Passive mechanical models of fish caudal fins: effects of shape and stiffness on self-propulsion

When to Go Against the Flow: Examining Patterns of Performance Over Multiday Migration Events in the Hawaiian Stream Fish, 'O'opu Nōpili (Sicyopterus stimpsoni)

Many animals migrate across regions of their geographic range as part of extended events, with groups of individuals proceeding through areas of travel on several successive days. Early migrating individuals may have an advantage over late migrating individuals by gaining early access to the resources at the eventual destination. For situations where early access to resources would provide an advantage, specific sets of locomotor traits might be found among individuals that are earlier migrators. We tested for associations between migration timing and traits related to escape responses, climbing, and morphology in the amphidromous Hawaiian stream goby, 'o'opu nōpili (Sicyopterus stimpsoni). In this species, juvenile fish migrate in pulses over several days immediately following flash floods. We collected daily measurements of escape responses and waterfall climbing from juvenile fish arriving at streams from the ocean. We found that escape performance showed mainly stochastic variation across migrating individuals tested on successive days. In contrast, some metrics of climbing performance decrease over successive pulses during a migration event. We also found more variation in body shape among fish from early pulses during migration events compared to later in pulses. These results could have implications for guiding conservation efforts, identifying critical time windows for protection as periods with the greatest likelihood of successful migrants.

Numerical Study on the Hydrodynamic Performance of a Flexible Caudal Fin with Different Trailing-Edge Shapes

This paper presents a three-dimensional fluid-structure-coupled simulation of a flexible caudal fin with different trailing-edge shapes. The influences of caudal-fin shape on hydrodynamic performance are investigated by comparing the results of a simplified model of a square caudal fin with forked and deeply forked caudal fins under a wider range of non-dimensional flapping frequency, 0.6 < f* < 1.5, where f* is the ratio of flapping frequency to the natural frequency of each caudal fin, i.e., f* = f/fn. The leading edge of each caudal fin is forced to oscillate vertically in a water tank with zero free-stream conditions. The numerical results show that the amount of forking in the geometry of the caudal fin has significant effects on its hydrodynamic performance. A comparison of thrust coefficients shows that the square caudal fin has a greater thrust coefficient in the non-dimensional frequency range of 0.6 < f* < 1.2, while the deeply forked caudal fin generates higher thrust when 1.2 < f* < 1.5. In terms of propulsive efficiency, the square caudal fin is more efficient when 0.6 < f* < 0.9, while the propulsive efficiency of a deeply forked caudal fin is significantly enhanced when 0.9 < f* < 1.5. Based on our results, the deeply forked caudal fin has greater thrust coefficients and a higher propulsive efficiency in a higher frequency range than the natural frequency of each caudal fin. The thrust characteristics and flow fields around each caudal fin are investigated in detail.

Insights into Flexible Bioinspired Fins for Unmanned Underwater Vehicle Systems through Deep Learning

The last few decades have led to the rise of research focused on propulsion and control systems for bio-inspired unmanned underwater vehicles (UUVs), which provide more maneuverable alternatives to traditional UUVs in underwater missions. Recent work has explored the use of time-series neural network surrogate models to predict thrust and power from vehicle design and fin kinematics. We expand upon this work, creating new forward neural network models that encapsulate the effects of the material stiffness of the fin on its kinematic performance, thrust, and power, and are able to interpolate to the full spectrum of kinematic gaits for each material. Notably, we demonstrate through testing of holdout data that our developed forward models capture the thrust and power associated with each set of parameters with high resolution, enabling highly accurate predictions of previously unseen gaits and thrust and FOM gains through proper materials and kinematics selection. As propulsive efficiency is of utmost importance for flapping-fin UUVs in order to extend their range and endurance for essential operations, a non-dimensional figure of merit (FOM), derived from measures of propulsive efficiency, is used to evaluate different fin designs and kinematics and allow for comparison with other bio-inspired platforms. We use the developed FOM to analyze optimal gaits and compare the performance between different fin materials. The forward model demonstrates the ability to capture the highest thrust and FOM with good precision, which enables us to improve thrust generation by 83.89% and efficiency by 137.58% with proper fin stiffness and kinematics selection, allowing us to improve material selection for bio-inspired fin design.

Effects of caudal fin stiffness on optimized forward swimming and turning maneuver in a robotic swimmer

In animal and robot swimmers of body and caudal fin (BCF) form, hydrodynamic thrust is mainly produced by their caudal fins, the stiffness of which has profound effects on both thrust and efficiency of swimming. Caudal fin stiffness also affects the motor control and resulting swimming gaits that correspond to optimal swimming performance; however, their relationship remains scarcely explored. Here using magnetic, modular, undulatory robots (μBots), we tested the effects of caudal fin stiffness on both forward swimming and turning maneuver. We developed six caudal fins with stiffness of more than three orders of difference. For aμBot equipped with each caudal fin (andμBot absent of caudal fin), we applied reinforcement learning in experiments to optimize the motor control for maximizing forward swimming speed or final heading change. The motor control ofμBot was generated by a central pattern generator for forward swimming or by a series of parameterized square waves for turning maneuver. In forward swimming, the variations in caudal fin stiffness gave rise to three modes of optimized motor frequencies and swimming gaits including no caudal fin (4.6 Hz), stiffness <10-4Pa m4(∼10.6 Hz) and stiffness >10-4Pa m4(∼8.4 Hz). Swimming speed, however, varied independently with the modes of swimming gaits, and reached maximal at stiffness of 0.23 × 10-4Pa m4, with theμBot without caudal fin achieving the lowest speed. In turning maneuver, caudal fin stiffness had considerable effects on the amplitudes of both initial head steering and subsequent recoil, as well as the final heading change. It had relatively minor effect on the turning motor program except for theμBots without caudal fin. Optimized forward swimming and turning maneuver shared an identical caudal fin stiffness and similar patterns of peduncle and caudal fin motion, suggesting simplicity in the form and function relationship inμBot swimming.

Hydrodynamics of Butterfly-Mode Flapping Propulsion of Dolphin Pectoral Fins with Elliptical Trajectories

This article aims to numerically study the hydrodynamic performance of the bionic dolphin equipped with a pair of rigid pectoral fins. We use dynamic-grid technology and user-defined functions to simulate a novel butterfly-mode flapping propulsion of the fins. This pattern of propulsion is composed of three angular degrees of freedom including the pitch angle ϕp, the azimuth angle ϕa and the roll angle ϕr, which can be divided into four stages for analysis within a single cycle. The stroke of one single pectoral fin can be approximated as an ellipse trajectory, where the amplitudes of ϕa and ϕp, respectively, determine the major and minor axes of the ellipse. The fluid dynamics involved in the specific butterfly pattern is mathematically formulated, and numerical simulation is conducted to investigate the propulsion quantitatively. The results show that the dolphin with a higher water striking frequency f can acquire higher propulsion speed and efficiency. Furthermore, the shape of the ellipse trajectory under different conditions could also have different propulsion effects. The periodic generation and disappearance of vortex structures in the butterfly flapping mode show the evolution process of fluid flow around a pair of pectoral fins, which reveals the influence of motion parameters on fluid dynamics under different working conditions.

