Gait and speed selection in slender inertial swimmers

BCL2L13 at endoplasmic reticulum-mitochondria contact sites regulates calcium homeostasis to maintain skeletal muscle function

The physical connection between mitochondria and endoplasmic reticulum (ER) is an essential signaling hub to ensure organelle and cellular functions. In skeletal muscle, ER-mitochondria calcium (Ca2+) signaling is crucial to maintain cellular homeostasis during physical activity. High expression of BCL2L13, a member of the BCL-2 family, was suggested as an adaptive response in endurance-trained human subjects. In adult zebrafish, we found that the loss of Bcl2l13 impairs skeletal muscle structure and function. Ca2+ signaling is altered in Bcl2l13 knockout animals and mitochondrial complexes activity is decreased. Organelle fractioning in mammalian cells shows BCL2L13 at mitochondria, ER, and mitochondria-associated membranes. ER-mitochondria contact sites number is not modified by BCL2L13 modulation, but knockdown of BCL2L13 in C2C12 cells changes cytosolic Ca2+ release and mitochondrial Ca2+ uptake. This suggests that BCL2L13 interaction with mitochondria and ER, and its role in Ca2+ signaling, contributes to proper skeletal muscle function.

Form and function of anguilliform swimming

Anguilliform swimmers are long and narrow animals that propel themselves by undulating their bodies. Observations in nature and recent investigations suggest that anguilliform swimming is highly efficient. However, understanding the underlying reasons for the efficiency of this type of locomotion requires interdisciplinary studies spanning from biology to hydrodynamics. Regrettably, these different fields are rarely discussed together, which hinders our ability to understand the repeated evolution of this swimming mode in vertebrates. This review compiles the current knowledge of the anatomical features that drive anguilliform swimming, compares the resulting kinematics across a wide range of anguilliform swimmers, and describes the resulting hydrodynamic interactions using data from both in vivo experiments and computational studies.

Robot motor learning shows emergence of frequency-modulated, robust swimming with an invariant Strouhal number

Fish locomotion emerges from diverse interactions among deformable structures, surrounding fluids and neuromuscular activations, i.e. fluid-structure interactions (FSI) controlled by fish's motor systems. Previous studies suggested that such motor-controlled FSI may possess embodied traits. However, their implications in motor learning, neuromuscular control, gait generation, and swimming performance remain to be uncovered. Using robot models, we studied the embodied traits in fish-inspired swimming. We developed modular robots with various designs and used central pattern generators (CPGs) to control the torque acting on robot body. We used reinforcement learning to learn CPG parameters for maximizing the swimming speed. The results showed that motor frequency converged faster than other parameters, and the emergent swimming gaits were robust against disruptions applied to motor control. For all robots and frequencies tested, swimming speed was proportional to the mean undulation velocity of body and caudal-fin combined, yielding an invariant, undulation-based Strouhal number. The Strouhal number also revealed two fundamental classes of undulatory swimming in both biological and robotic fishes. The robot actuators were also demonstrated to function as motors, virtual springs and virtual masses. These results provide novel insights in understanding fish-inspired locomotion.

Mechanical intelligence simplifies control in terrestrial limbless locomotion

Limbless locomotors, from microscopic worms to macroscopic snakes, traverse complex, heterogeneous natural environments typically using undulatory body wave propagation. Theoretical and robophysical models typically emphasize body kinematics and active neural/electronic control. However, we contend that because such approaches often neglect the role of passive, mechanically controlled processes (those involving "mechanical intelligence"), they fail to reproduce the performance of even the simplest organisms. To uncover principles of how mechanical intelligence aids limbless locomotion in heterogeneous terradynamic regimes, here we conduct a comparative study of locomotion in a model of heterogeneous terrain (lattices of rigid posts). We used a model biological system, the highly studied nematode worm Caenorhabditis elegans, and a robophysical device whose bilateral actuator morphology models that of limbless organisms across scales. The robot's kinematics quantitatively reproduced the performance of the nematodes with purely open-loop control; mechanical intelligence simplified control of obstacle navigation and exploitation by reducing the need for active sensing and feedback. An active behavior observed in C. elegans, undulatory wave reversal upon head collisions, robustified locomotion via exploitation of the systems' mechanical intelligence. Our study provides insights into how neurally simple limbless organisms like nematodes can leverage mechanical intelligence via appropriately tuned bilateral actuation to locomote in complex environments. These principles likely apply to neurally more sophisticated organisms and also provide a design and control paradigm for limbless robots for applications like search and rescue and planetary exploration.

