Force scaling and efficiency of elongated median fin propulsion

Several fishes swim by undulating a thin and elongated median fin while the body is mostly kept straight, allowing them to perform forward and directional maneuvers. We used a robotic vessel with similar fin propulsion to determine the thrust scaling and efficiency. Using precise force and swimming kinematics measurements with the robotic vessel, the thrust generated by the undulating fin was found to scale with the square of the relative velocity between the free streaming flow and the wave speed. A hydrodynamic efficiency is presented based on propulsive force measurements and modelling of the power required to oscillate the fin laterally. It was found that the propulsive efficiency has a broadly high performance versus swimming speed, with a maximum efficiency of 75%. An expression to calculate the swimming speed over wave speed was found to depend on two parameters:A_p/A_e(ratio between body frontal area to fin swept area) andC_D/C_x(ratio of body drag to fin thrust coefficient). The models used to calculate propulsive force and free-swimming speed were compared with experimental results. The broader impacts of these results are discussed in relation to morphology and the function of undulating fin swimmers. In particular, we suggest that the ratio of fin and body height found in natural swimmers could be due to a trade-off between swimming efficiency and swimming speed.

Knifefish turning control and hydrodynamics during forward swimming

Rapid turning and swimming contribute to ecologically important behaviors in fishes such as predator avoidance, prey capture, mating, and the navigation of complex environments. For riverine species, such as knifefishes, turning behaviors may also be important for navigating locomotive perturbations caused by turbulent flows. Most research on fish maneuvering focuses on fish with traditional fin and body morphologies, which primarily use body bending and the pectoral fins during turning. However, it is uncertain how fishes with uncommon morphologies, are able to achieve sudden and controllable turns. Here we studied the turning performance and the turning hydrodynamics of the Black ghost knifefish (Apteronotus albifrons, N=6) which has an atypical elongated ribbon fin. Fish were filmed while swimming forward at ∼2 BL s-1 and feeding from a fixed feeder (control) and an oscillating feeder (75 Hz) at two different amplitudes. 3D kinematic analysis of the body revealed the highest pitch angles and lowest body bending coefficients occurred during steady swimming. Low pitch angle, high maximum yaw angles and large body bending coefficients were characteristic of small and large turns. Asynchrony in pectoral fin use was low during turning, however ribbon fin wavelength, frequency, and wave speed were greatest during large turns. Digital particle image velocimetry (DPIV) showed larger counter-rotating vortex pairs produced during turning by the ribbon-fin in comparison to vortices rotating in the same direction during steady swimming. Our results highlight the ribbon fin's role in controlled rapid turning through modulation of wavelength, frequency, and wave speed.

Design and experimental evaluation of the novel undulatory propulsors for biomimetic underwater robots

Inspired by wide and elongated fins of aquatic species, robotic undulatory propulsors are developed to achieve advanced maneuverability. Through biological observation, undulatory fins are typically comprised of more than 100 fin rays to propagate continuous and diverse propulsive waves for agile locomotion. Due to practical engineering restrictions, most robotic undulatory propulsors are characterized by limit number of long fin rays which intersect flexible fin surfaces as backbones and partition them into multiple membrane-like segments. As spatially discrete surfaces affect waves traveling and thrust efficiency, a novel undulatory propulsor has been proposed in this paper. By taking advantage of an arc-shaped fin surface and its material properties, the newly developed undulatory propulsor is equipped with a series of custom designed fin rays, which are only fastened on the inner edge of fin surface so that the unconstrained part is flexural passively to form a smooth fin profile. To discuss appropriate fin surface configurations for such newly developed propulsor, a series of experiments have been conducted to explore the effects of fin surface material, thickness and morphology on thrust and power consumption. Results reveal the fin surface made of nitrile rubber with 2 mm thickness and aspect ratio of 0.33 is highly recommended when taking into account both propulsive forces and loads suffered by fin rays' actuators. To validate the improvement of thrust efficiency, comparison experiments have been carried out between the conventional and the newly developed undulatory propulsors. The findings indicate smooth sinusoid-like fin profiles contribute to wave propagation, which makes the newly developed undulatory fin outperform the conventional one. Finally, a rajiform-inspired robot prototype has been introduced to assess multi-DOFs maneuverability. The experiments show the biomimetic robot can achieve diverse locomotion including swimming forward, turning in-place and rising/diving propelled by a pair of undulatory propulsors.