The role of hydrodynamics in collective motions of fish schools and bioinspired underwater robots

Collective behaviour defines the lives of many animal species on the Earth. Underwater swarms span several orders of magnitude in size, from coral larvae and krill to tunas and dolphins. Agent-based algorithms have modelled collective movements of animal groups by use of social forces, which approximate the behaviour of individual animals. But details of how swarming individuals interact with the fluid environment are often under-examined. How do fluid forces shape aquatic swarms? How do fish use their flow-sensing capabilities to coordinate with their schooling mates? We propose viewing underwater collective behaviour from the framework of fluid stigmergy, which considers both physical interactions and information transfer in fluid environments. Understanding the role of hydrodynamics in aquatic collectives requires multi-disciplinary efforts across fluid mechanics, biology and biomimetic robotics. To facilitate future collaborations, we synthesize key studies in these fields.

The effect of tail stiffness on a sprawling quadruped locomotion

A distinctive feature of quadrupeds that is integral to their locomotion is the tail. Tails serve many purposes in biological systems, including propulsion, counterbalance, and stabilization while walking, running, climbing, or jumping. Similarly, tails in legged robots may augment the stability and maneuverability of legged robots by providing an additional point of contact with the ground. However, in the field of terrestrial bio-inspired legged robotics, the tail is often ignored because of the difficulties in design and control. In this study, we test the hypothesis that a variable stiffness robotic tail can improve the performance of a sprawling quadruped robot by enhancing its stability and maneuverability in various environments. In order to validate our hypothesis, we integrated a cable-driven, flexible tail with multiple segments into the underactuated sprawling quadruped robot, where a single servo motor working alongside a reel and cable mechanism regulates the tail's stiffness. Our results demonstrated that by controlling the stiffness of the tail, the stability of locomotion on rough terrain and the climbing ability of the robot are improved compared to the movement with a rigid tail and no tail. Our findings highlight that constant ground support provided by the flexible tail is key to maintaining stable locomotion. This ensured a predictable gait cycle, eliminating unexpected turning and slipping, resulting in an increase in locomotion speed and efficiency. Additionally, we observed the robot's enhanced climbing ability on surfaces inclined up to 20°. The flexibility of the tail enabled the robot to overcome obstacles without external sensing, exhibiting significant adaptability across various terrains.

A Comparative and Collaborative Study of the Hydrodynamics of Two Swimming Modes Applicable to Dolphins

This paper presents a hydrodynamics study that examines the comparison and collaboration of two swimming modes relevant to the universality of dolphins. This study utilizes a three-dimensional virtual swimmer model resembling a dolphin, which comprises a body and/or caudal fin (BCF) module, as well as a medium and/or paired fin (MPF) module, each equipped with predetermined kinematics. The manipulation of the dolphin to simulate various swimming modes is achieved through the application of overlapping grids in conjunction with the parallel hole cutting technique. The findings demonstrate that the swimming velocity and thrust attained through the single BCF mode consistently surpass those achieved through the single MPF mode and collaborative mode. Interestingly, the involvement of the MPF mode does not necessarily contribute to performance enhancement. Nevertheless, it is encouraging to note that adjusting the phase difference between the two modes can partially mitigate the limitations associated with the MPF mode. To further investigate the potential advantages of dual-mode collaboration, we conducted experiments by increasing the MPF frequency while keeping the BCF frequency constant, thus introducing the concept of frequency ratio (β). In comparison to the single BCF mode, the collaborative mode with a high β exhibits superior swimming velocity and thrust. Although its efficiency experiences a slight decrease, it tends to stabilize. The corresponding flow structure indirectly verifies the favorable impact of collaboration.

Experimental analysis of the sweepback angle effect on the thrust generation of a robotic penguin wing

Penguins have evolved excellent swimming skills as diving birds, benefiting from their agile wings. This paper experimentally analyzes the effects of the wing sweepback angle on thrust generation using a robotic penguin wing. A developed wing mechanism that can realize penguin-like flapping and feathering motion was used for actuating five alternative wing models, with different sweepback angles ranging from 0° to 50°. Force measurements under a steady water flow were conducted for both fixed and flapping states for all wing models. The results showed that small sweepback angles of 30° or less in the fixed state caused a steep lift curve and a moderate sweepback angle of 30° produced the largest lift-to-drag ratio. In the flapping state, the smaller sweepback wings generated a larger net thrust for the same wing motion, whereas the larger-sweepback wings produced more thrust under the same Strouhal number. The findings also revealed that larger sweepback wings more easily achieve the maximum net thrust in terms of less angle-of-attack control. In contrast, the hydrodynamic efficiency was not greatly affected by the sweepback. Regardless of the sweepback, the trend of the efficiency increasing with increasing flow speed indicates that the penguin wings can be more suitable for high-speed locomotion for higher hydrodynamic efficiency.

A tale of two fish tails: does a forked tail really perform better than a truncate tail when cruising?

Many fishes use their tail as the main thrust producer during swimming. This fin's diversity in shape and size influences its physical interactions with water as well as its ecological functions. Two distinct tail morphologies are common in bony fishes: flat, truncate tails which are best suited for fast accelerations via drag forces, and forked tails that promote economical, fast cruising by generating lift-based thrust. This assumption is based primarily on studies of the lunate caudal fin of Scombrids (i.e. tuna, mackerel), which is comparatively stiff and exhibits an airfoil-type cross-section. However, this is not representative of the more commonly observed and taxonomically widespread flexible forked tail, yet similar assumptions about economical cruising are widely accepted. Here, we present the first comparative experimental study of forked versus truncate tail shape and compare the fluid mechanical properties and energetics of two common nearshore fish species. We examined the hypothesis that forked tails provide a hydrodynamic advantage over truncate tails at typical cruising speeds. Using experimentally derived pressure fields, we show that the forked tail produces thrust via acceleration reaction forces like the truncate tail during cruising but at increased energetic costs. This reduced efficiency corresponds to differences in the performance of the two tail geometries and body kinematics to maintain similar overall thrust outputs. Our results offer insights into the benefits and tradeoffs of two common fish tail morphologies and shed light on the functional morphology of fish swimming to guide the development of bio-inspired underwater technologies.

