology alone. This methodological framework can be applied to other ophiuroid taxa to enable comparative functional analyses. It will also facilitate biomechanical analyses of other invertebrate groups to illuminate how appendage or locomotor function evolved.

The function of the ophiuroid nerve ring: how a decentralized nervous system controls coordinated locomotion

Echinoderms lack a centralized nervous control system yet each extant echinoderm class has evolved unique and effective strategies for locomotion. Brittle stars (Ophiuroidea) stride swiftly over the seafloor by coordinating motions of their five muscular arms. Their arms consist of many repeating segments, requiring them to use a complex control system to coordinate motions among segments and between arms. We conducted in vivo experiments with brittle stars to analyze the functional role of the nerve ring, which connects the nerves in each arm. These experiments were designed to determine how the ophiuroid nervous system performs complex decision-making and locomotory actions under decentralized control. Our results show that brittle star arms must be connected by the nerve ring for coordinated locomotion, but information can travel bidirectionally around the nerve ring so that it circumvents the severance. Evidence presented indicates that ophiuroids rely on adjacent nerve ring connections for sustained periodic movements. The number of arms connected via the nerve ring is correlated positively with the likelihood that the animal will show coordinated locomotion, indicating that integrated nerve ring tissue is critical for control. The results of the experiments should provide a basis for the advancement of complex artificial decentralized systems.