Beyond the Kármán gait: knifefish swimming in periodic and irregular vortex streets

Neotropical freshwater fishes such as knifefishes are commonly faced with navigating intense and highly unsteady streams. However, our knowledge on locomotion in apteronotids comes from laminar flows, where the ribbon fin dominates over the pectoral fins or body bending. Here, we studied the 3D kinematics and swimming control of seven black ghost knifefish (Apteronotus albifrons) moving in laminar flows (flow speed U∞≈1-5 BL s-1) and in periodic vortex streets (U∞≈2-4 BL s-1). Two different cylinders (∼2 and ∼3 cm diameter) were used to generate the latter. Additionally, fish were exposed to an irregular wake produced by a free oscillating cylinder (∼2 cm diameter; U∞≈2 BL s-1). In laminar flows, knifefish mainly used their ribbon fin, with wave frequency, speed and acceleration increasing with U∞. In contrast, knifefish swimming behind a fixed cylinder increased the use of pectoral fins, which resulted in changes in body orientation that mimicked steady backward swimming. Meanwhile, individuals behind the oscillating cylinder presented a combination of body bending and ribbon and pectoral fin movements that counteract the out-of-phase yaw oscillations induced by the irregular shedding of vortices. We corroborated passive out-of-phase oscillations by placing a printed knifefish model just downstream of the moving cylinder, but when placed one cylinder diameter downstream, the model oscillated in phase. Thus, the wake left behind an oscillating body is more challenging than a periodic vortex shedding for an animal located downstream, which may have consequences on inter- and intra-specific interactions.

Immersed Methods for Fluid-Structure Interaction

Fluid-structure interaction is ubiquitous in nature and occurs at all biological scales. Immersed methods provide mathematical and computational frameworks for modeling fluid-structure systems. These methods, which typically use an Eulerian description of the fluid and a Lagrangian description of the structure, can treat thin immersed boundaries and volumetric bodies, and they can model structures that are flexible or rigid or that move with prescribed deformational kinematics. Immersed formulations do not require body-fitted discretizations and thereby avoid the frequent grid regeneration that can otherwise be required for models involving large deformations and displacements. This article reviews immersed methods for both elastic structures and structures with prescribed kinematics. It considers formulations using integral operators to connect the Eulerian and Lagrangian frames and methods that directly apply jump conditions along fluid-structure interfaces. Benchmark problems demonstrate the effectiveness of these methods, and selected applications at Reynolds numbers up to approximately 20,000 highlight their impact in biological and biomedical modeling and simulation.

Robotic device shows lack of momentum enhancement for gymnotiform swimmers

Many fish generate thrust by undulating one or multiple elongated fins while keeping their body straight. This propulsion mechanism has stimulated interest in both biology and bio-inspired marine propulsion because its maneuverability and efficiency at low speed. Analytical studies have found that a fin attached to a rigid flat body can produce substantially higher thrust compared to a fin without a body, three- to four-fold for natural swimmers. However, this momentum enhancement has not been confirmed experimentally. In this work, a robotic ribbon fin model with an adjustable-height body was used to test the momentum enhancement for gymontiform swimmers where the undulating fin runs along the ventral side of the body. In a series of experiments, the force generated by the robotic device was measured as the body height of the robot, the undulating fin frequency and the flow speed were changed. It was found that the thrust generated by the ribbon fin is not affected by the presence of a body, thereby resulting in no momentum enhancement due to the fin-body interaction. These results suggest that if there is a benefit at a specific fin-body height ratio of the fishes, the momentum enhancement is not the reason. This result has broader implications in understanding the evolutionary adaption of undulatory fin propulsion and underwater vehicles designs.

Swimming performance of a bio-inspired robotic vessel with undulating fin propulsion

Undulatory fin propulsion exhibits a high degree of maneuver control-an ideal feature for underwater vessels exploring complex environments. In this work, we developed and tested a self-contained, free-swimming robot with a single undulating fin running along the length of the robot, which controls both forward motion and directional maneuvers. We successfully replicated several maneuvers including forward swimming, reversed motion, diving, station-keeping and vertical swimming. For each maneuver, a series of experiments was performed as a function of fin frequency, wavelength and traveling wave direction to measure swimming velocities, orientation angles and mean power consumption. In addition, 3D flow fields were measured during forward swimming and station-keeping using volumetric particle image velocimetry (PIV). The efficiency for forward swimming was compared using three metrics: cost of transport, wave efficiency and Strouhal number (St). The results indicate that the cost of transport exhibits a V-shape trend with the minimum value at low swimming velocity. The robot reaches optimal wave efficiency and locomotor performance at a range of 0.2-0.4 St. Volumetric PIV data reveal the shed of vortex tubes generated by the fin during forward swimming and station keeping. For forward swimming, a series of vortex tubes are shed off the fin edge with a lateral and downward direction with respect to the longitudinal axis of the fin. For station keeping, flow measurements suggest that the vortex tubes are shed at the mid-section of the fin while the posterior and anterior segment of the vortex stay attached to the fin. These results agree with the previous vortex structures based on simulations and 2D PIV. The development of this vessel with high maneuverability and station keeping performance has applications for oceanography, coastal exploration, defense, the oil industry and other marine industries where operations are unsafe or impractical for divers or human-piloted vessels.