How Non-Uniform Stiffness Affects the Propulsion Performance of a Biomimetic Robotic Fish

Live fish in nature exhibit various stiffness characteristics. The anguilliform swimmer, like eels, has a relatively flexible body, while the thunniform swimmer, like the swordfishes, has a much stiffer body. Correspondingly, in the design of biomimetic robotic fish, how to balance the non-uniform stiffness to achieve better propulsion performance is an essential question needed to be answered. In this paper, we conduct an experimental study on this question. First, a customized experimental platform is built, which eases the adjustment of the non-uniform stiffness ratio, the stiffness of the flexible part, the flapping frequency, and the flapping amplitude. Second, extensive experiments are carried out, finding that to maximize the propulsion performance of the biomimetic robotic fish, the non-uniform stiffness ratio is required to adapt to different locomotor parameters. Specifically, the non-uniform stiffness ratio needs to be reduced when the robotic fish works at low frequency, and it needs to be increased when the robotic fish works at high frequency. Finally, detailed discussions are given to further analyze the experimental results. Overall, this study can shed light on the design of a non-uniform biomimetic robotic fish, which helps to increase its propulsion performance.

Using natural language processing to find research topics in Living Machines conferences and their intersections with Bioinspiration & Biomimetics publications

The number of published scientific articles is increasing dramatically and makes it difficult to keep track of research topics. This is particularly difficult in interdisciplinary research areas where different communities from different disciplines are working together. It would be useful to develop methods to automate the detection of research topics in a research domain. Here we propose a natural language processing (NLP) based method to automatically detect topics in defined corpora. We start by automatically generating a global state of the art of Living Machines conferences. Our NLP-based method classifies all published papers into different clusters corresponding to the research topic published in these conferences. We perform the same study on all papers published in the journals Bioinspiration & Biomimetics and Soft Robotics. In total this analysis concerns 2099 articles. Next, we analyze the intersection between the research themes published in the conferences and the corpora of these two journals. We also examine the evolution of the number of papers per research theme which determines the research trends. Together, these analyses provide a snapshot of the current state of the field, help to highlight open questions, and provide insights into the future.

Thrust Improvement of a Biomimetic Robotic Fish by Using a Deformable Caudal Fin

In nature, live fish has various deformable fins which are capable to promote the swimming speed, efficiency, stability, and thrust generation. However, this feature is rarely possessed by current man-made biomimetic robotic fishes. In this paper, a novel deformable caudal fin platform is proposed to improve thrust generation of biomimetic robotic fish. First, the design of the deformable caudal fin is given, which includes a servo motor, a gear-based transmission mechanism, fin bones, and silica membrane. Second, an improved Central Pattern Generator (CPG) model was developed to coordinately control the flapping of the tail and the deformation of the caudal fin. More specifically, three deformation patterns, i.e., conventional nondeformable mode, sinusoidal-based mode, instant mode, of the caudal fin are investigated. Third, extensive experiments are conducted to explore the effects of deformation of the caudal fin on the thrust generation of the biomimetic robotic fish. It was found that the instant mode of the caudal fin has the largest thrust, which sees a 27.5% improvement compared to the conventional nondeformable mode, followed by the sinusoidal-based mode, which also sees an 18.2% improvement. This work provides a novel way to design and control the deformation of the caudal fin, which sheds light on the development of high-performance biomimetic robotic fish.

Biomimetic Aquatic Robots Based on Fluid-Driven Actuators: A Review

Biomimetic aquatic robots are a promising solution for marine applications such as internal pipe inspection, beach safety, and animal observation because of their strong manoeuvrability and low environmental damage. As the application field of robots has changed from a structured known environment to an unstructured and unknown territory, the disadvantage of the low efficiency of the propeller propulsion has become more crucial. Among the various actuation methods of biomimetic robots, many researchers have utilised fluid actuation as fluid is clean, environmentally friendly, and easy to obtain. This paper presents a literature review of the locomotion mode, actuation method, and typical works on fluid-driven bionic aquatic robots. The actuator and structural material selection is then discussed, followed by research direction and application prospects of fluid-driven bionic aquatic robots.

A fish-like soft-robotic model generates a diversity of swimming patterns

Fish display a versatile array of swimming patterns, and frequently demonstrate the ability to switch between these patterns altering kinematics as necessary. Many hard and soft robotic systems have sought to understand a variety of aspects pertaining to undulatory swimming, but most have been built to focus solely on a subset of those swimming patterns. We have expanded upon a previous soft robotic model, the pneufish, so that it can now simulate a variety of swimming patterns, much like a real fish. We explore the performance space available for this longer soft robotic model, which we call the quad-pneufish, with particular attention to the effects on lateral forces and z-torques produced during locomotion. We show that the quad-pneufish is capable of achieving a variety of midline patterns - including more realistic, fish-like patterns - and introducing a slight amount of co-activation between the left and right sides maintains forward thrust while decreasing lateral forces, indicating an increase in swimming efficiency. Robotic systems that are capable of producing an array of swimming movement patterns hold promise as experimental platforms for studying the diversity of fish locomotor patterns.

Tunable stiffness in fish robotics: mechanisms and advantages

One of the emerging themes of fish-inspired robotics is flexibility. Adding flexibility to the body, joints, or fins of fish-inspired robots can significantly improve thrust and/or efficiency during locomotion. However, the optimal stiffness depends on variables such as swimming speed, so there is no one 'best' stiffness that maximizes efficiency in all conditions. Fish are thought to solve this problem by using muscular activity to tune their body and fin stiffness in real-time. Inspired by fish, some recent robots sport polymer actuators, adjustable leaf springs, or artificial tendons that tune stiffness mechanically. Models and water channel tests are providing a theoretical framework for stiffness-tuning strategies that devices can implement. The strategies can be thought of as analogous to car transmissions, which allow users to improve efficiency by tuning gear ratio with driving speed. We provide an overview of the latest discoveries about (1) the propulsive benefits of flexibility, particularlytunableflexibility, and (2) the mechanisms and strategies that fish and fish-inspired robots use to tune stiffness while swimming.