Design of mechanosensory feedback during undulatory locomotion to enhance speed and stability

Undulatory locomotion relies on the propagation of a wave of excitation in the spinal cord leading to consequential activation of segmental skeletal muscles along the body. Although this process relies on self-generated oscillations of motor circuits in the spinal cord, mechanosensory feedback is crucial to entrain the underlying oscillatory activity and thereby, to enhance movement power and speed. This effect is achieved through directional projections of mechanosensory neurons either sensing stretching or compression of the trunk along the rostrocaudal axis. Different mechanosensory feedback pathways act in concert to shorten and fasten the excitatory wave propagating along the body. While inhibitory mechanosensory cells feedback inhibition on excitatory premotor interneurons and motor neurons, excitatory mechanosensory cells feedforward excitation to premotor excitatory interneurons. Together, diverse mechanosensory cells coordinate the activity of skeletal muscles controlling the head and tail to optimize speed and stabilize balance during fast locomotion.

Scaling the tail beat frequency and swimming speed in underwater undulatory swimming

Undulatory swimming is the predominant form of locomotion in aquatic vertebrates. A myriad of animals of different species and sizes oscillate their bodies to propel themselves in aquatic environments with swimming speed scaling as the product of the animal length by the oscillation frequency. Although frequency tuning is the primary means by which a swimmer selects its speed, there is no consensus on the mechanisms involved. In this article, we propose scaling laws for undulatory swimmers that relate oscillation frequency to length by taking into account both the biological characteristics of the muscles and the interaction of the moving swimmer with its environment. Results are supported by an extensive literature review including approximately 1200 individuals of different species, sizes and swimming environments. We highlight a crossover in size around 0.5-1 m. Below this value, the frequency can be tuned between 2-20 Hz due to biological constraints and the interplay between slow and fast muscles. Above this value, the fluid-swimmer interaction must be taken into account and the frequency is inversely proportional to the length of the animal. This approach predicts a maximum swimming speed around 5-10 m.s-1 for large swimmers, consistent with the threshold to prevent bubble cavitation.

Mechanosensory Feedback in Lamprey Swimming Models and Applications in the Field of Spinal Cord Regeneration

The central pattern generator (CPG) in anguilliform swimming has served as a model for examining the neural basis of locomotion. This system has been particularly valuable for the development of mathematical models. As our biological understanding of the neural basis of locomotion has expanded, so too have these models. Recently, there have been significant advancements in our understanding of the critical role that mechanosensory feedback plays in robust locomotion. This work has led to a push in the field of mathematical modeling to incorporate mechanosensory feedback into CPG models. In this perspective piece, we review advances in the development of these models and discuss how newer complex models can support biological investigation. We highlight lamprey spinal cord regeneration as an area that can both inform these models and benefit from them.

Dissolution-driven propulsion of floating solids

We show that unconstrained asymmetric dissolving solids floating in a fluid can move rectilinearly as a result of attached density currents which occur along their inclined surfaces. Solids in the form of boats composed of centimeter-scale sugar and salt slabs attached to a buoy are observed to move rapidly in water with speeds up to 5 mm/s determined by the inclination angle and orientation of the dissolving surfaces. While symmetric boats drift slowly, asymmetric boats are observed to accelerate rapidly along a line before reaching a terminal velocity when their drag matches the thrust generated by dissolution. By visualizing the flow around the body, we show that the boat velocity is always directed opposite to the horizontal component of the density current. We derive the thrust acting on the body from its measured kinematics and show that the propulsion mechanism is consistent with the unbalanced momentum generated by the attached density current. We obtain an analytical formula for the body speed depending on geometry and material properties and show that it captures the observed trends reasonably. Our analysis shows that the gravity current sets the scale of the body speed consistent with our observations, and we estimate that speeds can grow slowly as the cube root of the length of the inclined dissolving surface. The dynamics of dissolving solids demonstrated here applies equally well to solids undergoing phase change and may enhance the drift of melting icebergs, besides unraveling a primal strategy by which to achieve locomotion in active matter.