Propulsive performance of an under-actuated robotic ribbon fin

Many aquatic animals propelled by elongated undulatory fins can perform complex maneuvers and swim with high efficiency at low speeds. In this propulsion, one or multiple waves travel along an elastic fin composed of flexible rays. In this study, we explore the potential benefits or disadvantages of passive fin motion based on the coupling of fluid-structure interactions and elasto-mechanical responses of the undulatory fin. The motivation is to understand how an under-actuated undulating fin can modify its active and passive fin motion to effectively control the hydrodynamic force and propulsive efficiency. We study the kinematics and propulsive performance of an under-actuated ribbon fin using a robotic device. During two experimental sets for fully-actuated fin and under-actuated fin respectively, we measured fin kinematics, surge forces and power consumption. Our results show that under-actuated fin can generate smaller thrust but consume less power comparing to a fully-actuated counterpart. The thrust generated by an under-actuated fin scales similarly to a fully-actuated fin-linear with the enclosed area and quadratic with the relative velocity. Power consumption scales with cube of lateral tangential velocity. Furthermore, we find that the under-actuated fin can keep the same propulsive efficiency as the fully-actuated fin at low relative velocities. This finding has profound implications to both natural swimmers and underwater vehicles using undulating fin-based propulsion, as it suggests that they can potentially exploit passive fin motion without decrementing propulsive efficiency. For underwater vehicles with undulatory fins, an under-actuated design can greatly simplify the mechanical design and control complexity of a versatile propulsion system.

Computer Simulations Imply Forelimb-Dominated Underwater Flight in Plesiosaurs

Plesiosaurians are an extinct group of highly derived Mesozoic marine reptiles with a global distribution that spans 135 million years from the Early Jurassic to the Late Cretaceous. During their long evolutionary history they maintained a unique body plan with two pairs of large wing-like flippers, but their locomotion has been a topic of debate for almost 200 years. Key areas of controversy have concerned the most efficient biologically possible limb stroke, e.g. whether it consisted of rowing, underwater flight, or modified underwater flight, and how the four limbs moved in relation to each other: did they move in or out of phase? Previous studies have investigated plesiosaur swimming using a variety of methods, including skeletal analysis, human swimmers, and robotics. We adopt a novel approach using a digital, three-dimensional, articulated, free-swimming plesiosaur in a simulated fluid. We generated a large number of simulations under various joint degrees of freedom to investigate how the locomotory repertoire changes under different parameters. Within the biologically possible range of limb motion, the simulated plesiosaur swims primarily with its forelimbs using an unmodified underwater flight stroke, essentially the same as turtles and penguins. In contrast, the hindlimbs provide relatively weak thrust in all simulations. We conclude that plesiosaurs were forelimb-dominated swimmers that used their hind limbs mainly for maneuverability and stability.

Plesiosaurs are an extinct group of Mesozoic marine reptiles with a global distribution that spans 135 million years. They maintained a unique body plan with two pairs of large wing-like flippers throughout their long evolutionary history, but how plesiosaurs swam has remained a topic of debate for almost 200 years. We address the question of how plesiosaurs swam using a digital, three-dimensional, free-swimming model of a plesiosaur in a simulated fluid. We performed thousands of simulations under different parameters to investigate possible plesiosaur swimming patterns. Our simulations show that the forelimbs provide the majority of thrust, and that the thrust from the hindlimbs is weak. The plesiosaur swims primarily with its forelimbs using an underwater flight stroke, essentially the same as turtles and penguins.

Convergent evolution of mechanically optimal locomotion in aquatic invertebrates and vertebrates

Examples of animals evolving similar traits despite the absence of that trait in the last common ancestor, such as the wing and camera-type lens eye in vertebrates and invertebrates, are called cases of convergent evolution. Instances of convergent evolution of locomotory patterns that quantitatively agree with the mechanically optimal solution are very rare. Here, we show that, with respect to a very diverse group of aquatic animals, a mechanically optimal method of swimming with elongated fins has evolved independently at least eight times in both vertebrate and invertebrate swimmers across three different phyla. Specifically, if we take the length of an undulation along an animal's fin during swimming and divide it by the mean amplitude of undulations along the fin length, the result is consistently around twenty. We call this value the optimal specific wavelength (OSW). We show that the OSW maximizes the force generated by the body, which also maximizes swimming speed. We hypothesize a mechanical basis for this optimality and suggest reasons for its repeated emergence through evolution.

Experimental investigation and propulsion control for a bio-inspired robotic undulatory fin

Undulatory fin propulsion, inspired by the locomotion of aquatic species such as electric eels and cuttlefish, holds considerable potential for endowing underwater vehicles with enhanced propulsion and maneuvering abilities, to address the needs of a growing number of applications. However, there are still gaps in our understanding of the effect of the fin undulations' characteristics on the generated thrust, particularly within the context of developing propulsion control strategies for such robotic systems. Towards this end, we present the design and experimental evaluation of a robotic fin prototype, comprised of eight individually-actuated fin rays. An artificial central pattern generator (CPG) is used to produce the rays' undulatory motion pattern. Experiments are performed inside a water tank, with the robotic fin suspended from a carriage, whose motion is constrained via a linear guide. The results from a series of detailed parametric investigations reveal several important findings regarding the effect of the undulatory wave kinematics on the propulsion speed and efficiency. Based on these findings, two alternative strategies for propulsion control of the robotic fin are proposed. In the first one, the speed is varied through changes in the undulation amplitude, while the second one involves simultaneous adjustment of the undulation frequency and number of waves. These two strategies are evaluated via experiments demonstrating open-loop velocity control, as well as closed-loop position control of the prototype.

