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.

No difference between critical and sprint swimming speeds for two galaxiid species

Researchers have used laboratory experiments to examine how fish might be affected by anthropogenic alterations and conclude how best to adjust fish passage and culvert remediation designs in response. A common way to document swimming performance for this purpose is measuring fish critical swimming speed (U_crit ). Nonetheless, the U_crit protocol as defined by Brett [(1964) Journal of the Fisheries Research Board of Canada, 21, 1183-1226] may be inappropriate for studying swimming performance and determining how it relates to upstream migration in benthic fish, as they may not actively swim throughout the entire U_crit test. An alternative method to estimate swimming performance is sprint swimming speed (U_sprint ), which is suggested to be a measure of the burst speed of fish rather than maximum sustained swimming speed. The authors conducted comparative swimming performance experiments to evaluate whether U_sprint can be used to compare swimming performance of benthic species to that of pelagic, actively swimming species. They measured individual swimming speeds of īnanga (Galaxias maculatus), an actively swimming pelagic species, and banded kōkopu (Galaxias fasciatus), a fish that exhibits benthic station-holding behaviour, using both the U_sprint and U_crit test. Experiments revealed that no significant statistical difference between swimming speeds was estimated using the U_crit and U_sprint test protocols for both G. maculatus and G. fasciatus. The result of this study suggests that fish swimming speeds obtained using these two methods are comparable for the species used in this study. By using U_sprint for benthic-associated fish and U_crit for pelagic fish, we may be able to compare a broader range of species' swimming abilities for use in a fish passage context.

Bioinspired Propulsion System for a Thunniform Robotic Fish

The paper describes a bioinspired propulsion system for a robotic fish model. The system is based on a combination of an elastic chord with a tail fin fixed on it. The tail fin is connected to a servomotor by two symmetric movable thrusts simulating muscle contractions. The propulsion system provides the oscillatory tail movement with controllable amplitude and frequency. Tail oscillations translate into the movement of the robotic fish implementing the thunniform principle of locomotion. The shape of the body and the tail fin of the robotic fish were designed using a computational model simulating a virtual body in an aquatic medium. A prototype of a robotic fish was constructed and tested in experimental conditions. Dependencies of fish velocity on the dynamic characteristics of tail oscillations were analyzed. In particular, it was found that the robot's speed increased as the frequency of tail fin oscillations grew. We also found that for fixed frequencies, an increase in the oscillation amplitude lead to an increase in the swimming speed only up to a certain threshold. Further growth of the oscillation amplitude lead to a weak increase in speed at higher energy costs.

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.

Fishes regulate tail-beat kinematics to minimize speed-specific cost of transport

Energetic expenditure is an important factor in animal locomotion. Here we test the hypothesis that fishes control tail-beat kinematics to optimize energetic expenditure during undulatory swimming. We focus on two energetic indices used in swimming hydrodynamics, cost of transport and Froude efficiency. To rule out one index in favour of another, we use computational-fluid dynamics models to compare experimentally observed fish kinematics with predicted performance landscapes and identify energy-optimized kinematics for a carangiform swimmer, an anguilliform swimmer and larval fishes. By locating the areas in the predicted performance landscapes that are occupied by actual fishes, we found that fishes use combinations of tail-beat frequency and amplitude that minimize cost of transport. This energy-optimizing strategy also explains why fishes increase frequency rather than amplitude to swim faster, and why fishes swim within a narrow range of Strouhal numbers. By quantifying how undulatory-wave kinematics affect thrust, drag, and power, we explain why amplitude and frequency are not equivalent in speed control, and why Froude efficiency is not a reliable energetic indicator. These insights may inspire future research in aquatic organisms and bioinspired robotics using undulatory propulsion.