Inertial active Ornstein-Uhlenbeck particle in the presence of a magnetic field

We consider an inertial active Ornstein-Uhlenbeck particle in an athermal bath. The particle is charged, constrained to move in a two-dimensional harmonic trap, and a magnetic field is applied perpendicular to the plane of motion. The steady-state correlations and the mean-square displacement are studied when the particle is confined as well as when it is set free from the trap. With the help of both numerical simulation and analytical calculations, we observe that inertia plays a crucial role in the dynamics in the presence of a magnetic field. In a highly viscous medium where the inertial effects are negligible, the magnetic field has no influence on the correlated behavior of position as well as velocity. In the time asymptotic limit, the overall displacement of the confined harmonic particle gets enhanced by the presence of a magnetic field and saturates for a stronger magnetic field. On the other hand, when the particle is set free, the overall displacement gets suppressed and approaches zero when the strength of the field is very high. Interestingly, it is seen that in the time asymptotic limit, the confined harmonic particle behaves like a passive particle and becomes independent of the activity, especially in the presence of a very strong magnetic field. Similarly, for a free particle the mean-square displacement in the long time limit becomes independent of activity even for a longer persistence of noise cor- relation in the dynamics.

Hydrodynamic model of fish orientation in a channel flow

For over a century, scientists have sought to understand how fish orient against an incoming flow, even without visual and flow cues. Here, we elucidate a potential hydrodynamic mechanism of rheotaxis through the study of the bidirectional coupling between fish and the surrounding fluid. By modeling a fish as a vortex dipole in an infinite channel with an imposed background flow, we establish a planar dynamical system for the cross-stream coordinate and orientation. The system dynamics captures the existence of a critical flow speed for fish to successfully orient while performing cross-stream, periodic sweeping movements. Model predictions are examined in the context of experimental observations in the literature on the rheotactic behavior of fish deprived of visual and lateral line cues. The crucial role of bidirectional hydrodynamic interactions unveiled by this model points at an overlooked limitation of existing experimental paradigms to study rheotaxis in the laboratory.

One fascinating and perplexing fact about fish is that they tend to orient themselves and swim against the flow, rather than with it. This phenomenon is called rheotaxis, and it has countless examples, from salmon migrating upstream to lay their eggs to trout drift-foraging in a current. Yet, despite over a century of experimental studies, the mechanisms underlying rheotaxis remain poorly understood. There is general consensus that fish rely on water- and body-motion cues to vision, vestibular, tactile, and other senses. However, several questions remain unanswered, including how blind fish can perform rheotaxis or whether a passive hydrodynamic mechanism can support the phenomenon. One aspect that has been overlooked in studies of rheotaxis is the bidirectional hydrodynamic interaction between the fish and the surrounding flow, that is, how the presence of the fish alters the flow, which, in turn, affects the fish.

To address these open questions about rheotaxis, Porfiri, Zhang and Peterson wanted to develop a mathematical model of fish swimming, one that could help understand the passive hydrodynamic pathway that leads to swimming against a flow. Unlike experiments on live animals, a mathematical model offers the ability to remove cues to certain senses without interfering with animal behavior.

Porfiri, Zhang and Peterson modeled a fish as a pair of vortices located infinitely close to each other, rotating in opposite directions with the same strength. The vortex pair could freely move through an infinitely long channel with an imposed background flow, devoid of all sensory information expect of that accessed through the lateral line. Analyzing the resulting system revealed that there is a critical speed for the background flow above which the fish successfully orients itself against the flow, resulting in rheotaxis. This critical speed depends on the width of the channel the fish is swimming in. Depriving the fish of sensory information received through the lateral line does not preclude rheotaxis, indicating that rheotaxis could emerge in a completely passive manner.

The finding that the critical speed for rheotaxis depends on channel width could improve the design of experiments studying the phenomenon, since this effect could confound experiments where fish are confined in narrow channels. In this vein, Porfiri, Zhang and Peterson’s model could assist biologists in designing experiments detailing the multisensory nature of rheotaxis. Evidence of the importance of bidirectional hydrodynamic interactions on fish orientation may also inform modeling research on fish behavior.

Self-organized swimming with odd elasticity

We theoretically investigate self-oscillating waves of an active material, which were recently introduced as a nonsymmetric part of the elastic moduli, termed odd elasticity. Using Purcell's three-link swimmer model, we reveal that an odd-elastic filament at low Reynolds number can swim in a self-organized manner and that the time-periodic dynamics are characterized by a stable limit cycle generated by elastohydrodynamic interactions. Also, we consider a noisy shape gait and derive a swimming formula for a general elastic material in the Stokes regime with its elasticity modulus being represented by a nonsymmetric matrix, demonstrating that the odd elasticity produces biased net locomotion from random noise.

