Dynamic Model of the Octopus Arm. I. Biomechanics of the Octopus Reaching Movement

Passive elasticity properties of Octopus rubescens arms

In this report, passive elasticity properties of Octopus rubescens arm tissue are investigated using a multidisciplinary approach encompassing biomechanical experiments, computational modeling, and analyses. Tensile tests are conducted to obtain stress-strain relationships of the arm under axial stretch. Rheological tests are also performed to probe the dynamic shear response of the arm tissue. Based on these tests, comparisons against three different viscoelasticity models are reported.

Neuronal segmentation in cephalopod arms

The prehensile arms of the cephalopod are among these animals most remarkable features, but the neural circuitry governing arm and sucker movements remains largely unknown. We studied the neuronal organization of the adult axial nerve cord (ANC) of Octopus bimaculoides with molecular and cellular methods. The ANCs, which lie in the center of every arm, are the largest neuronal structures in the octopus, containing four times as many neurons as found in the central brain. In transverse cross section, the cell body layer (CBL) of the ANC wraps around its neuropil (NP) with little apparent segregation of sensory and motor neurons or nerve exits. Strikingly, when studied in longitudinal sections, the ANC is segmented. ANC neuronal cell bodies form columns separated by septa, with 15 segments overlying each pair of suckers. The segments underlie a modular organization to the ANC neuropil: neuronal cell bodies within each segment send the bulk of their processes directly into the adjoining neuropil, with some reaching the contralateral side. In addition, some nerve processes branch upon entering the NP, forming short-range projections to neighboring segments and mid-range projections to the ANC segments of adjoining suckers. The septa between the segments are employed as ANC nerve exits and as channels for ANC vasculature. Cellular analysis establishes that adjoining septa issue nerves with distinct fiber trajectories, which across two segments (or three septa) fully innervate the arm musculature. Sucker nerves also use the septa, setting up a nerve fiber "suckerotopy" in the sucker-side of the ANC. Comparative anatomy suggests a strong link between segmentation and flexible sucker-laden arms. In the squid Doryteuthis pealeii, the arms and the sucker-rich club of the tentacles have segments, but the sucker-poor stalk of the tentacles does not. The neural modules described here provide a new template for understanding the motor control of octopus soft tissues. In addition, this finding represents the first demonstration of nervous system segmentation in a mollusc.

Stiffness Change for Reconfiguration of Inflated Beam Robots

Abstract Active control of the shape of soft robots is challenging. Despite having an infinite number of passive degrees of freedom (DOFs), soft robots typically only have a few actively controllable DOFs, limited by the number of degrees of actuation (DOAs). The complexity of actuators restricts the number of DOAs that can be incorporated into soft robots. Active shape control is further complicated by the buckling of soft robots under compressive forces; this is particularly challenging for compliant continuum robots due to their long aspect ratios. In this study, we show how variable stiffness enables shape control of soft robots by addressing these challenges. Dynamically changing the stiffness of sections along a compliant continuum robot selectively "activates" discrete joints. By changing which joints are activated, the output of a single actuator can be reconfigured to actively control many different joints, thus decoupling the number of controllable DOFs from the number of DOAs. We demonstrate embedded positive pressure layer jamming as a simple method for stiffness change in inflated beam robots, its compatibility with growing robots, and its use as an "activating" technology. We experimentally characterize the stiffness change in a growing inflated beam robot and present finite element models that serve as guides for robot design and fabrication. We fabricate a multisegment everting inflated beam robot and demonstrate how stiffness change is compatible with growth through tip eversion, enables an increase in workspace, and achieves new actuation patterns not possible without stiffening.

Octopus-inspired sensorized soft arm for environmental interaction

Octopuses can whip their soft arms with a characteristic "bend propagation" motion to capture prey with sensitive suckers. This relatively simple strategy provides models for robotic grasping, controllable with a small number of inputs, and a highly deformable arm with sensing capabilities. Here, we implemented an electronics-integrated soft octopus arm (E-SOAM) capable of reaching, sensing, grasping, and interacting in a large domain. On the basis of the biological bend propagation of octopuses, E-SOAM uses a bending-elongation propagation model to move, reach, and grasp in a simple but efficient way. E-SOAM's distal part plays the role of a gripper and can process bending, suction, and temperature sensory information under highly deformed working states by integrating a stretchable, liquid-metal-based electronic circuit that can withstand uniaxial stretching of 710% and biaxial stretching of 270% to autonomously perform tasks in a confined environment. By combining this sensorized distal part with a soft arm, the E-SOAM can perform a reaching-grasping-withdrawing motion across a range up to 1.5 times its original arm length, similar to the biological counterpart. Through a wearable finger glove that produces suction sensations, a human can use just one finger to remotely and interactively control the robot's in-plane and out-of-plane reaching and grasping both in air and underwater. E-SOAM's results not only contribute to our understanding of the function of the motion of an octopus arm but also provide design insights into creating stretchable electronics-integrated bioinspired autonomous systems that can interact with humans and their environments.