Testing the effects of body depth on fish maneuverability via robophysical models

Fish show a wide diversity of body shapes which affect many aspects of their biology, including swimming and feeding performance, and defense from predators. Deep laterally compressed bodies are particularly common, and have evolved multiple times in different families. Functional hypotheses that explain these trends include predator defense and increased maneuverability. While there is strong evidence that increasing body depth helps fish avoid gape-limited predators, the evidence that body shape increases a fish's maneuverability is ambiguous. We used a two-pronged approach to explore the effects of body shape on the control of maneuvers using both live fish and a robotic model that allowed us to independently vary body shape. We captured ventral video of two tetra species (Gymnocorymbus ternetziandAphyocharax anisitsi) performing a wide range of maneuvers to confirm that both species of live fish utilize fundamentally similar body deformations to execute a turn, despite their different body depths. Both species use a propagating 'pulse' of midline curvature that is qualitatively similar to prior studies and displayed similar trends in the relationships between body kinematics and performance. We then tested the robotic model's maneuverability, defined as the total heading change and maximum centripetal acceleration generated during a single pulse, at a range of different input kinematics across three body shapes. We found that deepening bodies increase the robot's ability to change direction and centripetal acceleration, though centripetal acceleration exhibits diminishing returns beyond a certain body depth. By using a robotic model, we were able to isolate the effects of body shape on maneuverability and clarify this confounded relationship. Studying the functional morphology of complex traits such as body shape and their interaction with complex behavior like maneuverability benefits from both the broad view provided by comprehensive comparative studies, and the control of variables enabled by robophysical experiments.

Material and geometric effects on propulsion of a fish tail

We investigate the effects of material flexibility and aspect ratio on the propulsion of flapping tails. The tail, which is assumed to deform in the bending direction only, is modeled using the Euler-Bernoulli beam theory. The hydrodynamic loads generated by the flapping motion are calculated using the three-dimensional unsteady vortex lattice method. The finite element method is used to solve the coupled time-dependent equations of motion using an implicit solver for time integration. The results show improvement in the thrust and propulsive efficiency over a specific range of non-dimensional flexibility defined by the ratio of the elastic forces to fluid pressure forces. Structural and flow characteristics associated with the improved performance are discussed. As for geometric effects, the performance depends on the excitation frequency. At low frequencies, the improvement is continuous with increasing the aspect ratio in a manner similar to that of rigid tails. At higher frequencies, the improvement is limited to a region defined by aspect ratios that are less than 0.5. The extent of the improvement depends on the flexibility.

Fin-fin interactions during locomotion in a simplified biomimetic fish model

Fish median fins are extremely diverse, but their function is not yet fully understood. Various biological studies on fish and engineering studies on flapping foils have revealed that there are hydrodynamic interactions between fins arranged in tandem and that these interactions can lead to improved performance by the posterior fin. This performance improvement is often driven by the augmentation of a leading-edge vortex on the trailing fin. Past experimental studies have necessarily simplified fish anatomy to enable more detailed engineering analyses, but such simplifications then do not capture the complexities of an undulating fish-like body with fins attached. We present a flexible fish-like robotic model that better represents the kinematics of swimming fishes while still being simple enough to examine a range of morphologies and motion patterns. We then create statistical models that predict the individual effects of each kinematic and morphological variable. Our results demonstrate that having fins arranged in tandem on an undulating body can lead to more steady production of thrust forces determined by the distance between the fins and their relative motion. We find that these same variables also affect swimming speed. Specifically, when swimming at high frequencies, self-propelled speed decreases by 12%-26% due to out of phase fin motion. Flow visualization reveals that variation within this range is caused in part by fin-fin flow interactions that affect leading edge vortices. Our results indicate that undulatory swimmers should optimize both the positioning and relative motion of their median fins in order to reduce force oscillations and improve overall performance while swimming.

Hydrodynamic stress and phenotypic plasticity of the zebrafish regenerating fin

Understanding how extrinsic factors modulate genetically encoded information to produce a specific phenotype is of prime scientific interest. In particular, the feedback mechanism between abiotic forces and locomotory organs during morphogenesis to achieve efficient movement is a highly relevant example of such modulation. The study of this developmental process can provide unique insights on the transduction of cues at the interface between physics and biology. Here, we take advantage of the natural ability of adult zebrafish to regenerate their amputated fins to assess its morphogenic plasticity upon external modulations. Using a variety of surgical and chemical treatments, we could induce phenotypic responses to the structure of the fin. Through the ablation of specific rays in regenerating caudal fins, we generated artificially narrowed appendages in which the fin cleft depth and the positioning of rays bifurcations were perturbed compared with normal regenerates. To dissect the role of mechanotransduction in this process, we investigated the patterns of hydrodynamic forces acting on the surface of a zebrafish fin during regeneration by using particle tracking velocimetry on a range of biomimetic hydrofoils. This experimental approach enabled us to quantitatively compare hydrodynamic stress distributions over flapping fins of varying sizes and shapes. As a result, viscous shear stress acting on the distal margin of regenerating fins and the resulting internal tension are proposed as suitable signals for guiding the regulation of ray growth dynamics and branching pattern. Our findings suggest that mechanical forces are involved in the fine-tuning of the locomotory organ during fin morphogenesis.

Form and function of the caudal fin throughout the phylogeny of fishes

Fishes are the longest persisting living vertebrates and as such, display an incredible array of diversity. Variation in the tail, or caudal fin, is often a reflection of a fish's environment, and affects movement, predation, defense, and reproduction. Previous literature has discussed many aspects of caudal fin form and function in particular taxonomic groups; however, no previous work has synthesized these studies in order to detail how the caudal fin is structured, and what purpose this structure serves, throughout the phylogeny of fishes. This review examines the caudal fin throughout the main lineages of fish evolution, and highlights where changes in shape and usage have occurred. Such novelties in form and function tend to have far-reaching evolutionary consequences. Through integration of past and present work, this review creates a coherent picture of caudal fin evolution. Patterns and outliers that demonstrate how form and function of this appendage are intertwined can further inform hypotheses that fill critical gaps in knowledge concerning the caudal fin.

Constraints on the Ecomorphological Convergence of Zooplanktivorous Butterflyfishes

Whether distantly related organisms evolve similar strategies to meet the demands of a shared ecological niche depends on their evolutionary history and the nature of form-function relationships. In fishes, the visual identification and consumption of microscopic zooplankters, selective zooplanktivory, is a distinct type of foraging often associated with a suite of morphological specializations. Previous work has identified inconsistencies in the trajectory and magnitude of morphological change following transitions to selective zooplanktivory, alluding to the diversity and importance of ancestral effects. Here we investigate whether transitions to selective zooplanktivory have influenced the morphological evolution of marine butterflyfishes (family Chaetodontidae), a group of small-prey specialists well known for several types of high-precision benthivory. Using Bayesian ancestral state estimation, we inferred the recent evolution of zooplanktivory among benthivorous ancestors that hunted small invertebrates and browsed by picking or scraping coral polyps. Traits related to the capture of prey appear to be functionally versatile, with little morphological distinction between species with benthivorous and planktivorous foraging modes. In contrast, multiple traits related to prey detection or swimming performance are evolving toward novel, zooplanktivore-specific optima. Despite a relatively short evolutionary history, general morphological indistinctiveness, and evidence of constraint on the evolution of body size, convergent evolution has closed a near significant amount of the morphological distance between zooplanktivorous species. Overall, our findings describe the extent to which the functional demands associated with selective zooplanktivory have led to generalizable morphological features among butterflyfishes and highlight the importance of ancestral effects in shaping patterns of morphological convergence.