The performance of a flapping foil for a self-propelled fishlike body

Several fish species propel by oscillating the tail, while the remaining part of the body essentially contributes to the overall drag. Since in this case thrust and drag are in a way separable, most attention was focused on the study of propulsive efficiency for flapping foils under a prescribed stream. We claim here that the swimming performance should be evaluated, as for undulating fish whose drag and thrust are severely entangled, by turning to self-propelled locomotion to find the proper speed and the cost of transport for a given fishlike body. As a major finding, the minimum value of this quantity corresponds to a locomotion speed in a range markedly different from the one associated with the optimal efficiency of the propulsor. A large value of the feathering parameter characterizes the minimum cost of transport while the optimal efficiency is related to a large effective angle of attack. We adopt here a simple two-dimensional model for both inviscid and viscous flows to proof the above statements in the case of self-propelled axial swimming. We believe that such an easy approach gives a way for a direct extension to fully free swimming and to real-life configurations.

Friction modulation in limbless, three-dimensional gaits and heterogeneous terrains

Motivated by a possible convergence of terrestrial limbless locomotion strategies ultimately determined by interfacial effects, we show how both 3D gait alterations and locomotory adaptations to heterogeneous terrains can be understood through the lens of local friction modulation. Via an effective-friction modeling approach, compounded by 3D simulations, the emergence and disappearance of a range of locomotory behaviors observed in nature is systematically explained in relation to inhabited environments. Our approach also simplifies the treatment of terrain heterogeneity, whereby even solid obstacles may be seen as high friction regions, which we confirm against experiments of snakes ‘diffracting’ while traversing rows of posts, similar to optical waves. We further this optic analogy by illustrating snake refraction, reflection and lens focusing. We use these insights to engineer surface friction patterns and demonstrate passive snake navigation in complex topographies. Overall, our study outlines a unified view that connects active and passive 3D mechanics with heterogeneous interfacial effects to explain a broad set of biological observations, and potentially inspire engineering design.

A long puzzle in snake’s locomotion, sidewinding allows them to travel at an angle and reorient in some environments without loss of speed. Here, authors provide a mathematical argument to the evolution of sidewinding gaits and reinforce an analogy between limbless terrestrial locomotion and optics.

Orbital magnetism of an active particle in viscoelastic suspension

We consider an active (self-propelling) particle in a viscoelastic fluid. The particle is charged and constrained to move in a two-dimensional harmonic trap. Its dynamics is coupled to a constant magnetic field applied perpendicular to its plane of motion via Lorentz force. Due to the finite activity, the generalized fluctuation-dissipation relation (GFDR) breaks down, driving the system away from equilibrium. While breaking GFDR, we have shown that the system can have finite classical orbital magnetism only when the dynamics of the system contains finite inertia. The orbital magnetic moment has been calculated exactly. Remarkably, we find that when the elastic dissipation timescale of the medium is larger (smaller) than the persistence timescale of the self-propelling particle, it is diamagnetic (paramagnetic). Therefore, for a given strength of the magnetic field, the system undergoes a transition from diamagnetic to paramagnetic state (and vice versa) simply by tuning the timescales of underlying physical processes, such as active fluctuations and viscoelastic dissipation. Interestingly, we also find that the magnetic moment, which vanishes at equilibrium, behaves nonmonotonically with respect to increasing persistence of self-propulsion, which drives the system out of equilibrium.

Fish can save energy via proprioceptive sensing

Fish have evolved diverse and robust locomotive strategies to swim efficiently in complex fluid environments. However, we know little, if anything, about how these strategies can be achieved. Although most studies suggest that fish rely on the lateral line system to sense local flow and optimise body undulation, recent work has shown that fish are still able to gain benefits from the local flow even with the lateral line impaired. In this paper, we hypothesise that fish can save energy by extracting vortices shed from their neighbours using only simple proprioceptive sensing with the caudal fin. We tested this hypothesis on both computational and robotic fish by synthesising a central pattern generator (CPG) with feedback, proprioceptive sensing, and reinforcement learning. The CPG controller adjusts the body undulation after receiving feedback from the proprioceptive sensing signal, decoded via reinforcement learning. In our study, we consider potential proprioceptive sensing inputs to consist of low-dimensional signals (e.g. perceived forces) detected from the flow. With simulations on a computational robot and experiments on a robotic fish swimming in unknown dynamic flows, we show that the simple proprioceptive sensing is sufficient to optimise the body undulation to save energy, without any input from the lateral line. Our results reveal a new sensory-motor mechanism in schooling fish and shed new light on the strategy of control for robotic fish swimming in complex flows with high efficiency.