Mechanisms of octopus arm search behavior without visual feedback

The octopus coordinates multiple, highly flexible arms with the support of a complex distributed nervous system. The octopus's suckers, staggered along each arm, are employed in a wide range of behaviors. Many of these behaviors, such as foraging in visually occluded spaces, are executed under conditions of limited or absent visual feedback. In coordinating unseen limbs with seemingly infinite degrees of freedom across a variety of adaptive behaviors, the octopus appears to have solved a significant control problem facing the field of soft-bodied robotics. To study the strategies that the octopus uses to find and capture prey within unseen spaces, we designed and 3D printed visually occluded foraging tasks and tracked arm motion as the octopus attempted to find and retrieve a food reward. By varying the location of the food reward within these tasks, we can characterize how the arms and suckers adapt to their environment to find and capture prey. We compared these results to simulated experimental conditions performed by a model octopus arm to isolate the primary mechanisms driving our experimental observations. We found that the octopus relies on a contact-based search strategy that emerges from local sucker coordination to simplify the control of its soft, highly flexible limbs.

Biomechanics, motor control and dynamic models of the soft limbs of the octopus and other cephalopods

Muscular hydrostats are organs composed entirely of packed arrays of incompressible muscles and lacking any skeletal support. Found in both vertebrates and invertebrates, they are of great interest for comparative biomechanics from engineering and evolutionary perspectives. The arms of cephalopods (e.g. octopus and squid) are particularly interesting muscular hydrostats because of their flexibility and ability to generate complex behaviors exploiting elaborate nervous systems. Several lines of evidence from octopus studies point to the use of both brain and arm-embedded motor control strategies that have evolved to simplify the complexities associated with the control of flexible and hyper-redundant limbs and bodies. Here, we review earlier and more recent experimental studies on octopus arm biomechanics and neural motor control. We review several dynamic models used to predict the kinematic characteristics of several basic motion primitives, noting the shortcomings of the current models in accounting for behavioral observations. We also discuss the significance of impedance (stiffness and viscosity) in controlling the octopus's motor behavior. These factors are considered in light of several new models of muscle biomechanics that could be used in future research to gain a better understanding of motor control in the octopus. There is also a need for updated models that encompass stiffness and viscosity for designing and controlling soft robotic arms. The field of soft robotics has boomed over the past 15 years and would benefit significantly from further progress in biomechanical and motor control studies on octopus and other muscular hydrostats.

Energy-shaping control of a muscular octopus arm moving in three dimensions

Flexible octopus arms exhibit an exceptional ability to coordinate large numbers of degrees of freedom and perform complex manipulation tasks. As a consequence, these systems continue to attract the attention of biologists and roboticists alike. In this article, we develop a three-dimensional model of a soft octopus arm, equipped with biomechanically realistic muscle actuation. Internal forces and couples exerted by all major muscle groups are considered. An energy-shaping control method is described to coordinate muscle activity so as to grasp and reach in three-dimensional space. Key contributions of this article are as follows: (i) modelling of major muscle groups to elicit three-dimensional movements; (ii) a mathematical formulation for muscle activations based on a stored energy function; and (iii) a computationally efficient procedure to design task-specific equilibrium configurations, obtained by solving an optimization problem in the Special Euclidean group SE ( 3 ) . Muscle controls are then iteratively computed based on the co-state variable arising from the solution of the optimization problem. The approach is numerically demonstrated in the physically accurate software environment Elastica . Results of numerical experiments mimicking observed octopus behaviours are reported.

Digital light processing of liquid crystal elastomers for self-sensing artificial muscles

Artificial muscles based on stimuli-responsive polymers usually exhibit mechanical compliance, versatility, and high power-to-weight ratio, showing great promise to potentially replace conventional rigid motors for next-generation soft robots, wearable electronics, and biomedical devices. In particular, thermomechanical liquid crystal elastomers (LCEs) constitute artificial muscle-like actuators that can be remotely triggered for large stroke, fast response, and highly repeatable actuations. Here, we introduce a digital light processing (DLP)-based additive manufacturing approach that automatically shear aligns mesogenic oligomers, layer-by-layer, to achieve high orientational order in the photocrosslinked structures; this ordering yields high specific work capacity (63 J kg^-1) and energy density (0.18 MJ m^-3). We demonstrate actuators composed of these DLP printed LCEs' applications in soft robotics, such as reversible grasping, untethered crawling, and weightlifting. Furthermore, we present an LCE self-sensing system that exploits thermally induced optical transition as an intrinsic option toward feedback control.

Shape Changing Robots: Bioinspiration, Simulation, and Physical Realization

One of the key differentiators between biological and artificial systems is the dynamic plasticity of living tissues, enabling adaptation to different environmental conditions, tasks, or damage by reconfiguring physical structure and behavioral control policies. Lack of dynamic plasticity is a significant limitation for artificial systems that must robustly operate in the natural world. Recently, researchers have begun to leverage insights from regenerating and metamorphosing organisms, designing robots capable of editing their own structure to more efficiently perform tasks under changing demands and creating new algorithms to control these changing anatomies. Here, an overview of the literature related to robots that change shape to enhance and expand their functionality is presented. Related grand challenges, including shape sensing, finding, and changing, which rely on innovations in multifunctional materials, distributed actuation and sensing, and somatic control to enable next-generation shape changing robots are also discussed.