Hydrodynamic Analysis for the Morphing Median Fins of Tuna during Yaw Motions

Tuna can change the area and shape of the median fins, including the first dorsal, second dorsal, and anal fins. The morphing median fins have the ability of adjusting the hydrodynamic forces, thereby affecting the yaw mobility of tuna to a certain extent. In this paper, the hydrodynamic analysis of the median fins under different morphing states is carried out by the numerical method, so as to clarify the influence of the erected median fins on the yaw maneuvers. By comparing the two morphing states of erected and depressed, it can be concluded that the erected median fins can increase their own hydrodynamic forces during the yaw movement. However, the second dorsal and anal fins have limited influence on the yaw maneuverability, and they tend to maintain the stability of tuna. The first dorsal fin has more lift increment in the erection state, which can obviously affect the hydrodynamic performance of tuna. Moreover, as the median fins are erected, the hydrodynamic forces of the tuna's body increase synchronously due to the interaction between the body and the median fins, which is also very beneficial to the yaw motion. This study indicates that tuna can use the morphing median fins to adjust its mobility and stability, which provides a new idea for the design of robotic fish.

Evolutionary determinism and convergence associated with water-column transitions in marine fishes

Repeatable, convergent outcomes are prima facie evidence for determinism in evolutionary processes. Among fishes, well-known examples include microevolutionary habitat transitions into the water column, where freshwater populations (e.g., sticklebacks, cichlids, and whitefishes) recurrently diverge toward slender-bodied pelagic forms and deep-bodied benthic forms. However, the consequences of such processes at deeper macroevolutionary scales in the marine environment are less clear. We applied a phylogenomics-based integrative, comparative approach to test hypotheses about the scope and strength of convergence in a marine fish clade with a worldwide distribution (snappers and fusiliers, family Lutjanidae) featuring multiple water-column transitions over the past 45 million years. We collected genome-wide exon data for 110 (∼80%) species in the group and aggregated data layers for body shape, habitat occupancy, geographic distribution, and paleontological and geological information. We also implemented approaches using genomic subsets to account for phylogenetic uncertainty in comparative analyses. Our results show independent incursions into the water column by ancestral benthic lineages in all major oceanic basins. These evolutionary transitions are persistently associated with convergent phenotypes, where deep-bodied benthic forms with truncate caudal fins repeatedly evolve into slender midwater species with furcate caudal fins. Lineage diversification and transition dynamics vary asymmetrically between habitats, with benthic lineages diversifying faster and colonizing midwater habitats more often than the reverse. Convergent ecological and functional phenotypes along the benthic-pelagic axis are pervasive among different lineages and across vastly different evolutionary scales, achieving predictable high-fitness solutions for similar environmental challenges, ultimately demonstrating strong determinism in fish body-shape evolution.

The effect of variable stiffness of tuna-like fish body and fin on swimming performance

The work in this paper focuses on the examination of the effect of variable stiffness distributions on the kinematics and propulsion performance of a tuna-like swimmer. This is performed with the use of a recently developed fully coupled fluid-structure interaction solver. The two different scenarios considered in the present study are the stiffness varied along the fish body and the caudal fin, respectively. Our results show that it is feasible to replicate the similar kinematics and propulsive capability to that of the real fish via purely passive structural deformations. In addition, propulsion performance improvement is mainly dependent on the better orientation of the force near the posterior part of swimmers towards the thrust direction. Specifically, when a variable body stiffness scenario is considered, the bionic body stiffness profile results in better performance in most cases studied herein compared with a uniform stiffness commonly investigated in previous studies. Given the second scenario, where the stiffness is varied only in the spanwise direction of the tail, similar tail kinematics to that of the live scombrid fish only occurs in association with the heterocercal flexural rigidity profile. The resulting asymmetric tail conformation also yields performance improvement at intermediate stiffness in comparison to the cupping and uniform stiffness.

Fish-like aquatic propulsion studied using a pneumatically-actuated soft-robotic model

Fish locomotion is characterized by waves of muscle electrical activity that proceed from head to tail, and result in an undulatory pattern of body bending that generates thrust during locomotion. Isolating the effects of parameters like body stiffness, co-activation between the right and left sides of the body, and frequency on thrust generation has proven to be difficult in live fishes. We use a pneumatically-actuated fish-like model to investigate how these parameters affect locomotor force generation. We measure thrust as well as side forces and torques generated during propulsion. Using a statistical linear model we examine the effects of input parameter combinations on thrust generation. We show that both stiffness and frequency substantially affect swimming kinematics, and that there are complex interactive effects of these two parameters on thrust. The stiffer the backbone the more impact that increasing frequency has on thrust production. For stiffer models, increasing frequency resulted in higher values for both thrust and lateral forces. Large side forces reduce swimming efficiency but this effect could be mitigated by decreasing undulatory wavelength and allowing appropriate phasing of left and right body movements to reduce amplitudes of side force.

Tunas as a high-performance fish platform for inspiring the next generation of autonomous underwater vehicles

Tunas of the genus Thunnus are a group of high-performance pelagic fishes with many locomotor traits that are convergently shared with other high-performance fish groups. Because of their swimming abilities, tunas continue to be an inspiration for both comparative biomechanics and the design of biomimetic autonomous underwater vehicles (AUVs). Despite the strong history of studies in tuna physiology and current interest in tuna biomechanics and bio-inspired design, we lack quantitative data on the function of many features of tunas. Here we present data on the morphology, behavior, and function of tunas, focusing especially on experimentally examining the function of tuna lateral keels, finlets, and pectoral fins by using simple physical models. We find that both triangular lateral keels and flexible finlets decrease power requirements during swimming, likely by reducing lateral forces and yaw torques (compared to models either without keels or with rectangular keels, and models with stiff finlets or strip fins of equal area, respectively). However, both triangular keels and flexible finlets generate less thrust than other models either without these features or with modified keels or finlets, leading to a tradeoff between power consumption and thrust. In addition, we use micro computed tomography (µCT) to show that the flexible lateral keels possess a lateral line canal, suggesting these keels have a sensory function. The curved and fully-attached base of tuna pectoral fins provides high lift-to-drag ratio at low angles of attack, and generates the highest torques across speeds and angles of attack. Therefore, curved, fully-attached pectoral fins grant both better gliding and maneuvering performance compared to flat or curved, partially-attached designs. We provide both 3D models of tuna morphology derived from µCT scans and conclusions about the performance effects of tuna-like features as a resource for future biological and engineering work for next-generation tuna-inspired AUV designs.