Gait change in tongue movement

During locomotion, humans switch gaits from walking to running, and horses from walking to trotting to cantering to galloping, as they increase their movement rate. It is unknown whether gait change leading to a wider movement rate range is limited to locomotive-type behaviours, or instead is a general property of any rate-varying motor system. The tongue during speech provides a motor system that can address this gap. In controlled speech experiments, using phrases containing complex tongue-movement sequences, we demonstrate distinct gaits in tongue movement at different speech rates. As speakers widen their tongue-front displacement range, they gain access to wider speech-rate ranges. At the widest displacement ranges, speakers also produce categorically different patterns for their slowest and fastest speech. Speakers with the narrowest tongue-front displacement ranges show one stable speech-gait pattern, and speakers with widest ranges show two. Critical fluctuation analysis of tongue motion over the time-course of speech revealed these speakers used greater effort at the beginning of phrases—such end-state-comfort effects indicate speech planning. Based on these findings, we expect that categorical motion solutions may emerge in any motor system, providing that system with access to wider movement-rate ranges.

Emergence of robust self-organized undulatory swimming based on local hydrodynamic force sensing

Undulatory swimming represents an ideal behavior to investigate locomotion control and the role of the underlying central and peripheral components in the spinal cord. Many vertebrate swimmers have central pattern generators and local pressure-sensitive receptors that provide information about the surrounding fluid. However, it remains difficult to study experimentally how these sensors influence motor commands in these animals. Here, using a specifically designed robot that captures the essential components of the animal neuromechanical system and using simulations, we tested the hypothesis that sensed hydrodynamic pressure forces can entrain body actuation through local feedback loops. We found evidence that this peripheral mechanism leads to self-organized undulatory swimming by providing intersegmental coordination and body oscillations. Swimming can be redundantly induced by central mechanisms, and we show that, therefore, a combination of both central and peripheral mechanisms offers a higher robustness against neural disruptions than any of them alone, which potentially explains how some vertebrates retain locomotor capabilities after spinal cord lesions. These results broaden our understanding of animal locomotion and expand our knowledge for the design of robust and modular robots that physically interact with the environment.

Resilience of neural networks for locomotion

Locomotion is an essential behaviour for the survival of all animals. The neural circuitry underlying locomotion is therefore highly robust to a wide variety of perturbations, including injury and abrupt changes in the environment. In the short term, fault tolerance in neural networks allows locomotion to persist immediately after mild to moderate injury. In the longer term, in many invertebrates and vertebrates, neural reorganization including anatomical regeneration can restore locomotion after severe perturbations that initially caused paralysis. Despite decades of research, very little is known about the mechanisms underlying locomotor resilience at the level of the underlying neural circuits and coordination of central pattern generators (CPGs). Undulatory locomotion is an ideal behaviour for exploring principles of circuit organization, neural control and resilience of locomotion, offering a number of unique advantages including experimental accessibility and modelling tractability. In comparing three well-characterized undulatory swimmers, lampreys, larval zebrafish and Caenorhabditis elegans, we find similarities in the manifestation of locomotor resilience. To advance our understanding, we propose a comparative approach, integrating experimental and modelling studies, that will allow the field to begin identifying shared and distinct solutions for overcoming perturbations to persist in orchestrating this essential behaviour.

Proprioceptive Mechanism for Bioinspired Fish Swimming

In this Letter, we propose a mechanism for driving bioinspired fish swimming locomotion based on proprioceptive sensing. Proprioception provides information about and representation of a body's position, motion, and acceleration in addition to the usual five senses. We hypothesize that a feedback loop based on this "sixth" sense results in an instability, driving the locomotion. In order to test our assumptions, we use a biomimetic robot and compare the experimental results to a simple yet generic model with excellent agreement.