Development and Motion Testing of a Robotic Ray

Biomimetics takes nature as a model for inspiration to immensely help abstract new principles and ideas to develop various devices for real applications. In order to improve the stability and maneuvering of biomimetic fish like underwater propulsors, we selected bluespotted ray that propel themselves by taking advantage of their pectoral fins as target. First, a biomimetic robotic undulating fin driven propulsor was built based on the simplified pectoral structure of living bluespotted ray. The mechanical structure and control circuit were then presented. The fin undulating motion patterns, fin ray angle, and fin shape to be investigated are briefly introduced. Later, the kinematic analysis of fin ray and the whole fin is discussed. The influence of various kinematic parameters and morphological parameters on the average propulsion velocity of the propulsor was analyzed. Finally, we conclude that the average propulsion velocity generally increases with the increase of kinematic parameters such as frequency, amplitude, and wavelength, respectively. Moreover, it also has a certain relationship with fin undulating motion patterns, fin ray angle, fin shape, and fin aspect ratio.

Separability of drag and thrust in undulatory animals and machines

For nearly a century, researchers have tried to understand the swimming of aquatic animals in terms of a balance between the forward thrust from swimming movements and drag on the body. Prior approaches have failed to provide a separation of these two forces for undulatory swimmers such as lamprey and eels, where most parts of the body are simultaneously generating drag and thrust. We nonetheless show that this separation is possible, and delineate its fundamental basis in undulatory swimmers. Our approach unifies a vast diversity of undulatory aquatic animals (anguilliform, sub-carangiform, gymnotiform, bal-istiform, rajiform) and provides design principles for highly agile bioinspired underwater vehicles. This approach has practical utility within biology as well as engineering. It is a predictive tool for use in understanding the role of the mechanics of movement in the evolutionary emergence of morphological features relating to locomotion. For example, we demonstrate that the drag-thrust separation framework helps to predict the observed height of the ribbon fin of electric knifefish, a diverse group of neotropical fish which are an important model system in sensory neurobiology. We also show how drag-thrust separation leads to models that can predict the swimming velocity of an organism or a robotic vehicle.

Locomotion of free-swimming ghost knifefish: anal fin kinematics during four behaviors

The maneuverability demonstrated by the weakly electric ghost knifefish (Apteronotus albifrons) is a result of its highly flexible ribbon-like anal fin, which extends nearly three-quarters the length of its body and is composed of approximately 150 individual fin rays. To understand how movement of the anal fin controls locomotion we examined kinematics of the whole fin, as well as selected individual fin rays, during four locomotor behaviors executed by free-swimming ghost knifefish: forward swimming, backward swimming, heave (vertical) motion, and hovering. We used high-speed video (1000 fps) to examine the motion of the entire anal fin and we measured the three-dimensional curvature of four adjacent fin rays in the middle of the fin during each behavior to determine how individual fin rays bend along their length during swimming. Canonical discriminant analysis separated all four behaviors on anal fin kinematic variables and showed that forward and backward swimming behaviors contrasted the most: forward behaviors exhibited a large anterior wavelength and posterior amplitude while during backward locomotion the anal fin exhibited both a large posterior wavelength and anterior amplitude. Heave and hover behaviors were defined by similar kinematic variables; however, for each variable, the mean values for heave motions were generally greater than for hovering. Individual fin rays in the middle of the anal fin curved substantially along their length during swimming, and the magnitude of this curvature was nearly twice the previously measured maximum curvature for ray-finned fish fin rays during locomotion. Fin rays were often curved into the direction of motion, indicating active control of fin ray curvature, and not just passive bending in response to fluid loading.

Feedback control as a framework for understanding tradeoffs in biology

Control theory arose from a need to control synthetic systems. From regulating steam engines to tuning radios to devices capable of autonomous movement, it provided a formal mathematical basis for understanding the role of feedback in the stability (or change) of dynamical systems. It provides a framework for understanding any system with regulation via feedback, including biological ones such as regulatory gene networks, cellular metabolic systems, sensorimotor dynamics of moving animals, and even ecological or evolutionary dynamics of organisms and populations. Here, we focus on four case studies of the sensorimotor dynamics of animals, each of which involves the application of principles from control theory to probe stability and feedback in an organism's response to perturbations. We use examples from aquatic (two behaviors performed by electric fish), terrestrial (following of walls by cockroaches), and aerial environments (flight control by moths) to highlight how one can use control theory to understand the way feedback mechanisms interact with the physical dynamics of animals to determine their stability and response to sensory inputs and perturbations. Each case study is cast as a control problem with sensory input, neural processing, and motor dynamics, the output of which feeds back to the sensory inputs. Collectively, the interaction of these systems in a closed loop determines the behavior of the entire system.