Hydrodynamic advantages of in-line schooling

Fish benefit energetically when swimming in groups, which is reflected in lower tail-beat frequencies for maintaining a given speed. Recent studies further show that fish save the most energy when swimming behind their neighbor such that both the leader and the follower benefit. However, the mechanisms underlying such hydrodynamic advantages have thus far not been established conclusively. The long-standing drafting hypothesis-reduction of drag forces by judicious positioning in regions of reduced oncoming flow-fails to explain advantages of in-line schooling described in this work. We present an alternate hypothesis for the hydrodynamic benefits of in-line swimming based on enhancement of propulsive thrust. Specifically, we show that an idealized school consisting of in-line pitching foils gains hydrodynamic benefits via two mechanisms that are rooted in the undulatory jet leaving the leading foil and impinging on the trailing foil: (i) leading-edge suction on the trailer foil, and (ii) added-mass push on the leader foil. Our results demonstrate that the savings in power can reach as high as 70% for a school swimming in a compact arrangement. Informed by these findings, we designed a modification of the tail propulsor that yielded power savings of up to 56% in a self-propelled autonomous swimming robot. Our findings provide insights into hydrodynamic advantages of fish schooling, and also enable bioinspired designs for significantly more efficient propulsion systems that can harvest some of their energy left in the flow.

Tunabot Flex: a tuna-inspired robot with body flexibility improves high-performance swimming

Tunas are flexible, high-performance open ocean swimmers that operate at high frequencies to achieve high swimming speeds. Most fish-like robotic systems operate at low frequencies (≤3 Hz) resulting in low swim speeds (≤1.5 body lengths per second), and the cost of transport (COT) is often one to four orders of magnitude higher than that of tunas. Furthermore, the impact of body flexibility on high-performance fish swimming remains unknown. Here we design and test a research platform based on yellowfin tuna (Thunnus albacares) to investigate the role of body flexibility and to close the performance gap between robotic and biological systems. This single-motor platform, termed Tunabot Flex, measures 25.5 cm in length. Flexibility is varied through joints in the tail to produce three tested configurations. We find that increasing body flexibility improves self-propelled swimming speeds on average by 0.5 body lengths per second while reducing the minimum COT by 53%. The most flexible configuration swims 4.60 body lengths per second with a tail beat frequency of 8.0 Hz and a COT measuring 18.4 J kg^-1m^-1. We then compare these results in addition to the midline kinematics, stride length, and Strouhal number with yellowfin tuna data. The COT of Tunabot Flex's most flexible configuration is less than a half-order of magnitude greater than that of yellowfin tuna across all tested speeds. Tunabot Flex provides a new baseline for the development of future bio-inspired underwater vehicles that aim to explore a fish-like, high-performance space and close the gap between engineered robotic systems and fish swimming ability.

Fish-like three-dimensional swimming with an autonomous, multi-fin, and biomimetic robot

Fish migrate across considerable distances and exhibit remarkable agility to avoid predators and feed. Fish swimming performance and maneuverability remain unparalleled when compared to robotic systems, partly because previous work has focused on robots and flapping foil systems that are either big and complex, or tethered to external actuators and power sources. By contrast, we present a robot-the Finbot-that combines high degrees of autonomy, maneuverability, and biomimicry with miniature size (160 cm³). Thus, it is well-suited for controlled three-dimensional experiments on fish swimming in confined laboratory test beds. Finbot uses four independently controllable fins and sensory feedback for precise closed-loop underwater locomotion. Different caudal fins can be attached magnetically to reconfigure Finbot for swimming at top speed (122 mm s^-1≡ 1 BL s^-1) or minimal cost of transport (CoT = 8.2) at Strouhal numbers as low as 0.53. We conducted more than 150 experiments with 12 different caudal fins to measure three key characteristics of swimming fish: (i) linear speed-frequency relationships, (ii) U-shaped CoT, and (iii) reverse Kármán wakes (visualized with particle image velocimetry). More fish-like wakes appeared where the CoT was low. By replicating autonomous multi-fin fish-like swimming, Finbot narrows the gap between fish and fish-like robots and can address open questions in aquatic locomotion, such as optimized propulsion for new fish robots, or the hydrodynamic principles governing the energy savings in fish schools.

Modal decompositions of the kinematics of Crevalle jack and the fluid-caudal fin interaction

To understand the governing mechanisms of bio-inspired swimming has always been challenging due to intense interactions between flexible bodies of natural aquatic species and water around them. Advanced modal decomposition techniques provide us with tools to develop more in-depth understating about these complex dynamical systems. In this paper, we employ proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques to extract energetically strongest spatio-temporal orthonormal components of complex kinematics of a Crevalle jack (Caranx hippos) fish. Then, we present a computational framework for handling fluid-structure interaction related problems in order to investigate their contributions towards the overall dynamics of highly nonlinear systems. We find that the undulating motion of this fish can be described by only two standing-wave like spatially orthonormal modes. Constructing the data set from our numerical simulations for flows over the membranous caudal fin of the jack fish, our modal analyses reveal that only the first few modes receive energy from both the fluid and structure, but the contribution of the structure in the remaining modes is minimal. For the viscous and transitional flow conditions considered here, both spatially and temporally orthonormal modes show strikingly similar coherent flow structures. Our investigations are expected to assist in developing data-driven reduced-order mathematical models to examine the dynamics of bio-inspired swimming robots and develop new and effective control strategies to bring their performance closer to real fish species.