A spinal organ of proprioception for integrated motor action feedback

Proprioception is essential for behavior and provides a sense of our body movements in physical space. Proprioceptor organs are thought to be only in the periphery. Whether the central nervous system can intrinsically sense its own movement remains unclear. Here we identify a segmental organ of proprioception in the adult zebrafish spinal cord, which is embedded by intraspinal mechanosensory neurons expressing Piezo2 channels. These cells are late-born, inhibitory, commissural neurons with unique molecular and physiological profiles reflecting a dual sensory and motor function. The central proprioceptive organ locally detects lateral body movements during locomotion and provides direct inhibitory feedback onto rhythm-generating interneurons responsible for the central motor program. This dynamically aligns central pattern generation with movement outcome for efficient locomotion. Our results demonstrate that a central proprioceptive organ monitors self-movement using hybrid neurons that merge sensory and motor entities into a unified network.

Learning hydrodynamic signatures through proprioceptive sensing by bioinspired swimmers

Objects moving in water or stationary objects in streams create a vortex wake. Such vortex wakes encode information about the objects and the flow conditions. Underwater robots that often function with constrained sensing capabilities can benefit from extracting this information from vortex wakes. Many species of fish do exactly this, by sensing flow features using their lateral lines as part of their multimodal sensing. To replicate such capabilities in robots, significant research has been devoted to developing artificial lateral line sensors that can be placed on the surface of a robot to detect pressure and velocity gradients. We advance an alternative view of embodied sensing in this paper; the kinematics of a swimmer's body in response to the hydrodynamic forcing by the vortex wake can encode information about the vortex wake. Here we show that using artificial neural networks that take the angular velocity of the body as input, fish-like swimmers can be trained to label vortex wakes which are hydrodynamic signatures of other moving bodies and thus acquire a capability to 'blindly' identify them.

Diving into a Simple Anguilliform Swimmer’s Sensitivity

Computational models of aquatic locomotion range from modest individual simple swimmers in 2D to sophisticated 3D multi-swimmer models that attempt to parse collective behavioral dynamics. Each of these models contain a multitude of model input parameters to which its outputs are inherently dependent, that is, various performance metrics. In this work, the swimming performance’s sensitivity to parameters is investigated for an idealized, simple anguilliform swimming model in 2D. The swimmer considered here propagates forward by dynamically varying its body curvature, similar to motion of a Caenorhabditis elegans. The parameter sensitivities were explored with respect to the fluid scale (Reynolds number), stroke (undulation) frequency, as well as a kinematic parameter controlling the velocity and acceleration of each upstroke and downstroke. The input Reynolds number and stroke frequencies sampled were from [450, 2200] and [1, 3] Hz, respectively. In total, 5000 fluid–structure interaction simulations were performed, each with a unique parameter combination selected via a Sobol sequence, in order to conduct global sensitivity analysis. Results indicate that the swimmer’s performance is most sensitive to variations in its stroke frequency. Trends in swimming performance were discovered by projecting the performance data onto particular 2D subspaces. Pareto-like optimal fronts were identified. This work is a natural extension of the parameter explorations of the same model from Battista in 2020.

Elastohydrodynamic Scaling Law for Heart Rates

Animal hearts are soft shells that actively pump blood to oxygenate tissues. Here, we propose an allometric scaling law for the heart rate based on the idea of elastohydrodynamic resonance of a fluid-loaded soft active elastic shell that buckles and contracts axially when twisted periodically. We show that this picture is consistent with numerical simulations of soft cylindrical shells that twist-buckle while pumping a viscous fluid, yielding optimum ejection fractions of 35%-40% when driven resonantly. Our scaling law is consistent with experimental measurements of heart rates over 2 orders of magnitude, and provides a mechanistic basis for how metabolism scales with organism size. In addition to providing a physical rationale for the heart rate and metabolism of an organism, our results suggest a simple design principle for soft fluidic pumps.

Soft Robotics as an Enabling Technology for Agroforestry Practice and Research

The shortage of qualified human labor is a key challenge facing farmers, limiting profit margins and preventing the adoption of sustainable and diversified agroecosystems, such as agroforestry. New technologies in robotics could offer a solution to such limitations. Advances in soft arms and manipulators can enable agricultural robots that can have better reach and dexterity around plants than traditional robots equipped with hard industrial robotic arms. Soft robotic arms and manipulators can be far less expensive to manufacture and significantly lighter than their hard counterparts. Furthermore, they can be simpler to design and manufacture since they rely on fluidic pressurization as the primary mechanisms of operation. However, current soft robotic arms are difficult to design and control, slow to actuate, and have limited payloads. In this paper, we discuss the benefits and challenges of soft robotics technology and what it could mean for sustainable agriculture and agroforestry.

