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.

Reinforcement learning-based optimization of locomotion controller using multiple coupled CPG oscillators for elongated undulating fin propulsion

This article proposes a locomotion controller inspired by black Knifefish for undulating elongated fin robot. The proposed controller is built by a modified CPG network using sixteen coupled Hopf oscillators with the feedback of the angle of each fin-ray. The convergence rate of the modified CPG network is optimized by a reinforcement learning algorithm. By employing the proposed controller, the undulating elongated fin robot can realize swimming pattern transformations naturally. Additionally, the proposed controller enables the configuration of the swimming pattern parameters known as the amplitude envelope, the oscillatory frequency to perform various swimming patterns. The implementation processing of the reinforcement learning-based optimization is discussed. The simulation and experimental results show the capability and effectiveness of the proposed controller through the performance of several swimming patterns in the varying oscillatory frequency and the amplitude envelope of each fin-ray.

Fins as Mechanosensors for Movement and Touch-Related Behaviors

Mechanosensation is a universal feature of animals that is essential for behavior, allowing detection of animals' own body movement and position as well as physical characteristics of the environment. The extraordinary morphological and behavioral diversity that exists across fish species provide rich opportunities for comparative mechanosensory studies in fins. The fins of fishes have been found to function as proprioceptors, by providing feedback on fin ray position and movement, and as tactile sensors, by encoding pressures applied to the fin surface. Across fish species, and among fins, the afferent response is remarkably consistent, suggesting that the ability of fin rays and membrane to sense deformation is a fundamental feature of fish fins. While fin mechanosensation has been known in select, often highly specialized, species for decades, only in the last decade have we explored mechanosensation in typical propulsive fins and considered its role in behavior, particularly locomotion. In this paper, we synthesize the current understanding of the anatomy and physiology of fin mechanosensation, looking toward key directions for research. We argue that a mechanosensory perspective informs studies of fin-based propulsion and other fin-driven behaviors and should be considered in the interpretation of fin morphology and behavior. In addition, we compare the mechanosensory system innervating the fins of fishes to the systems innervating the limbs of mammals and wings of insects in order to identify shared mechanosensory strategies and how different organisms have evolved to meet similar functional challenges. Finally, we discuss how understanding the biological organization and function of fin sensors can inform the design of control systems for engineered fins and fin-driven robotics.

Energetics and behavior of coral reef fishes during oscillatory swimming in a simulated wave surge

Oxygen consumption rates were measured for coral reef fishes during swimming in a bidirectional, oscillatory pattern to simulate station-holding in wave-induced, shallow-water flows. For all species examined, increases in wave intensity, as simulated by increases in frequency and amplitude of oscillation, yielded increased metabolic rates and net costs of swimming (NCOS; swimming metabolic rate minus standard metabolic rate). Comparing species with different swimming modes, the caudal fin swimming Kuhlia spp. (Kuhliidae) and simultaneous pectoral-caudal fin swimming Amphiprion ocellaris (Pomacentridae) turned around to face the direction of swimming most of the time, whereas the median-paired fin (MPF) swimmers, the pectoral fin swimming Ctenochaetus strigosus (Acanthuridae) and dorsal-anal fin swimming Sufflamen bursa (Balistidae), more frequently swam in reverse for one half of the oscillation to avoid turning. Contrary to expectations, the body-caudal fin (BCF) swimming Kuhlia spp. had the lowest overall NCOS in the oscillatory swimming regime compared with the MPF swimmers. However, when examining the effect of increasing frequency of oscillation at similar average velocities, Ku hlia spp. showed a 24% increase in NCOS with a 50% increase in direction changes and accelerations. The two strict MPF swimmers had lower increases on average, suggestive of reduced added costs with increasing frequency of direction changes with this swimming mode. Further studies are needed on the costs of unsteady swimming to determine whether these differences can explain the observed prevalence of fishes using the MPF pectoral fin swimming mode in reef habitats exposed to high, wave-surge-induced water flows.