Center of mass motion in swimming fish: effects of speed and locomotor mode during undulatory propulsion

Studies of center of mass (COM) motion are fundamental to understanding the dynamics of animal movement, and have been carried out extensively for terrestrial and aerial locomotion. But despite a large amount of literature describing different body movement patterns in fishes, analyses of how the center of mass moves during undulatory propulsion are not available. These data would be valuable for understanding the dynamics of different body movement patterns and the effect of differing body shapes on locomotor force production. In the present study, we analyzed the magnitude and frequency components of COM motion in three dimensions (x: surge, y: sway, z: heave) in three fish species (eel, bluegill sunfish, and clown knifefish) swimming with four locomotor modes at three speeds using high-speed video, and used an image cross-correlation technique to estimate COM motion, thus enabling untethered and unrestrained locomotion. Anguilliform swimming by eels shows reduced COM surge oscillation magnitude relative to carangiform swimming, but not compared to knifefish using a gymnotiform locomotor style. Labriform swimming (bluegill at 0.5 body lengths/s) displays reduced COM sway oscillation relative to swimming in a carangiform style at higher speeds. Oscillation frequency of the COM in the surge direction occurs at twice the tail beat frequency for carangiform and anguilliform swimming, but at the same frequency as the tail beat for gymnotiform locomotion in clown knifefish. Scaling analysis of COM heave oscillation for terrestrial locomotion suggests that COM heave motion scales with positive allometry, and that fish have relatively low COM oscillations for their body size.

Evaluating the Fin-Ray Trajectory Tracking of Bio-Inspired Robotic Undulating Fins via an Experimental-Numerical Approach

In the past decade, biomimetic undulating fin propulsion has been one of the main topics considered by scientists and researchers in the field of robotic fish. This technology is inspired by the biological wave-like propulsion of ribbon-finned fish. The swimming modes have aquatic application potentials with greater manoeuvrability, less detectable noise or wake and better efficiency at low speeds. The present work concentrates on the evaluation of fin-ray trajectory tracking of biorobotic undulating fins at the levels of kinematics and hydrodynamics by using an experimental-numerical approach. Firstly, fin-ray tracking inconsistence between the desired and actual undulating trajectories is embodied with experimental data of the fin prototype. Next, the dynamics' nonlinearity is numerically and analytically unveiled by using the computational fluid dynamics (CFD) method, from the viewpoint of vortex shedding and the hydro-effect. The evaluation of fin-ray tracking performance creates a good basis for control design to improve the fin-ray undulation of prototypes.

Mutually opposing forces during locomotion can eliminate the tradeoff between maneuverability and stability

A surprising feature of animal locomotion is that organisms typically produce substantial forces in directions other than what is necessary to move the animal through its environment, such as perpendicular to, or counter to, the direction of travel. The effect of these forces has been difficult to observe because they are often mutually opposing and therefore cancel out. Indeed, it is likely that these forces do not contribute directly to movement but may serve an equally important role: to simplify and enhance the control of locomotion. To test this hypothesis, we examined a well-suited model system, the glass knifefish Eigenmannia virescens, which produces mutually opposing forces during a hovering behavior that is analogous to a hummingbird feeding from a moving flower. Our results and analyses, which include kinematic data from the fish, a mathematical model of its swimming dynamics, and experiments with a biomimetic robot, demonstrate that the production and differential control of mutually opposing forces is a strategy that generates passive stabilization while simultaneously enhancing maneuverability. Mutually opposing forces during locomotion are widespread across animal taxa, and these results indicate that such forces can eliminate the tradeoff between stability and maneuverability, thereby simplifying neural control.

Kinematics of ribbon-fin locomotion in the bowfin, Amia calva

An elongated dorsal and/or anal ribbon-fin to produce forward and backward propulsion has independently evolved in several groups of fishes. In these fishes, fin ray movements along the fin generate a series of waves that drive propulsion. There are no published data on the use of the dorsal ribbon-fin in the basal freshwater bowfin, Amia calva. In this study, frequency, amplitude, wavelength, and wave speed along the fin were measured in Amia swimming at different speeds (up to 1.0 body length/sec) to understand how the ribbon-fin generates propulsion. These wave properties were analyzed to (1) determine whether regional specialization occurs along the ribbon-fin, and (2) to reveal how the undulatory waves are used to control swimming speed. Wave properties were also compared between swimming with sole use of the ribbon-fin, and swimming with simultaneous use of the ribbon and pectoral fins. Statistical analysis of ribbon-fin kinematics revealed no differences in kinematic patterns along the ribbon-fin, and that forward propulsive speed in Amia is controlled by the frequency of the wave in the ribbon-fin, irrespective of the contribution of the pectoral fin. This study is the first kinematic analysis of the ribbon-fin in a basal fish and the model species for Amiiform locomotion, providing a basis for understanding ribbon-fin locomotion among a broad range of teleosts.