Octopus arms exhibit exceptional flexibility

The octopus arm is often referred to as one of the most flexible limbs in nature, yet this assumption requires detailed inspection given that this has not been measured comprehensively for all portions of each arm. We investigated the diversity of arm deformations in Octopus bimaculoides with a frame-by-frame observational analysis of laboratory video footage in which animals were challenged with different tasks. Diverse movements in these hydrostatic arms are produced by some combination of four basic deformations: bending (orally, aborally; inward, outward), torsion (clockwise, counter-clockwise), elongation, and shortening. More than 16,500 arm deformations were observed in 120 min of video. Results showed that all eight arms were capable of all four types of deformation along their lengths and in all directions. Arms function primarily to bring the sucker-lined oral surface in contact with target surfaces. Bending was the most common deformation observed, although the proximal third of the arms performed relatively less bending and more shortening and elongation as compared with other arm regions. These findings demonstrate the exceptional flexibility of the octopus arm and provide a basis for investigating motor control of the entire arm, which may aid the future development of soft robotics.

Model-free motion control of continuum robots based on a zeroing neurodynamic approach

As a result of inherent flexibility and structural compliance, continuum robots have great potential in practical applications and are attracting more and more attentions. However, these characteristics make it difficult to acquire the accurate kinematics of continuum robots due to uncertainties, deformation and external loads. This paper introduces a method based on a zeroing neurodynamic approach to solve the trajectory tracking problem of continuum robots. The proposed method can achieve the control of a bellows-driven continuum robot just relying on the actuator input and sensory output information, without knowing any information of the kinematic model. This approach reduces the computational load and can guarantee the real time control. The convergence, stability, and robustness of the proposed approach are proved by theoretical analyses. The effectiveness of the proposed method is verified by simulation studies including tracking performance, comparisons with other three methods, and robustness tests.

The control of nocifensive movements in the caterpillar Manduca sexta

In response to a noxious stimulus on the abdomen, caterpillars lunge their head towards the site of stimulation. This nocifensive 'strike' behavior is fast (∼0.5 s duration), targeted and usually unilateral. It is not clear how the fast strike movement is generated and controlled, because caterpillar muscle develops peak force relatively slowly (∼1 s) and the baseline hemolymph pressure is low (<2 kPa). Here, we show that strike movements are largely driven by ipsilateral muscle activation that propagates from anterior to posterior segments. There is no sustained pre-strike muscle activation that would be expected for movements powered by the rapid release of stored elastic energy. Although muscle activation on the ipsilateral side is correlated with segment shortening, activity on the contralateral side consists of two phases of muscle stimulation and a marked decline between them. This decrease in motor activity precedes rapid expansion of the segment on the contralateral side, presumably allowing the body wall to stretch more easily. The subsequent increase in contralateral motor activation may slow or stabilize movements as the head reaches its target. Strike behavior is therefore a controlled fast movement involving the coordination of muscle activity on each side and along the length of the body.

OctoPartenopin: Identification and Preliminary Characterization of a Novel Antimicrobial Peptide from the Suckers of Octopus vulgaris

Microorganism resistance to conventional antibiotics represents one of the major global health concerns. This paper focuses on a peptide (OctoPartenopin) extracted from suckers of Octopus vulgaris; bioassay-guided chromatographic fractionation was used to identify this sequence, which holds significant antibacterial activity against Gram-positive and Gram-negative bacteria. OctoPartenopin is encrypted within the calponin sequence and was associated with the high levels of proteolytic activity already reported in octopus arm suckers. We synthesized the parent peptide and four analogues; all peptide were tested for their antibacterial and antibiofilm activities. Preliminary antibiofilm experiments showed that that one of the analogues had the best activity in both inhibition and eradication of biofilm of all three microorganisms tested. The occurrence of OctoPartenopin in arm suckers provided novel speculative information on animal behavior, as concerns maternal care of fertilized eggs. Our results highlight that suckers are a rich source of multifaceted peptides to develop alternative antimicrobial agents and food preservatives.

A review on recent advances in soft surgical robots for endoscopic applications

BACKGROUND

Soft materials, with their compliant properties, enable conformity and safe interaction with human body. With the advance in actuation and sensing of soft materials, new paradigm in robotics called "soft robotics" emerges. Soft robotics has become a new approach in designing medical devices such as wearable robotic gloves and exoskeleton. However, application of soft robotics in surgical instrument inside human body is still in its infancy.

AIMS

In this paper, current application and design of soft robots specifically applied for endoscopy are reviewed.