Flowfields produced by a robotic sea lion foreflipper starting from rest

Sea lions swim using primarily their foreflippers, which is uncommon among aquatic mammals. While a significant body of literature exists which investigates the hydrodynamics of body-caudal swimming, relatively little research has looked at sea lion propulsion. In this work, particle imaging velocimetry is used to observe the flow around a robotic model sea lion flipper. The model flipper was cast in silicone from a high-resolution scan of a sample sea lion foreflipper. The model flipper was actuated at the root, and its motion was controlled by a programmable servomotor. It was observed that the thrust-producing clapping motion of the flipper entrained significant fluid momentum on the suction side of the flipper, which developed into a shed vortex and contributed to downstream momentum (and therefore thrust). Rotating the robotic flipper more quickly produced greater downstream jet velocities, but at a lower conversion of rotational velocity, suggesting that this mechanism of propulsion can be optimized based on the system needs.

Effects of fish caudal fin sweep angle and kinematics on thrust production during low-speed thunniform swimming

Scombrid fish lunate caudal fins are characterized by a wide range of sweep angles. Scombrid that have small sweep-angle caudal fins move at higher swimming speeds, suggesting that smaller angles produce more thrust. Furthermore, scombrids occasionally use high angles of attack (AoA) suggesting this also has some thrust benefit. This work examined the hypothesis that a smaller sweep angle and higher AoA improved thrust in swimmers by experimentally analyzing a robophysical model. The robophysical model was tested in a water tunnel at speeds between 0.35 and 0.7 body lengths per second. Three swept caudal fins were analyzed at three different AoA, three different freestream velocities, and four different Strouhal numbers, for a total of 108 cases. Results demonstrated that the fin with the largest sweep angle of 50° resulted in lower thrust production than the 40° and 30° fins, especially at higher Strouhal numbers. Larger AoA up to 25° increased thrust production at the higher Strouhal numbers, but at lower Strouhal numbers, produced less thrust. Differences in thrust production due to fin sweep angle and AoA were attributed to the variation in spanwise flow and leading edge vortex dynamics.

Summary: The study examines the impact of scombrid fish caudal fin sweep angle and angle of attack on thrust production across a range of Strouhal numbers using a robophysical model.

Fluid-structure interaction modeling on a 3D ray-strengthened caudal fin

In this paper, we present a numerical model capable of solving the fluid-structure interaction problems involved in the dynamics of skeleton-reinforced fish fins. In this model, the fluid dynamics is simulated by solving the Navier-Stokes equations using a finite-volume method based on an overset, multi-block structured grid system. The bony rays embedded in the fin are modeled as nonlinear Euler-Bernoulli beams. To demonstrate the capability of this model, we numerically investigate the effect of various ray stiffness distributions on the deformation and propulsion performance of a 3D caudal fin. Our numerical results show that with specific ray stiffness distributions, certain caudal fin deformation patterns observed in real fish (e.g. the cupping deformation) can be reproduced through passive structural deformations. Among the four different stiffness distributions (uniform, cupping, W-shape and heterocercal) considered here, we find that the cupping distribution requires the least power expenditure. The uniform distribution, on the other hand, performs the best in terms of thrust generation and efficiency. The uniform stiffness distribution, per se, also leads to 'cupping' deformation patterns with relatively smaller phase differences between various rays. The present model paves the way for future work on dynamics of skeleton-reinforced membranes.

Intermittent locomotion of a fish-like swimmer driven by passive elastic mechanism

The intermittent locomotion performance of a fish-like elastic swimmer is studied numerically in this paper. The actuation is imposed only at the head and the locomotion is indirectly driven by passive elastic mechanism. For intermittent swimming, certain time durations of passive coasting are interspersed between two half-periods of active bursting. To facilitate the comparison of energy efficiencies in continuous and intermittent swimming at the same cruising speed, we consider both intermittent swimming at various duty cycles and also continuous swimming at reduced actuation frequencies. The result indicates that the intermittent style is more economical than the continuous style only when the cruising Reynolds number is sufficiently large and the duty cycle is moderate. We also explore the passive tail-beating pattern and wake structure for intermittent swimming. It is found that the kinematics of the tail contains a preparatory burst phase which lies in between the active bursting and the passive coasting phases. Three vortex streets are found in the wake structures behind the intermittent swimmers. The two oblique streets consist of strong vortex dipoles and the horizontal street is made up of weak vortices. The results of this study can provide some insight into the burst-and-coast swimming of fish and also inform the design of efficient bio-mimetic under-water vehicles.

Robotics-inspired biology

For centuries, designers and engineers have looked to biology for inspiration. Biologically inspired robots are just one example of the application of knowledge of the natural world to engineering problems. However, recent work by biologists and interdisciplinary teams have flipped this approach, using robots and physical models to set the course for experiments on biological systems and to generate new hypotheses for biological research. We call this approach robotics-inspired biology; it involves performing experiments on robotic systems aimed at the discovery of new biological phenomena or generation of new hypotheses about how organisms function that can then be tested on living organisms. This new and exciting direction has emerged from the extensive use of physical models by biologists and is already making significant advances in the areas of biomechanics, locomotion, neuromechanics and sensorimotor control. Here, we provide an introduction and overview of robotics-inspired biology, describe two case studies and suggest several directions for the future of this exciting new research area.

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.

A pressure-based force and torque prediction technique for the study of fish-like swimming

Many outstanding questions about the evolution and function of fish morphology are linked to swimming dynamics, and a detailed knowledge of time-varying forces and torques along the animal’s body is a key component in answering many of these questions. Yet, quantifying these forces and torques experimentally represents a major challenge that to date prevents a full understanding of fish-like swimming. Here, we develop a method for obtaining these force and torque data non-invasively using standard 2D digital particle image velocimetry in conjunction with a pressure field algorithm. We use a mechanical flapping foil apparatus to model fish-like swimming and measure forces and torques directly with a load cell, and compare these measured values to those estimated simultaneously using our pressure-based approach. We demonstrate that, when out-of-plane flows are relatively small compared to the planar flow, and when pressure effects sufficiently dominate shear effects, this technique is able to accurately reproduce the shape, magnitude, and timing of locomotor forces and torques experienced by a fish-like swimmer. We conclude by exploring of the limits of this approach and its feasibility in the study of freely-swimming fishes.