Efficient sliding locomotion with isotropic friction

Snakes' bodies are covered in scales that make it easier to slide in some directions than in others. This frictional anisotropy allows for sliding locomotion with an undulatory gait, one of the most common for snakes. Isotropic friction is a simpler situation (that arises with snake robots, for example) but is less understood. In this work we regularize a model for sliding locomotion to allow for static friction. We then propose a robust iterative numerical method to study the efficiency of a wide range of motions under isotropic Coulomb friction. We find that simple undulatory motions give little net locomotion in the isotropic regime. We compute general time-harmonic motions of three-link bodies and find three local optima for efficiency. The top two involve static friction to some extent. We then propose a class of smooth body motions that have similarities to concertina locomotion (including the involvement of static friction) and can achieve optimal efficiency for both isotropic and anisotropic friction.

The role of curvature feedback in the energetics and dynamics of lamprey swimming: A closed-loop model

Like other animals, lampreys have a central pattern generator (CPG) circuit that activates muscles for locomotion and also adjusts the activity to respond to sensory inputs from the environment. Such a feedback system is crucial for responding appropriately to unexpected perturbations, but it is also active during normal unperturbed steady swimming and influences the baseline swimming pattern. In this study, we investigate different functional forms of body curvature-based sensory feedback and evaluate their effects on steady swimming energetics and kinematics, since little is known experimentally about the functional form of curvature feedback. The distributed CPG is modeled as chains of coupled oscillators. Pairs of phase oscillators represent the left and right sides of segments along the lamprey body. These activate muscles that flex the body and move the lamprey through a fluid environment, which is simulated using a full Navier-Stokes model. The emergent curvature of the body then serves as an input to the CPG oscillators, closing the loop. We consider two forms of feedback, each consistent with experimental results on lamprey proprioceptive sensory receptors. The first, referred to as directional feedback, excites or inhibits the oscillators on the same side, depending on the sign of a chosen gain parameter, and has the opposite effect on oscillators on the opposite side. We find that directional feedback does not affect beat frequency, but does change the duration of muscle activity. The second feedback model, referred to as magnitude feedback, provides a symmetric excitatory or inhibitory effect to oscillators on both sides. This model tends to increase beat frequency and reduces the energetic cost to the lamprey when the gain is high and positive. With both types of feedback, the body curvature has a similar magnitude. Thus, these results indicate that the same magnitude of curvature-based feedback on the CPG with different functional forms can cause distinct differences in swimming performance.

When animals move, they receive sensory inputs, which in turn are used to modulate the movement. Relatively little is known about how these inputs affect performance during steady locomotion. Using a computational model of a swimming lamprey, we investigated two different types of feedback, both consistent with experimental data. Both have strong, but different, effects on swimming speed and energy consumption, suggesting that sensory feedback is crucial not just for responding to perturbations, but also for high performance steady locomotion.

Forward and inverse problems in the mechanics of soft filaments

Soft slender structures are ubiquitous in natural and artificial systems, in active and passive settings and across scales, from polymers and flagella, to snakes and space tethers. In this paper, we demonstrate the use of a simple and practical numerical implementation based on the Cosserat rod model to simulate the dynamics of filaments that can bend, twist, stretch and shear while interacting with complex environments via muscular activity, surface contact, friction and hydrodynamics. We validate our simulations by solving a number of forward problems involving the mechanics of passive filaments and comparing them with known analytical results, and extend them to study instabilities in stretched and twisted filaments that form solenoidal and plectonemic structures. We then study active filaments such as snakes and other slender organisms by solving inverse problems to identify optimal gaits for limbless locomotion on solid surfaces and in bulk liquids.