MATERIALS & METHODS

Different aspects in the implementation of soft robotics in endoscope design were reviewed. The key studies about MIS and NOTES were reviewed to establish the clinical background and extract the limitations of current endoscopic device in the last decade.

RESULTS AND DISCUSSION

In this review study, the implementation of soft robotics concepts in endoscopic application, with highlights on different features of several soft endoscopes, were evaluated. The progress in different aspects of soft robotics endoscope, current state, and future perspectives were also discussed.

CONCLUSION

Based on the survey on the structural specification, actuation, sensing, and stiffening the future soft surgical endoscopes are recommended to fulfil the following specifications: safe especially from pressure leakage, fully biocompatible materials, MR-compatible, capable for large bending in at least two antagonistic directions, modularity, adjustable stiffness.

From synaptic input to muscle contraction: arm muscle cells of Octopus vulgaris show unique neuromuscular junction and excitation-contraction coupling properties

The muscular-hydrostat configuration of octopus arms allows high manoeuvrability together with the efficient motor performance necessary for its multitasking abilities. To control this flexible and hyper-redundant system the octopus has evolved unique strategies at the various levels of its brain-to-body organization. We focus here on the arm neuromuscular junction (NMJ) and excitation-contraction (E-C) properties of the arm muscle cells. We show that muscle cells are cholinergically innervated at single eye-shaped locations where acetylcholine receptors (AChR) are concentrated, resembling the vertebrate neuromuscular endplates. Na⁺ and K⁺ contribute nearly equally to the ACh-activated synaptic current mediating membrane depolarization, thereby activating voltage-dependent L-type Ca²⁺ channels. We show that cell contraction can be mediated directly by the inward Ca²⁺ current and also indirectly by calcium-induced calcium release (CICR) from internal stores. Indeed, caffeine-induced cell contraction and immunohistochemical staining revealed the presence and close association of dihydropyridine (DHPR) and ryanodine (RyR) receptor complexes, which probably mediate the CICR. We suggest that the dynamics of octopus arm contraction can be controlled in two ways; motoneurons with large synaptic inputs activate vigorous contraction via activation of the two routs of Ca²⁺ induced contraction, while motoneurons with lower-amplitude inputs may regulate a graded contraction through frequency-dependent summation of EPSP trains that recruit the CICR. Our results thus suggest that these motoneuronal pools are likely to be involved in the activation of different E-C coupling modes, thus enabling a dynamics of muscles activation appropriate for various tasks such as stiffening versus motion generation.

Motion Simulation of Ionic Liquid Gel Soft Actuators Based on CPG Control

The ionic liquid gel (ILG), a new type of soft actuator material, is a mixture of 1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF₄), hydroxyethyl methacrylate (HEMA), diethoxyacetophenone (DEAP), and ZrO₂ polymerized into a gel state under ultraviolet (UV) light irradiation. The soft actuator structure consists of a layer of ionic liquid polymer gel sandwiched between two layers of activated carbon capped with gold foil. The volume of the cationic BMIM⁺ in the ionic liquid BMIMBF₄ is much larger than that of the anionic BF₄ ^-. When voltages are applied to both sides of the actuator, the anions and cations move toward the anode and cathode of the electrode, respectively, under the electric field. The volume of the ILG cathode side therefore expands, and the volume of the ILG anode side shrinks, hence bending the entire actuator toward the anode side. The Ogden model was selected as the hyperelastic constitutive model to study the mechanical properties of the ILG by nonlinear analysis. As the ILG is an ideal material for the preparation of a supercapacitor, the equivalent circuit of the ILG can be modeled by the supercapacitor theory to identify the transfer function of the soft actuator. The central pattern generator (CPG) control is widely used in the area of biology, and CPGs based on bioinspired control methods have attracted great attention from researchers worldwide. After the continuum soft actuator is discretized, the CPG-based bioinspired method can be used to control the soft robot drivers. According to the simulation analysis results, the soft actuator can be smooth enough to reach the specified location.

Motor control pathways in the nervous system of Octopus vulgaris arm

The octopus’s arms have virtually infinite degrees of freedom, providing a unique opportunity for studying movement control in a redundant motor system. Here, we investigated the organization of the connections between the brain and arms through the cerebrobrachial tracts (CBT). To do this, we analyzed the neuronal activity associated with the contraction of a small muscle strand left connected at the middle of a long isolated CBT. Both electrical activity in the CBT and muscle contraction could be induced at low threshold values irrespective of stimulus direction and distance from the muscle strand. This suggests that axons associated with transmitting motor commands run along the CBT and innervate a large pool of motor neurons en passant. This type of innervation implies that central and peripheral motor commands involve the simultaneous recruitment of large groups of motor neurons along the arm as required, for example, in arm stiffening, and that the site of movement initiation along the arm may be determined through a unique interplay between global central commands and local sensory signals.