Biomimetic and bio-inspired robotics in electric fish research

Weakly electric knifefish have intrigued both biologists and engineers for decades with their unique electrosensory system and agile swimming mechanics. Study of these fish has resulted in models that illuminate the principles behind their electrosensory system and unique swimming abilities. These models have uncovered the mechanisms by which knifefish generate thrust for swimming forward and backward, hovering, and heaving dorsally using a ventral elongated median fin. Engineered active electrosensory models inspired by electric fish allow for close-range sensing in turbid waters where other sensing modalities fail. Artificial electrosense is capable of aiding navigation, detection and discrimination of objects, and mapping the environment, all tasks for which the fish use electrosense extensively. While robotic ribbon fin and artificial electrosense research has been pursued separately to reduce complications that arise when they are combined, electric fish have succeeded in their ecological niche through close coupling of their sensing and mechanical systems. Future integration of electrosense and ribbon fin technology into a knifefish robot should likewise result in a vehicle capable of navigating complex 3D geometries unreachable with current underwater vehicles, as well as provide insights into how to design mobile robots that integrate high bandwidth sensing with highly responsive multidirectional movement.

Organization of the gymnotiform fish pallium in relation to learning and memory: II. Extrinsic connections

This study describes the extrinsic connections of the dorsal telencephalon (pallium) of gymnotiform fish. We show that the afferents to the dorsolateral and dorsomedial pallial subdivisions of gymnotiform fish arise from the preglomerular complex. The preglomerular complex receives input from four clearly distinct regions: (1) descending input from the pallium itself (dorsomedial and dorsocentral subdivisions and nucleus taenia); (2) other diencephalic nuclei (centroposterior, glomerular, and anterior tuberal nuclei and nucleus of the posterior tuberculum); (3) mesencephalic sensory structures (optic tectum, dorsal and ventral torus semicircularis); and (4) basal forebrain, preoptic area, and hypothalamic nuclei. Previous studies have implicated the majority of the diencephalic and mesencephalic nuclei in electrosensory, visual, and acousticolateral functions. Here we discuss the implications of preglomerular/pallial electrosensory-associated afferents with respect to a major functional dichotomy of the electric sense. The results allow us to hypothesize that a functional distinction between electrocommunication vs. electrolocation is maintained within the input and output pathways of the gymnotiform pallium. Electrocommunication information is conveyed to the pallium through complex indirect pathways that originate in the nucleus electrosensorius, whereas electrolocation processing follows a conservative pathway inherent to all vertebrates, through the optic tectum. We hypothesize that cells responsive to communication signals do not converge onto the same targets in the preglomerular complex as cells responsive to moving objects. We also hypothesize that efferents from the dorsocentral (DC) telencephalon project to the dorsal torus semicircularis to regulate processing of electrocommunication signals, whereas DC efferents to the tectum modulate sensory control of movement.

Undulating fins produce off-axis thrust and flow structures

While wake structures of many forms of swimming and flying are well characterized, the wake generated by a freely-swimming undulating fin has not yet been analyzed. These elongated fins allow fish to achieve enhanced agility exemplified by the forward, backward, and vertical swimming capabilities of knifefish and also have potential applications in the design of more maneuverable underwater vehicles. We present the flow structure of an undulating robotic fin model using particle image velocimetry to measure fluid velocity fields in the wake. We supplement the experimental robotic work with high-fidelity computational fluid dynamics, simulating the hydrodynamics of both a virtual fish whose fin kinematics and fin plus body morphology are measured from a freely-swimming knifefish as well as a virtual rendering of our robot. Our results indicate a series of linked vortex tubes is shed off the long edge of the fin as the undulatory wave travels lengthwise along the fin. A jet at an oblique angle to the fin is associated with the successive vortex tubes, propelling the fish forward. The vortex structure bears similarity to the linked vortex ring structure trailing the oscillating caudal fin of a carangiform swimmer, though the vortex rings are distorted due to the undulatory kinematics of the elongated fin.

Comparable ages for the independent origins of electrogenesis in African and South American weakly electric fishes

One of the most remarkable examples of convergent evolution among vertebrates is illustrated by the independent origins of an active electric sense in South American and African weakly electric fishes, the Gymnotiformes and Mormyroidea, respectively. These groups independently evolved similar complex systems for object localization and communication via the generation and reception of weak electric fields. While good estimates of divergence times are critical to understanding the temporal context for the evolution and diversification of these two groups, their respective ages have been difficult to estimate due to the absence of an informative fossil record, use of strict molecular clock models in previous studies, and/or incomplete taxonomic sampling. Here, we examine the timing of the origins of the Gymnotiformes and the Mormyroidea using complete mitogenome sequences and a parametric bayesian method for divergence time reconstruction. Under two different fossil-based calibration methods, we estimated similar ages for the independent origins of the Mormyroidea and Gymnotiformes. Our absolute estimates for the origins of these groups either slightly postdate, or just predate, the final separation of Africa and South America by continental drift. The most recent common ancestor of the Mormyroidea and Gymnotiformes was found to be a non-electrogenic basal teleost living more than 85 millions years earlier. For both electric fish lineages, we also estimated similar intervals (16-19 or 22-26 million years, depending on calibration method) between the appearance of electroreception and the origin of myogenic electric organs, providing rough upper estimates for the time periods during which these complex electric organs evolved de novo from skeletal muscle precursors. The fact that the Gymnotiformes and Mormyroidea are of similar age enhances the comparative value of the weakly electric fish system for investigating pathways to evolutionary novelty, as well as the influences of key innovations in communication on the process of species radiation.