Structure of supporting elements in the dorsal fin of percid fishes

The dorsal fin is one of the most varied swimming structures in Acanthomorpha, the spiny-finned fishes. This fin can be present as a single contiguous structure supported by bony spines and soft lepidotrichia, or it may be divided into an anterior, spiny dorsal fin and a posterior, soft dorsal fin. The freshwater fish family Percidae exhibits especially great variation in dorsal fin spacing, including fishes with separated fins of varying gap length and fishes with contiguous fins. We hypothesized that fishes with separated dorsal fins, especially those with large gaps between fins, would have stiffened fin elements at the leading edge of the soft dorsal fin to resist hydrodynamic loading during locomotion. For 10 percid species, we measured the spacing between dorsal fins and calculated the second moment of area of selected spines and lepidotrichia from museum specimens. There was no significant relationship between the spacing between dorsal fins and the second moment of area of the leading edge of the soft dorsal fin.

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.

Performance variation due to stiffness in a tuna-inspired flexible foil model

Tuna are fast, economical swimmers in part due to their stiff, high aspect ratio caudal fins and streamlined bodies. Previous studies using passive caudal fin models have suggested that while high aspect ratio tail shapes such as a tuna's generally perform well, tail performance cannot be determined from shape alone. In this study, we analyzed the swimming performance of tuna-tail-shaped hydrofoils of a wide range of stiffnesses, heave amplitudes, and frequencies to determine how stiffness and kinematics affect multiple swimming performance parameters for a single foil shape. We then compared the foil models' kinematics with published data from a live swimming tuna to determine how well the hydrofoil models could mimic fish kinematics. Foil kinematics over a wide range of motion programs generally showed a minimum lateral displacement at the narrowest part of the foil, and, immediately anterior to that, a local area of large lateral body displacement. These two kinematic patterns may enhance thrust in foils of intermediate stiffness. Stiffness and kinematics exhibited subtle interacting effects on hydrodynamic efficiency, with no one stiffness maximizing both thrust and efficiency. Foils of intermediate stiffnesses typically had the greatest coefficients of thrust at the highest heave amplitudes and frequencies. The comparison of foil kinematics with tuna kinematics showed that tuna motion is better approximated by a zero angle of attack foil motion program than by programs that do not incorporate pitch. These results indicate that open questions in biomechanics may be well served by foil models, given appropriate choice of model characteristics and control programs. Accurate replication of biological movements will require refinement of motion control programs and physical models, including the creation of models of variable stiffness.

Correlated evolution of body and fin morphology in the cichlid fishes

Body and fin shapes are chief determinants of swimming performance in fishes. Different configurations of body and fin shapes can suit different locomotor specializations. The success of any configuration is dependent upon the hydrodynamic interactions between body and fins. Despite the importance of body-fin interactions for swimming, there are few data indicating whether body and fin configurations evolve in concert, or whether these structures vary independently. The cichlid fishes are a diverse family whose well-studied phylogenetic relationships make them ideal for the study of macroevolution of ecomorphology. This study measured body, and caudal and median fin morphology from radiographs of 131 cichlid genera, using morphometrics and phylogenetic comparative methods to determine whether these traits exhibit correlated evolution. Partial least squares canonical analysis revealed that body, caudal fin, dorsal fin, and anal fin shapes all exhibited strong correlated evolution consistent with locomotor ecomorphology. Major patterns included the evolution of deep body profiles with long fins, suggestive of maneuvering specialization; and the evolution of narrow, elongate caudal peduncles with concave tails, a combination that characterizes economical cruisers. These results demonstrate that body shape evolution does not occur independently of other traits, but among a suite of other morphological changes that augment locomotor specialization.

Consequences of lost endings: caudal autotomy as a lens for focusing attention on tail function during locomotion

Autotomy has evolved in many animal lineages as a means of predator escape, and involves the voluntary shedding of body parts. In vertebrates, caudal autotomy (or tail shedding) is the most common form, and it is particularly widespread in lizards. Here, we develop a framework for thinking about how tail loss can have fitness consequences, particularly through its impacts on locomotion. Caudal autotomy is fundamentally an alteration of morphology that affects an animal's mass and mass distribution. These morphological changes affect balance and stability, along with the performance of a range of locomotor activities, from running and climbing to jumping and swimming. These locomotor effects can impact on activities critical for survival and reproduction, including escaping predators, capturing prey and acquiring mates. In this Commentary, we first review work illustrating the (mostly) negative effects of tail loss on locomotor performance, and highlight what these consequences reveal about tail function during locomotion. We also identify important areas of future study, including the exploration of new behaviors (e.g. prey capture), increased use of biomechanical measurements and the incorporation of more field-based studies to continue to build our understanding of the tail, an ancestral and nearly ubiquitous feature of the vertebrate body plan.

Mechanisms of anguilliform locomotion in fishes studied using simple three-dimensional physical models

Physical models enable researchers to systematically examine complex and dynamic mechanisms of underwater locomotion in ways that would be challenging with freely swimming animals. Previous research on undulatory locomotion, for example, has used rectangular flexible panels that are effectively two-dimensional as proxies for the propulsive surfaces of swimming fishes, but these bear little resemblance to the bodies of elongate eel-like swimming animals. In this paper we use a polyurethane rod (round cross-section) and bar (square cross-section) to represent the body of a swimming Pacific hagfish (Eptatretus stoutii). We actuated the rod and bar in both heave and pitch using a mechanical controller to generate a propulsive wave at frequencies between 0.5 and 2.5 Hz. We present data on (1) how kinematic swimming patterns change with driving frequency in these elongate fish-like models, (2) the thrust-generating capability of these simple models, (3) how forces and work done during propulsion compare between cross-sectional shapes, (4) the wake flow patterns in these swimming models using particle image velocimetry. We also contrast kinematic and hydrodynamic patterns produced by bar and rod models to comparable new experimental data on kinematics and wake flow patterns from freely swimming hagfish. Increasing the driving frequency of bar and rod models reduced trailing edge amplitude and wavelength, and above 2 Hz a nodal point appeared in the kinematic wave. Above 1 Hz, both the rod and bar generated net thrust, with the work per cycle reaching a minimum at 1.5 Hz, and the bar always requiring more work per cycle than the rod. Wake flow patterns generated by the swimming rod and bar included clearly visible lateral jets, but not the caudolaterally directed flows seen in the wakes from freely swimming hagfish.