Deep Reinforcement Learning for Soft, Flexible Robots: Brief Review with Impending Challenges

The increasing trend of studying the innate softness of robotic structures and amalgamating it with the benefits of the extensive developments in the field of embodied intelligence has led to the sprouting of a relatively new yet rewarding sphere of technology in intelligent soft robotics. The fusion of deep reinforcement algorithms with soft bio-inspired structures positively directs to a fruitful prospect of designing completely self-sufficient agents that are capable of learning from observations collected from their environment. For soft robotic structures possessing countless degrees of freedom, it is at times not convenient to formulate mathematical models necessary for training a deep reinforcement learning (DRL) agent. Deploying current imitation learning algorithms on soft robotic systems has provided competent results. This review article posits an overview of various such algorithms along with instances of being applied to real-world scenarios, yielding frontier results. Brief descriptions highlight the various pristine branches of DRL research in soft robotics.

Sense and Insensibility - An Appraisal of the Effects of Clinical Anesthetics on Gastropod and Cephalopod Molluscs as a Step to Improved Welfare of Cephalopods

Recent progress in animal welfare legislation stresses the need to treat cephalopod molluscs, such as Octopus vulgaris, humanely, to have regard for their wellbeing and to reduce their pain and suffering resulting from experimental procedures. Thus, appropriate measures for their sedation and analgesia are being introduced. Clinical anesthetics are renowned for their ability to produce unconsciousness in vertebrate species, but their exact mechanisms of action still elude investigators. In vertebrates it can prove difficult to specify the differences of response of particular neuron types given the multiplicity of neurons in the CNS. However, gastropod molluscs such as Aplysia, Lymnaea, or Helix, with their large uniquely identifiable nerve cells, make studies on the cellular, subcellular, network and behavioral actions of anesthetics much more feasible, particularly as identified cells may also be studied in culture, isolated from the rest of the nervous system. To date, the sorts of study outlined above have never been performed on cephalopods in the same way as on gastropods. However, criteria previously applied to gastropods and vertebrates have proved successful in developing a method for humanely anesthetizing Octopus with clinical doses of isoflurane, i.e., changes in respiratory rate, color pattern and withdrawal responses. However, in the long term, further refinements will be needed, including recordings from the CNS of intact animals in the presence of a variety of different anesthetic agents and their adjuvants. Clues as to their likely responsiveness to other appropriate anesthetic agents and muscle relaxants can be gained from background studies on gastropods such as Lymnaea, given their evolutionary history.

The tongue as a gripper

Frogs, chameleons and anteaters are striking examples of animals that can grab food using only their tongue. How does the soft and wet surface of a tongue grip onto objects before they are ingested? Here, we review the diversity of tongue projection methods, tongue roughnesses and tongue coatings, our goal being to highlight conditions for effective grip and mobility. A softer tongue can reach farther: the frog Rana pipiens tongue is 10 times softer than the human tongue and can extend to 130% of its length when propelled in a whip-like motion. Roughness can improve a tongue's grip: the spikes on a penguin Eudyptes chrysolophus tongue can be as large as fingernails, and help the penguin swallow fish. The saliva coating on the tongue, a non-Newtonian biofluid, can either lubricate or adhere to food. Frog saliva is 175 times more viscous than human saliva, adhering the tongue to slippery, furry or feathery food. We pay particular attention to using mathematical models such as the theory of capillarity, elasticity and friction to elucidate the parameters for effective tongue use across a variety of vertebrate species. Finally, we postulate how the use of wet and rough surfaces to simultaneously sense and grip may inspire new strategies in emerging technologies such as soft robots.

The Natural-CCD Algorithm, a Novel Method to Solve the Inverse Kinematics of Hyper-redundant and Soft Robots

This article presents a new method to solve the inverse kinematics problem of hyper-redundant and soft manipulators. From an engineering perspective, this kind of robots are underdetermined systems. Therefore, they exhibit an infinite number of solutions for the inverse kinematics problem, and to choose the best one can be a great challenge. A new algorithm based on the cyclic coordinate descent (CCD) and named as natural-CCD is proposed to solve this issue. It takes its name as a result of generating very harmonious robot movements and trajectories that also appear in nature, such as the golden spiral. In addition, it has been applied to perform continuous trajectories, to develop whole-body movements, to analyze motion planning in complex environments, and to study fault tolerance, even for both prismatic and rotational joints. The proposed algorithm is very simple, precise, and computationally efficient. It works for robots either in two or three spatial dimensions and handles a large amount of degrees-of-freedom. Because of this, it is aimed to break down barriers between discrete hyper-redundant and continuum soft robots.

Nonparametric Online Learning Control for Soft Continuum Robot: An Enabling Technique for Effective Endoscopic Navigation

Bioinspired robotic structures comprising soft actuation units have attracted increasing research interest. Taking advantage of its inherent compliance, soft robots can assure safe interaction with external environments, provided that precise and effective manipulation could be achieved. Endoscopy is a typical application. However, previous model-based control approaches often require simplified geometric assumptions on the soft manipulator, but which could be very inaccurate in the presence of unmodeled external interaction forces. In this study, we propose a generic control framework based on nonparametric and online, as well as local, training to learn the inverse model directly, without prior knowledge of the robot's structural parameters. Detailed experimental evaluation was conducted on a soft robot prototype with control redundancy, performing trajectory tracking in dynamically constrained environments. Advanced element formulation of finite element analysis is employed to initialize the control policy, hence eliminating the need for random exploration in the robot's workspace. The proposed control framework enabled a soft fluid-driven continuum robot to follow a 3D trajectory precisely, even under dynamic external disturbance. Such enhanced control accuracy and adaptability would facilitate effective endoscopic navigation in complex and changing environments.