Kinematics of the ribbon fin in hovering and swimming of the electric ghost knifefish

Weakly electric knifefish are exceptionally maneuverable swimmers. In prior work, we have shown that they are able to move their entire body omnidirectionally so that they can rapidly reach prey up to several centimeters away. Consequently, in addition to being a focus of efforts to understand the neural basis of sensory signal processing in vertebrates, knifefish are increasingly the subject of biomechanical analysis to understand the coupling of signal acquisition and biomechanics. Here, we focus on a key subset of the knifefish's omnidirectional mechanical abilities: hovering in place, and swimming forward at variable speed. Using high speed video and a markerless motion capture system to capture fin position, we show that hovering is achieved by generating two traveling waves, one from the caudal edge of the fin, and one from the rostral edge, moving toward each other. These two traveling waves overlap at a nodal point near the center of the fin, cancelling fore-aft propulsion. During forward swimming at low velocities, the caudal region of the fin continues to have counter-propagating waves, directly retarding forward movement. The gait transition from hovering to forward swimming is accompanied by a shift in the nodal point toward the caudal end of the fin. While frequency varies significantly to increase speed at low velocities, beyond about one body length per second, the frequency stays near 10~Hz, and amplitude modulation becomes more prominent despite its higher energetic costs. A coupled central pattern generator model is able to reproduce qualitative features of fin motion and suggest hypotheses regarding the fin's neural control.

Mechanical properties of a bio-inspired robotic knifefish with an undulatory propulsor

South American electric knifefish are a leading model system within neurobiology. Recent efforts have focused on understanding their biomechanics and relating this to their neural processing strategies. Knifefish swim by means of an undulatory fin that runs most of the length of their body, affixed to the belly. Propelling themselves with this fin enables them to keep their body relatively straight while swimming, enabling straightforward robotic implementation with a rigid hull. In this study, we examined the basic properties of undulatory swimming through use of a robot that was similar in some key respects to the knifefish. As we varied critical fin kinematic variables such as frequency, amplitude, and wavelength of sinusoidal traveling waves, we measured the force generated by the robot when it swam against a stationary sensor, and its velocity while swimming freely within a flow tunnel system. Our results show that there is an optimal operational region in the fin's kinematic parameter space. The optimal actuation parameters found for the robotic knifefish are similar to previously observed parameters for the black ghost knifefish, Apteronotus albifrons. Finally, we used our experimental results to show how the force generated by the robotic fin can be decomposed into thrust and drag terms. Our findings are useful for future bio-inspired underwater vehicles as well as for understanding the mechanics of knifefish swimming.

Stimulus predictability mediates a switch in locomotor smooth pursuit performance for Eigenmannia virescens

The weakly electric glass knifefish, Eigenmannia virescens, will swim forward and backward, using propulsion from an anal ribbon fin, in response to motion of a computer-controlled moving refuge. Fish were recorded performing a refuge-tracking behavior for sinusoidal (predictable) and sum-of-sines (pseudo-random) refuge trajectories. For all trials, we observed high coherence between refuge and fish trajectories, suggesting linearity of the tracking dynamics. But superposition failed: we observed categorical differences in tracking between the predictable single-sine stimuli and the unpredictable sum-of-sines stimuli. This nonlinearity suggests a stimulus-mediated adaptation. At all frequencies tested, fish demonstrated reduced tracking error when tracking single-sine trajectories and this was typically accompanied by a reduction in overall movement. Most notably, fish demonstrated reduced phase lag when tracking single-sine trajectories. These data support the hypothesis that fish generate an internal dynamical model of the stimulus motion, hence improving tracking of predictable trajectories (relative to unpredictable ones) despite similar or reduced motor cost. Similar predictive mechanisms based on the dynamics of stimulus movement have been proposed recently, but almost exclusively for nonlocomotor tasks by humans, such as oculomotor target tracking and posture control. These data suggest that such mechanisms might be common across taxa and behaviors.

Design, Implementation and Control of a Fish Robot with Undulating Fins

Biomimetic robots can potentially perform better than conventional robots in underwater vehicle designing. This paper describes the design of the propulsion system and depth control of a robotic fish. In this study, inspired by knife fish, we have designed and implemented an undulating fin to produce propulsive force. This undulating fin is a segmental anal fin that produces sinusoidal wave to propel the robot. The relationship between the individual fin segment and phase angles with the overall fin trajectory has also been discussed. This propulsive force can be adjusted and directed for fish robot manoeuvre by a mechanical system with two servomotors. These servomotors regulate the direction and depth of swimming. A wireless remote control system is designed to adjust the servomotors which enables us to control revolution, speed and phase differences of neighbor servomotors of fins. Finally, Field trials are conducted in an outdoor pool to demonstrate the relationship between robotic fish speed and fin parameters like phase difference, the number of phase and undulatory amplitude.