Jumping archer fish exhibit multiple modes of fin-fin interaction

Aquatic organisms jumping for aerial prey require high-performance propulsion, accurate aim, and trajectory control to succeed. Archer fish, capable of jumping up to twice their body length out of the water, address these considerations through multifaceted fin and body kinematics. In this study, we utilized 3D synthetic aperture particle image velocimetry to visualize the wakes of archer fish throughout the jumping process. We found that multiple modes of interaction between the anal and caudal fins occur during jump behaviors. Time-resolved volumetric measurements presented herein illustrate the hydrodynamics of each interaction mode in detail. Additionally, regardless of which fin uses and interactions were exhibited during a jump, we found similar relationships between the cumulative impulse of multiple propulsive vortices in the wake and the instantaneous ballistic momentum of the fish. Our results suggests that fin use may compensate for variations in individual kinematic events and in the aiming posture assumed prior to jumping and highlight how interactions between tailbeats and other fins help the archer fish reach necessary prey heights in a spatially- and visually-constrained environment. In the broader context of bioinspired propulsion, the archer fish exemplifies that multiple beneficial hydrodynamic interactions can be generated in a high-performance scenario using a single set of actuators.

Airfoil-like mechanics generate thrust on the anterior body of swimming fishes

The anterior body of many fishes is shaped like an airfoil turned on its side. With an oscillating angle to the swimming direction, such an airfoil experiences negative pressure due to both its shape and pitching movements. This negative pressure acts as thrust forces on the anterior body. Here, we apply a high-resolution, pressure-based approach to describe how two fishes, bluegill sunfish (Lepomis macrochirus Rafinesque) and brook trout (Salvelinus fontinalis Mitchill), swimming in the carangiform mode, the most common fish swimming mode, generate thrust on their anterior bodies using leading-edge suction mechanics, much like an airfoil. These mechanics contrast with those previously reported in lampreys-anguilliform swimmers-which produce thrust with negative pressure but do so through undulatory mechanics. The thrust produced on the anterior bodies of these carangiform swimmers through negative pressure comprises 28% of the total thrust produced over the body and caudal fin, substantially decreasing the net drag on the anterior body. On the posterior region, subtle differences in body shape and kinematics allow trout to produce more thrust than bluegill, suggesting that they may swim more effectively. Despite the large phylogenetic distance between these species, and differences near the tail, the pressure profiles around the anterior body are similar. We suggest that such airfoil-like mechanics are highly efficient, because they require very little movement and therefore relatively little active muscular energy, and may be used by a wide range of fishes since many species have appropriately shaped bodies.

Aracaniform Swimming: A Proposed New Category of Swimming Mode in Bony Fishes (Teleostei: Tetraodontiformes: Aracanidae)

The deepwater boxfishes of the family Aracanidae are the phylogenetic sister group of the shallow-water, generally more tropical boxfishes of the family Ostraciidae. Both families are among the most derived groups of teleosts. All members of both families have armored bodies, the forward 70% of which are enclosed in rigid bony boxes (carapaces). There is substantial intragroup variation in both groups in body shapes, sizes, and ornamentation of the carapaces. Swimming-related morphology, swimming mode, biomechanics, kinematics, and hydrodynamics have been studied in detail in multiple species of the ostraciids. Ostraciids are all relatively high-performance median and paired fin swimmers. They are highly maneuverable. They swim rectilinearly with substantial dynamic stability and efficiency. Aracanids have not been previously studied in these respects. This article describes swimming-related aspects of morphology, swimming modes, biomechanics, and kinematics in two south Australian species (striped cowfish and ornate cowfish) that are possibly representative of the entire group. These species differ morphologically in many respects, both from each other and from ostraciids. There are differences in numbers, sizes, and placements of keels on carapaces. The most important differences from ostraciids are openings in the posterior edges of the carapaces behind the dorsal and anal fins. The bases of those fins in ostraciids are enclosed in bone. The openings in aracanids free the fins and tail to move. As a result, aracanids are body and caudal fin swimmers. Their overall swimming performances are less stable, efficient, and effective. We propose establishing a new category of swimming mode for bony fishes called "aracaniform swimming."