Molecular Determinants of Cephalopod Muscles and Their Implication in Muscle Regeneration

The ability to regenerate whole-body structures has been studied for many decades and is of particular interest for stem cell research due to its therapeutic potential. Several vertebrate and invertebrate species have been used as model systems to study pathways involved in regeneration in the past. Among invertebrates, cephalopods are considered as highly evolved organisms, which exhibit elaborate behavioral characteristics when compared to other mollusks including active predation, extraordinary manipulation, and learning abilities. These are enabled by a complex nervous system and a number of adaptations of their body plan, which were acquired over evolutionary time. Some of these novel features show similarities to structures present in vertebrates and seem to have evolved through a convergent evolutionary process. Octopus vulgaris (the common octopus) is a representative of modern cephalopods and is characterized by a sophisticated motor and sensory system as well as highly developed cognitive capabilities. Due to its phylogenetic position and its high regenerative power the octopus has become of increasing interest for studies on regenerative processes. In this paper we provide an overview over the current knowledge of cephalopod muscle types and structures and present a possible link between these characteristics and their high regenerative potential. This may help identify conserved molecular pathways underlying regeneration in invertebrate and vertebrate animal species as well as discover new leads for targeted tissue treatments in humans.

The Musculature of Coleoid Cephalopod Arms and Tentacles

The regeneration of coleoid cephalopod arms and tentacles is a common occurrence, recognized since Aristotle. The complexity of the arrangement of the muscle and connective tissues of these appendages make them of great interest for research on regeneration. They lack rigid skeletal elements and consist of a three-dimensional array of muscle fibers, relying on a type of skeletal support system called a muscular hydrostat. Support and movement in the arms and tentacles depends on the fact that muscle tissue resists volume change. The basic principle of function is straightforward; because the volume of the appendage is essentially constant, a decrease in one dimension must result in an increase in another dimension. Since the muscle fibers are arranged in three mutually perpendicular directions, all three dimensions can be actively controlled and thus a remarkable diversity of movements and deformations can be produced. In the arms and tentacles of coleoids, three main muscle orientations are observed: (1) transverse muscle fibers arranged in planes perpendicular to the longitudinal axis; (2) longitudinal muscle fibers typically arranged in bundles parallel to the longitudinal axis; and (3) helical or obliquely arranged layers of muscle fibers, arranged in both right- and left-handed helixes. By selective activation of these muscle groups, elongation, shortening, bending, torsion and stiffening of the appendage can be produced. The predominant muscle fiber type is obliquely striated. Cross-striated fibers are found only in the transverse muscle mass of the prey capture tentacles of squid and cuttlefish. These fibers have unusually short myofilaments and sarcomeres, generating the high shortening velocity required for rapid elongation of the tentacles. It is likely that coleoid cephalopods use ultrastructural modifications rather than tissue-specific myosin isoforms to tune contraction velocities.

Coupling relationship between the central pattern generator and the cerebral cortex with time delay

Brain activity is a cooperative process among neurons and involves the coupling relationship, which is crucial to perform operational tasks in various specialized areas of the nervous system. A finite signal transmission speed along the axons results in a space-dependent time delay. The central pattern generator (CPG) can in principle produce basic locomotor rhythm in the absence of inputs from higher brain centers and peripheral sensory feedback. To study the dynamic performance of CPG with time delay and its coupling relationship with the cerebral cortex, a new CPG model with time delay and a model of the neural mass model (NMM) and the CPG are developed. The coupling model is based on biological experimental results. Bifurcation theories and maximal Lyapunov exponent are used to analyze the dynamic performance. From the results, some CPGs are suggested to be embedded in limbs and composed of the parameters space which corresponds to the one of the cerebral cortex. This embodiment of humans can reduce the burden of the brain and simplify the control of the locomotion. The results also show that the phase diagram of the CPG cannot keep the limit cycle, and that the state of the NMM becomes increasingly chaotic as time delay increases. This finding implies that a person with slow reaction can easily lose the stability of his or her locomotion.