Aquatic manoeuvering with counter-propagating waves: a novel locomotive strategy

Many aquatic organisms swim by means of an undulating fin. These undulations often form a single wave travelling from one end of the fin to the other. However, when these aquatic animals are holding station or hovering, there is often a travelling wave from the head to the tail, and another moving from the tail to the head, meeting in the middle of the fin. Our study uses a biomimetic fish robot and computational fluid dynamics on a model of a real fish to uncover the mechanics of these inward counter-propagating waves. In addition, we compare the flow structure and upward force generated by inward counter-propagating waves to standing waves, unidirectional waves, and outward counter-propagating waves (i.e. one wave travelling from the middle of the fin to the head, and another wave travelling from the middle of the fin to the tail). Using digital particle image velocimetry to capture the flow structure around the fish robot, and computational fluid dynamics, we show that inward counter-propagating waves generate a clear mushroom-cloud-like flow structure with an inverted jet. The two streams of fluid set up by the two travelling waves 'collide' together (forming the mushroom cap) and collect into a narrow jet away from the cap (the mushroom stem). The reaction force from this jet acts to push the body in the opposite direction to the jet, perpendicular to the direction of movement provided by a single travelling wave. This downward jet provides a substantial increase in the perpendicular force when compared with the other types of fin actuation. Animals can thereby move upward if the fin is along the bottom midline of the body (or downward if on top); or left-right if the fins are along the lateral margins. In addition to illuminating how a large number of undulatory swimmers can use elongated fins to move in unexpected directions, the phenomenon of counter-propagating waves provides novel motion capabilities for systems using robotic undulators, an emerging technology for propelling underwater vehicles.

Energy-information trade-offs between movement and sensing

While there is accumulating evidence for the importance of the metabolic cost of information in sensory systems, how these costs are traded-off with movement when sensing is closely linked to movement is poorly understood. For example, if an animal needs to search a given amount of space beyond the range of its vision system, is it better to evolve a higher acuity visual system, or evolve a body movement system that can more rapidly move the body over that space? How is this trade-off dependent upon the three-dimensional shape of the field of sensory sensitivity (hereafter, sensorium)? How is it dependent upon sensorium mobility, either through rotation of the sensorium via muscles at the base of the sense organ (e.g., eye or pinna muscles) or neck rotation, or by whole body movement through space? Here we show that in an aquatic model system, the electric fish, a choice to swim in a more inefficient manner during prey search results in a higher prey encounter rate due to better sensory performance. The increase in prey encounter rate more than counterbalances the additional energy expended in swimming inefficiently. The reduction of swimming efficiency for improved sensing arises because positioning the sensory receptor surface to scan more space per unit time results in an increase in the area of the body pushing through the fluid, increasing wasteful body drag forces. We show that the improvement in sensory performance that occurs with the costly repositioning of the body depends upon having an elongated sensorium shape. Finally, we show that if the fish was able to reorient their sensorium independent of body movement, as fish with movable eyes can, there would be significant energy savings. This provides insight into the ubiquity of sensory organ mobility in animal design. This study exposes important links between the morphology of the sensorium, sensorium mobility, and behavioral strategy for maximally extracting energy from the environment. An “infomechanical” approach to complex behavior helps to elucidate how animals distribute functions across sensory systems and movement systems with their diverse energy loads.

Animals thrive by sensing their environment and using the information they've gathered to guide their movement. But collecting better information can result in less efficient movement: Bicycling while standing up on the pedals may help you see over obstacles ahead of you, but it causes more air drag, forcing your legs to work harder. Nocturnal weakly electric fish search for prey with their body tilted. This tilting more than doubles the resistance to movement from the water, but because the fish's ability to sense prey improves when tilted, it is better to swim this way. Beyond a certain amount of tilt, the costs of movement become too great. Interestingly, the benefit of tilting is dependent on the shape of the volume around the fish where it detects prey. We also found that if the fish was able to swivel its region of prey sensitivity, like a vision-based animal can shift its gaze, it would save energy. This conclusion helps us understand why animals like us can move our eyes. A Polish folk saying succinctly captures the gist: “He who doesn't have it in the head has it in the legs” (Ten kto nie ma w głowie ma w nogach).

Optimal movement in the prey strikes of weakly electric fish: a case study of the interplay of body plan and movement capability

Animal behaviour arises through a complex mixture of biomechanical, neuronal, sensory and control constraints. By focusing on a simple, stereotyped movement, the prey capture strike of a weakly electric fish, we show that the trajectory of a strike is one which minimizes effort. Specifically, we model the fish as a rigid ellipsoid moving through a fluid with no viscosity, governed by Kirchhoff's equations. This formulation allows us to exploit methods of discrete mechanics and optimal control to compute idealized fish trajectories that minimize a cost function. We compare these with the measured prey capture strikes of weakly electric fish from a previous study. The fish has certain movement limitations that are not incorporated in the mathematical model, such as not being able to move sideways. Nonetheless, we show quantitatively that the computed least-cost trajectories are remarkably similar to the measured trajectories. Since, in this simplified model, the basic geometry of the idealized fish determines the favourable modes of movement, this suggests a high degree of influence between body shape and movement capability. Simplified minimal models and optimization methods can give significant insight into how body morphology and movement capability are closely attuned in fish locomotion.