Simple phalanx pattern leads to energy saving in cohesive fish schooling

The question of how individuals in a population organize when living in groups arises for systems as different as a swarm of microorganisms or a flock of seagulls. The different patterns for moving collectively involve a wide spectrum of reasons, such as evading predators or optimizing food prospection. Also, the schooling pattern has often been associated with an advantage in terms of energy consumption. In this study, we use a popular aquarium fish, the red nose tetra fish, Hemigrammus bleheri, which is known to swim in highly cohesive groups, to analyze the schooling dynamics. In our experiments, fish swim in a shallow-water tunnel with controlled velocity, and stereoscopic video recordings are used to track the 3D positions of each individual in a school, as well as their tail-beating kinematics. Challenging the widespread idea of fish favoring a diamond pattern to swim more efficiently [Weihs D (1973) Nature 241:290-291], we observe that when fish are forced to swim fast-well above their free-swimming typical velocity, and hence in a situation where efficient swimming would be favored-the most frequent configuration is the "phalanx" or "soldier" formation, with all individuals swimming side by side. We explain this observation by considering the advantages of tail-beating synchronization between neighbors, which we have also characterized. Most importantly, we show that schooling is advantageous as compared with swimming alone from an energy-efficiency perspective.

Analytical insights into optimality and resonance in fish swimming

This paper provides analytical insights into the hypothesis that fish exploit resonance to reduce the mechanical cost of swimming. A simple body-fluid fish model, representing carangiform locomotion, is developed. Steady swimming at various speeds is analysed using optimal gait theory by minimizing bending moment over tail movements and stiffness, and the results are shown to match with data from observed swimming. Our analysis indicates the following: thrust-drag balance leads to the Strouhal number being predetermined based on the drag coefficient and the ratio of wetted body area to cross-sectional area of accelerated fluid. Muscle tension is reduced when undulation frequency matches resonance frequency, which maximizes the ratio of tail-tip velocity to bending moment. Finally, hydrodynamic resonance determines tail-beat frequency, whereas muscle stiffness is actively adjusted, so that overall body-fluid resonance is exploited.

The effect of flow speed and body size on Kármán gait kinematics in rainbow trout

We have little understanding of how fish hold station in unsteady flows. Here, we investigated the effect of flow speed and body size on the kinematics of rainbow trout Kármán gaiting behind a 5 cm diameter cylinder. We established a set of criteria revealing that not all fish positioned in a vortex street are Kármán gaiting. By far the highest probability of Kármán gaiting occurred at intermediate flow speeds between 30 and 70 cm s(-1). We show that trout Kármán gait in a region of the cylinder wake where the velocity deficit is about 40% of the nominal flow. We observed that the relationships between certain kinematic and flow variables are largely preserved across flow speeds. Tail-beat frequency matched the measured vortex shedding frequency, which increased linearly with flow speed. Body wave speed was about 25% faster than the nominal flow velocity. At speeds where fish have a high probability of Kármán gaiting, body wavelength was about 25% longer than the cylinder wake wavelength. Likewise, the lateral (i.e. cross-stream) amplitude of the tail tip was about 50% greater than the expected lateral spacing of the cylinder vortices, while the body center amplitude was about 70% less. Lateral body center acceleration increased quadratically with speed. Head angle decreased with flow speed. While these values are different from those found in fish swimming in uniform flow, the strategy for locomotion is the same; fish adjust to increasing flow by increasing their tail-beat frequency. Body size also played a role in Kármán gaiting kinematics. Tail-beat amplitudes of Kármán gaiting increased with body size, as in freestream swimming, but were almost three times larger in magnitude. Larger fish had a shorter body wavelength and slower body wave speed than smaller fish, which is a surprising result compared with freestream swimming, where body wavelength and wave speed increased with size. In contrast to freestream swimming, tail-beat frequency for Kármán gaiting fish did not depend on body size and was a function of the vortex shedding frequency.