Octopus-inspired multi-arm robotic swimming

The outstanding locomotor and manipulation characteristics of the octopus have recently inspired the development, by our group, of multi-functional robotic swimmers, featuring both manipulation and locomotion capabilities, which could be of significant engineering interest in underwater applications. During its little-studied arm-swimming behavior, as opposed to the better known jetting via the siphon, the animal appears to generate considerable propulsive thrust and rapid acceleration, predominantly employing movements of its arms. In this work, we capture the fundamental characteristics of the corresponding complex pattern of arm motion by a sculling profile, involving a fast power stroke and a slow recovery stroke. We investigate the propulsive capabilities of a multi-arm robotic system under various swimming gaits, namely patterns of arm coordination, which achieve the generation of forward, as well as backward, propulsion and turning. A lumped-element model of the robotic swimmer, which considers arm compliance and the interaction with the aquatic environment, was used to study the characteristics of these gaits, the effect of various kinematic parameters on propulsion, and the generation of complex trajectories. This investigation focuses on relatively high-stiffness arms. Experiments employing a compliant-body robotic prototype swimmer with eight compliant arms, all made of polyurethane, inside a water tank, successfully demonstrated this novel mode of underwater propulsion. Speeds of up to 0.26 body lengths per second (approximately 100 mm s(-1)), and propulsive forces of up to 3.5 N were achieved, with a non-dimensional cost of transport of 1.42 with all eight arms and of 0.9 with only two active arms. The experiments confirmed the computational results and verified the multi-arm maneuverability and simultaneous object grasping capability of such systems.

Arm coordination in octopus crawling involves unique motor control strategies

To cope with the exceptional computational complexity that is involved in the control of its hyper-redundant arms [1], the octopus has adopted unique motor control strategies in which the central brain activates rather autonomous motor programs in the elaborated peripheral nervous system of the arms [2, 3]. How octopuses coordinate their eight long and flexible arms in locomotion is still unknown. Here, we present the first detailed kinematic analysis of octopus arm coordination in crawling. The results are surprising in several respects: (1) despite its bilaterally symmetrical body, the octopus can crawl in any direction relative to its body orientation; (2) body and crawling orientation are monotonically and independently controlled; and (3) contrasting known animal locomotion, octopus crawling lacks any apparent rhythmical patterns in limb coordination, suggesting a unique non-rhythmical output of the octopus central controller. We show that this uncommon maneuverability is derived from the radial symmetry of the arms around the body and the simple pushing-by-elongation mechanism by which the arms create the crawling thrust. These two together enable a mechanism whereby the central controller chooses in a moment-to-moment fashion which arms to recruit for pushing the body in an instantaneous direction. Our findings suggest that the soft molluscan body has affected in an embodied way [4, 5] the emergence of the adaptive motor behavior of the octopus.

Conformational Modeling of Continuum Structures in Robotics and Structural Biology: A Review

Hyper-redundant (or snakelike) manipulators have many more degrees of freedom than are required to position and orient an object in space. They have been employed in a variety of applications ranging from search-and-rescue to minimally invasive surgical procedures, and recently they even have been proposed as solutions to problems in maintaining civil infrastructure and the repair of satellites. The kinematic and dynamic properties of snakelike robots are captured naturally using a continuum backbone curve equipped with a naturally evolving set of reference frames, stiffness properties, and mass density. When the snakelike robot has a continuum architecture, the backbone curve corresponds with the physical device itself. Interestingly, these same modeling ideas can be used to describe conformational shapes of DNA molecules and filamentous protein structures in solution and in cells. This paper reviews several classes of snakelike robots: (1) hyper-redundant manipulators guided by backbone curves; (2) flexible steerable needles; and (3) concentric tube continuum robots. It is then shown how the same mathematical modeling methods used in these robotics contexts can be used to model molecules such as DNA. All of these problems are treated in the context of a common mathematical framework based on the differential geometry of curves, continuum mechanics, and variational calculus. Both coordinate-dependent Euler-Lagrange formulations and coordinate-free Euler-Poincaré approaches are reviewed.

Simulation of Octopus Arm Based on Coupled CPGs

The octopus arm has attracted many researchers’ interests and became a research hot spot because of its amazing features. Several dynamic models inspired by an octopus arm are presented to realize the structure with a large number of degrees of freedom. The octopus arm is made of a soft material introducing high-dimensionality, nonlinearity, and elasticity, which makes the octopus arm difficult to control. In this paper, three coupled central pattern generators (CPGs) are built and a 2-dimensional dynamic model of the octopus arm is presented to explore possible strategies of the octopus movement control. And the CPGs’ signals treated as activation are added on the ventral, dorsal, and transversal sides, respectively. The effects of the octopus arm are discussed when the parameters of the CPGs are changed. Simulations show that the octopus arm movements are mainly determined by the shapes of three CPGs’ phase diagrams. Therefore, some locomotion modes are supposed to be embedded in the neuromuscular system of the octopus arm. And the octopus arm movements can be achieved by modulating the parameters of the CPGs. The results are beneficial for researchers to understand the octopus movement further.