Robotic device shows lack of momentum enhancement for gymnotiform swimmers

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

New approaches for assessing squid fin motions: coupling proper orthogonal decomposition with volumetric particle tracking velocimetry

Squid, which swim using a coupled fin/jet system powered by muscular hydrostats, pose unique challenges for the study of locomotion. The high flexibility of the fins and complex flow fields generated by distinct propulsion systems require innovative techniques for locomotive assessment. For this study, we used proper orthogonal decomposition (POD) to decouple components of the fin motions and defocusing digital particle tracking velocimetry (DDPTV) to quantify the resultant 3D flow fields. Kinematic footage and DDPTV data were collected from brief squid, Lolliguncula brevis [3.1-6.5 cm dorsal mantle length (DML)], swimming freely in a water tunnel at speeds of 0.39-7.20 DML s^-1 Both flap and wave components were present in all fin motions, but the relative importance of the wave components was higher for arms-first swimming than for tail-first swimming and for slower versus higher speed swimming. When prominent wave components were present, more complex interconnected vortex ring wakes were observed, while fin movements dominated by flapping resulted in more spatially separated vortex ring patterns. Although the jet often produced the majority of the thrust for steady rectilinear swimming, our results demonstrated that the fins can contribute more thrust than the jet at times, consistently produce comparable levels of lift to the jet during arms-first swimming, and can boost overall propulsive efficiency. By producing significant drag signatures, the fins can also aid in stabilization and maneuvering. Clearly, fins play multiple roles in squid locomotion, and when coupled with the jet, allow squid to perform a range of swimming behaviors integral to their ecological success.

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

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

A review on locomotion robophysics: the study of movement at the intersection of robotics, soft matter and dynamical systems

Discovery of fundamental principles which govern and limit effective locomotion (self-propulsion) is of intellectual interest and practical importance. Human technology has created robotic moving systems that excel in movement on and within environments of societal interest: paved roads, open air and water. However, such devices cannot yet robustly and efficiently navigate (as animals do) the enormous diversity of natural environments which might be of future interest for autonomous robots; examples include vertical surfaces like trees and cliffs, heterogeneous ground like desert rubble and brush, turbulent flows found near seashores, and deformable/flowable substrates like sand, mud and soil. In this review we argue for the creation of a physics of moving systems-a 'locomotion robophysics'-which we define as the pursuit of principles of self-generated motion. Robophysics can provide an important intellectual complement to the discipline of robotics, largely the domain of researchers from engineering and computer science. The essential idea is that we must complement the study of complex robots in complex situations with systematic study of simplified robotic devices in controlled laboratory settings and in simplified theoretical models. We must thus use the methods of physics to examine both locomotor successes and failures using parameter space exploration, systematic control, and techniques from dynamical systems. Using examples from our and others' research, we will discuss how such robophysical studies have begun to aid engineers in the creation of devices that have begun to achieve life-like locomotor abilities on and within complex environments, have inspired interesting physics questions in low dimensional dynamical systems, geometric mechanics and soft matter physics, and have been useful to develop models for biological locomotion in complex terrain. The rapidly decreasing cost of constructing robot models with easy access to significant computational power bodes well for scientists and engineers to engage in a discipline which can readily integrate experiment, theory and computation.

Development of a bio-inspired transformable robotic fin

Fish swim by oscillating their pectoral fins forwards and backwards in a cyclic motion such that their geometric parameters and aspect ratios change according to how fast or slow a fish wants to swim; these complex motions result in a complicated hydrodynamic response. This paper focuses on the dynamic change in the shape of a fin to improve the underwater propulsion of bio-inspired mechanism. To do this, a novel transformable robotic fin has been developed to investigate how this change in shape affects the hydrodynamic forces acting on the fin. This robotic fin has a multi-link frame and a flexible surface skin where changes in shape are activated by a purpose designed multi-link mechanism driven by a transformation motor. A drag platform has been designed to study the performance of this variable robotic fin. Numerous experiments were carried out to determine how various controlling modes affect the thrust capability of this fin. The kinematic parameters associated with this robotic fin include the oscillating frequency and amplitude, and the drag velocity. The fin has four modes to control the cyclic motion; these were also investigated in combination with the variable kinematic parameters. The results will help us understand the locomotion performance of this transformable robotic fin. Note that different controlling modes influence the propulsive performance of this robotic fin, which means its propulsive performance can be optimized in a changing environment by adapting its shape. This study facilitates the development of bio-inspired unmanned underwater vehicles with a very high swimming performance.

Convergent evolution of mechanically optimal locomotion in aquatic invertebrates and vertebrates

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

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

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

Separability of drag and thrust in undulatory animals and machines

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

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

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