Investigation of Fish Caudal Fin Locomotion Using a Bio-Inspired Robotic Model

Due to its advantages of realizing repeatable experiments, collecting data and isolating key factors, the bio-robotic model is becoming increasingly important in the study of biomechanics. The caudal fin of fish has long been understood to be central to propulsion performance, yet its contribution to manoeuverability, especially for homocercal caudal fin, has not been studied in depth. In the research outlined in this paper, we designed and fabricated a robotic caudal fin to mimic the morphology and the three-dimensional (3D) locomotion of the tail of the Bluegill Sunfish ( Lepomis macrochirus). We applied heave and pitch motions to the robot to model the movement of the caudal peduncle of its biological counterpart. Force measurements and 2D and 3D digital particle image velocimetry were then conducted under different movement patterns and flow speeds. From the force data, we found the addition of the 3D caudal fin locomotion significantly enhanced the lift force magnitude. The phase difference between the caudal fin ray and peduncle motion was a key factor in simultaneously controlling the thrust and lift. The increased flow speed had a negative impact on the generation of lift force. From the average 2D velocity field, we observed that the vortex wake directed water both axially and vertically, and formed a jet-like structure with notable wake velocity. The 3D instantaneous velocity field at 0.6 T indicated the 3D motion of the caudal fin may result in asymmetry wake flow patterns relative to the mid-sagittal plane and change the heading direction of the shedding vortexes. Based on these results, we hypothesized that live fish may actively tune the movement between the caudal fin rays and the peduncle to change the wake structure behind the tail and hence obtain different thrust and lift forces, which contributes to its high manoeuvrability.

Evolutionary multiobjective design of a flexible caudal fin for robotic fish

Robotic fish accomplish swimming by deforming their bodies or other fin-like appendages. As an emerging class of embedded computing system, robotic fish are anticipated to play an important role in environmental monitoring, inspection of underwater structures, tracking of hazardous wastes and oil spills, and the study of live fish behaviors. While integration of flexible materials (into the fins and/or body) holds the promise of improved swimming performance (in terms of both speed and maneuverability) for these robots, such components also introduce significant design challenges due to the complex material mechanics and hydrodynamic interactions. The problem is further exacerbated by the need for the robots to meet multiple objectives (e.g., both speed and energy efficiency). In this paper, we propose an evolutionary multiobjective optimization approach to the design and control of a robotic fish with a flexible caudal fin. Specifically, we use the NSGA-II algorithm to investigate morphological and control parameter values that optimize swimming speed and power usage. Several evolved fin designs are validated experimentally with a small robotic fish, where fins of different stiffness values and sizes are printed with a multi-material 3D printer. Experimental results confirm the effectiveness of the proposed design approach in balancing the two competing objectives.

Hydrodynamic function of biomimetic shark skin: effect of denticle pattern and spacing

The structure of shark skin has been the subject of numerous studies and recently biomimetic shark skin has been fabricated with rigid denticles (scales) on a flexible substrate. This artificial skin can bend and generate thrust when attached to a mechanical controller. The ability to control the manufacture of biomimetic shark skin facilitates manipulation of surface parameters and understanding the effects of changing denticle patterns on locomotion. In this paper we investigate the effect of changing the spacing and arrangement of denticles on the surface of biomimetic shark skin on both static and dynamic locomotor performance. We designed 3D-printed flexible membranes with different denticle patterns and spacings: (1) staggered-overlapped, (2) linear-overlapped, and (3) linear-non-overlapped, and compared these to a 3D-printed smooth-surfaced control. These 3D printed shark skin models were then tested in a flow tank with a mechanical flapping device that allowed us to either hold the models in a stationary position or move them dynamically. We swam the membranes at a frequency of 1 Hz with different heave amplitudes (from ±1 cm to ±3 cm) while measuring forces, torques, self-propelled swimming speed, and cost of transport (COT). Static tests revealed drag reduction of denticle patterns compared to a smooth control at low speeds, but increased drag at speeds above 25 cm s(-1). However, during dynamic (swimming) tests, the staggered-overlapped pattern produced the fastest swimming speeds with no significant increase in the COT at lower heave values. For instance, at a heave frequency of 1 Hz and amplitude of ±1 cm, swimming speed of the staggered-overlapped pattern increased by 25.2% over the smooth control. At higher heave amplitudes, significantly faster self-propelled swimming speeds were achieved by the staggered-overlapped pattern, but with higher COT. Only the staggered-overlapped pattern provides a significant swimming performance advantage over the smooth control and the other two denticle patterns. Quantitative hydrodynamic comparisons among skin models where control over manufacture allows alteration of design parameters provides a useful experimental tool for future work on the considerable natural diversity of shark skin denticles both among species and on different body locations.

Collective Flow Enhancement by Tandem Flapping Wings

We examine the fluid-mechanical interactions that occur between arrays of flapping wings when operating in close proximity at a moderate Reynolds number (Re≈100-1000). Pairs of flapping wings are oscillated sinusoidally at frequency f, amplitude θ_{M}, phase offset ϕ, and wing separation distance D^{*}, and outflow speed v^{*} is measured. At a fixed separation distance, v^{*} is sensitive to both f and ϕ, and we observe both constructive and destructive interference in airspeed. v^{*} is maximized at an optimum phase offset, ϕ_{max}, which varies with wing separation distance, D^{*}. We propose a model of collective flow interactions between flapping wings based on vortex advection, which reproduces our experimental data.

Effects of non-uniform stiffness on the swimming performance of a passively-flexing, fish-like foil model

Simple mechanical models emulating fish have been used recently to enable targeted study of individual factors contributing to swimming locomotion without the confounding complexity of the whole fish body. Yet, unlike these uniform models, the fish body is notable for its non-uniform material properties. In particular, flexural stiffness decreases along the fish's anterior-posterior axis. To identify the role of non-uniform bending stiffness during fish-like propulsion, we studied four foil model configurations made by adhering layers of plastic sheets to produce discrete regions of high (5.5 × 10(-5) Nm(2)) and low (1.9 × 10(-5) Nm(2)) flexural stiffness of biologically-relevant magnitudes. This resulted in two uniform control foils and two foils with anterior regions of high stiffness and posterior regions of low stiffness. With a mechanical flapping foil controller, we measured forces and torques in three directions and quantified swimming performance under both heaving (no pitch) and constant 0° angle of attack programs. Foils self-propelled at Reynolds number 21 000-115 000 and Strouhal number ∼0.20-0.25, values characteristic of fish locomotion. Although previous models have emphasized uniform distributions and heaving motions, the combination of non-uniform stiffness distributions and 0° angle of attack pitching program was better able to reproduce the kinematics of freely-swimming fish. This combination was likewise crucial in maximizing swimming performance and resulted in high self-propelled speeds at low costs of transport and large thrust coefficients at relatively high efficiency. Because these metrics were not all maximized together, selection of the 'best' stiffness distribution will depend on actuation constraints and performance goals. These improved models enable more detailed, accurate analyses of fish-like swimming.