Design, modeling and control of a pneumatically actuated manipulator inspired by biological continuum structures

Biological tentacles, such as octopus arms, have entirely flexible structures and virtually infinite degrees of freedom (DOF) that allow for elongation, shortening and bending at any point along the arm length. The amazing dexterity of biological tentacles has driven the growing implementation of continuum manipulators in robotic systems. This paper presents a pneumatic manipulator inspired by biological continuum structures in some of their key features and functions, such as continuum morphology, intrinsic compliance and stereotyped motions with hyper redundant DOF. The kinematics and dynamics of the manipulator are formulated and identified, and a hierarchical controller taking inspiration from the structure of an octopus nervous system is used to relate desired stereotyped motions to individual actuator inputs. Simulations and experiments are carried out to validate the model and prototype where good agreement was found between the two.

Arm regeneration in two species of cuttlefish Sepia officinalis and Sepia pharaonis

To provide quantitative information on arm regeneration in cuttlefish, the regenerating arms of two cuttlefish species, Sepia officinalis and Sepia pharaonis, were observed at regular intervals after surgical amputation. The third right arm of each individual was amputated to ~10-20 % starting length. Arm length, suction cup number, presence of chromatophores, and behavioral measures were collected every 2-3 days over a 39-day period and compared to the contralateral control arm. By day 39, the regenerating arm reached a mean 95.5 ± 0.3 % of the control for S. officinalis and 94.9 ± 1.3 % for S. pharaonis. The process of regeneration was divided into five separate stages based on macroscopic morphological events: Stage I (days 0-3 was marked by a frayed leading edge; Stage II (days 4-15) by a smooth hemispherical leading edge; Stage III (days 16-20) by the appearance of a growth bud; Stage IV (days 21-24) by the emergence of an elongated tip; and Stage V (days 25-39) by a tapering of the elongated tip matching the other intact arms. Behavioral deficiencies in swimming, body postures during social communication, and food manipulation were observed immediately after arm amputation and throughout Stages I and II, returning to normal by Stage III. New chromatophores and suction cups in the regenerating arm were observed as early as Stage II and by Stage IV suction cup number equaled that of control arms. New chromatophores were used in the generation of complex body patterns by Stage V. These results show that both species of cuttlefish are capable of fully regenerating lost arms, that the regeneration process is predictable and consistent within and across species, and provide the first quantified data on the rate of arm lengthening and suction cup addition during regeneration.

Incremental learning of skill collections based on intrinsic motivation

Life-long learning of reusable, versatile skills is a key prerequisite for embodied agents that act in a complex, dynamic environment and are faced with different tasks over their lifetime. We address the question of how an agent can learn useful skills efficiently during a developmental period, i.e., when no task is imposed on him and no external reward signal is provided. Learning of skills in a developmental period needs to be incremental and self-motivated. We propose a new incremental, task-independent skill discovery approach that is suited for continuous domains. Furthermore, the agent learns specific skills based on intrinsic motivation mechanisms that determine on which skills learning is focused at a given point in time. We evaluate the approach in a reinforcement learning setup in two continuous domains with complex dynamics. We show that an intrinsically motivated, skill learning agent outperforms an agent which learns task solutions from scratch. Furthermore, we compare different intrinsic motivation mechanisms and how efficiently they make use of the agent's developmental period.

A soft body as a reservoir: case studies in a dynamic model of octopus-inspired soft robotic arm

The behaviors of the animals or embodied agents are characterized by the dynamic coupling between the brain, the body, and the environment. This implies that control, which is conventionally thought to be handled by the brain or a controller, can partially be outsourced to the physical body and the interaction with the environment. This idea has been demonstrated in a number of recently constructed robots, in particular from the field of “soft robotics”. Soft robots are made of a soft material introducing high-dimensionality, non-linearity, and elasticity, which often makes the robots difficult to control. Biological systems such as the octopus are mastering their complex bodies in highly sophisticated manners by capitalizing on their body dynamics. We will demonstrate that the structure of the octopus arm cannot only be exploited for generating behavior but also, in a sense, as a computational resource. By using a soft robotic arm inspired by the octopus we show in a number of experiments how control is partially incorporated into the physical arm's dynamics and how the arm's dynamics can be exploited to approximate non-linear dynamical systems and embed non-linear limit cycles. Future application scenarios as well as the implications of the results for the octopus biology are also discussed.

Kinematic decomposition and classification of octopus arm movements

The octopus arm is a muscular hydrostat and due to its deformable and highly flexible structure it is capable of a rich repertoire of motor behaviors. Its motor control system uses planning principles and control strategies unique to muscular hydrostats. We previously reconstructed a data set of octopus arm movements from records of natural movements using a sequence of 3D curves describing the virtual backbone of arm configurations. Here we describe a novel representation of octopus arm movements in which a movement is characterized by a pair of surfaces that represent the curvature and torsion values of points along the arm as a function of time. This representation allowed us to explore whether the movements are built up of elementary kinematic units by decomposing each surface into a weighted combination of 2D Gaussian functions. The resulting Gaussian functions can be considered as motion primitives at the kinematic level of octopus arm movements. These can be used to examine underlying principles of movement generation. Here we used combination of such kinematic primitives to decompose different octopus arm movements and characterize several movement prototypes according to their composition. The representation and methodology can be applied to the movement of any organ which can be modeled by means of a continuous 3D curve.