Dynamics and locomotion of flexible foils in a frictional environment

Over the past few decades, oscillating flexible foils have been used to study the physics of organismal propulsion in different fluid environments. Here, we extend this work to a study of flexible foils in a frictional environment. When the foil is oscillated by heaving at one end but is not free to locomote, the dynamics change from periodic to non-periodic and chaotic as the heaving amplitude increases or the bending rigidity decreases. For friction coefficients lying in a certain range, the transition passes through a sequence of N-periodic and asymmetric states before reaching chaotic dynamics. Resonant peaks are damped and shifted by friction and large heaving amplitudes, leading to bistable states. When the foil is free to locomote, the horizontal motion smoothes the resonant behaviours. For moderate frictional coefficients, steady but slow locomotion is obtained. For large transverse friction and small tangential friction corresponding to wheeled snake robots, faster locomotion is obtained. Travelling wave motions arise spontaneously, and move with horizontal speeds that scale as transverse friction coefficient to the power 1/4 and input power that scales as the transverse friction coefficient to the power 5/12. These scalings are consistent with a boundary layer form of the solutions near the foil's leading edge.

Phototactic guidance of a tissue-engineered soft-robotic ray

Inspired by the relatively simple morphological blueprint provided by batoid fish such as stingrays and skates, we created a biohybrid system that enables an artificial animal--a tissue-engineered ray--to swim and phototactically follow a light cue. By patterning dissociated rat cardiomyocytes on an elastomeric body enclosing a microfabricated gold skeleton, we replicated fish morphology at 1/10 scale and captured basic fin deflection patterns of batoid fish. Optogenetics allows for phototactic guidance, steering, and turning maneuvers. Optical stimulation induced sequential muscle activation via serpentine-patterned muscle circuits, leading to coordinated undulatory swimming. The speed and direction of the ray was controlled by modulating light frequency and by independently eliciting right and left fins, allowing the biohybrid machine to maneuver through an obstacle course.

Fish optimize sensing and respiration during undulatory swimming

Previous work in fishes considers undulation as a means of propulsion without addressing how it may affect other functions such as sensing and respiration. Here we show that undulation can optimize propulsion, flow sensing and respiration concurrently without any apparent tradeoffs when head movements are coupled correctly with the movements of the body. This finding challenges a long-held assumption that head movements are simply an unintended consequence of undulation, existing only because of the recoil of an oscillating tail. We use a combination of theoretical, biological and physical experiments to reveal the hydrodynamic mechanisms underlying this concerted optimization. Based on our results we develop a parsimonious control architecture that can be used by both undulatory animals and machines in dynamic environments.

Suction-based propulsion as a basis for efficient animal swimming

A central and long-standing tenet in the conceptualization of animal swimming is the idea that propulsive thrust is generated by pushing the surrounding water rearward. Inherent in this perspective is the assumption that locomotion involves the generation of locally elevated pressures in the fluid to achieve the expected downstream push of the surrounding water mass. Here we show that rather than pushing against the surrounding fluid, efficient swimming animals primarily pull themselves through the water via suction. This distinction is manifested in dominant low-pressure regions generated in the fluid surrounding the animal body, which are observed by using particle image velocimetry and a pressure calculation algorithm applied to freely swimming lampreys and jellyfish. These results suggest a rethinking of the evolutionary adaptations observed in swimming animals as well as the mechanistic basis for bio-inspired and biomimetic engineered vehicles.

Swimming animals are generally assumed to generate forward thrust by pushing surrounding water rearwards. Here, Gemmell et al. show that efficient swimming in lampreys and jellyfish is achieved primarily through suction, as vortex-associated low pressure regions are synchronized by undulations of the body.

Resistive thrust production can be as crucial as added mass mechanisms for inertial undulatory swimmers

In this Rapid Communication, we address a crucial point regarding the description of moderate to high Reynolds numbers aquatic swimmers. For decades, swimming animals have been classified in two different families of propulsive mechanisms based on the Reynolds number: the resistive swimmers, using local friction to produce the necessary thrust force for locomotion at low Reynolds number, and the reactive swimmers, lying in the high Reynolds range, and using added mass acceleration (described by perfect fluid theory). However, inertial swimmers are also systems that dissipate energy, due to their finite size, therefore involving strong resistive contributions, even for high Reynolds numbers. Using a complete model for the hydrodynamic forces, involving both reactive and resistive contributions, we revisit here the physical mechanisms responsible for the thrust production of such swimmers. We show, for instance, that the resistive part of the force balance is as crucial as added mass effects in the modeling of the thrust force, especially for elongated species. The conclusions brought by this work may have significant contributions to the understanding of complex swimming mechanisms, especially for the future design of artificial swimmers.