Erik J. Anderson

Fish biorobotics: kinematics and hydrodynamics of self-propulsion

SUMMARY As a result of years of research on the comparative biomechanics and physiology of moving through water, biologists and engineers have made considerable progress in understanding how animals moving underwater use their muscles to power movement, in describing body and appendage motion during propulsion, and in conducting experimental and computational analyses of fluid movement and attendant forces. But it is clear that substantial future progress in understanding aquatic propulsion will require new lines of attack. Recent years have seen the advent of one such new avenue that promises to greatly broaden the scope of intellectual opportunity available to researchers: the use of biorobotic models. In this paper we discuss, using aquatic propulsion in fishes as our focal example, how using robotic models can lead to new insights in the study of aquatic propulsion. We use two examples: (1) pectoral fin function, and (2) hydrodynamic interactions between dorsal and caudal fins. Pectoral fin function is characterized by considerable deformation of individual fin rays, as well as spanwise (along the length) and chordwise (across the fin) deformation and area change. The pectoral fin can generate thrust on both the outstroke and instroke. A robotic model of the pectoral fin replicates this result, and demonstrates the effect of altering stroke kinematics on the pattern of force production. The soft dorsal fin of fishes sheds a distinct vortex wake that dramatically alters incoming flow to the tail: the dorsal fin and caudal fin act as dual flapping foils in series. This design can be replicated with a dual-foil flapping robotic device that demonstrates this phenomenon and allows examination of regions of the flapping performance space not available to fishes. We show how the robotic flapping foil device can also be used to better understand the significance of flexible propulsive surfaces for locomotor performance. Finally we emphasize the utility of self-propelled robotic devices as a means of understanding how locomotor forces are generated, and review different conceptual designs for robotic models of aquatic propulsion.

Dynamics of freely swimming flexible foils

We use modeling and simulations guided by initial experiments to study thin foils which are oscillated at the leading edge and are free to move unidirectionally under the resulting fluid forces. We find resonant-like peaks in the swimming speed as a function of foil length and rigidity. We find good agreement between the inviscid model and the experiment in the foil motions (particularly the wavelengths of their shapes), the dependences of their swimming speeds on foil length and rigidity, and the corresponding flows. The model predicts that the foil speed is proportional to foil length to the −1/3 power and foil rigidity to the 2/15 power. These scalings give a good collapse of the experimental data.

Disentangling the Functional Roles of Morphology and Motion in the Swimming of Fish

In fishes the shape of the body and the swimming mode generally are correlated. Slender-bodied fishes such as eels, lampreys, and many sharks tend to swim in the anguilliform mode, in which much of the body undulates at high amplitude. Fishes with broad tails and a narrow caudal peduncle, in contrast, tend to swim in the carangiform mode, in which the tail undulates at high amplitude. Such fishes also tend to have different wake structures. Carangiform swimmers generally produce two staggered vortices per tail beat and a strong downstream jet, while anguilliform swimmers produce a more complex wake, containing at least two pairs of vortices per tail beat and relatively little downstream flow. Are these differences a result of the different swimming modes or of the different body shapes, or both? Disentangling the functional roles requires a multipronged approach, using experiments on live fishes as well as computational simulations and physical models. We present experimental results from swimming eels (anguilliform), bluegill sunfish (carangiform), and rainbow trout (subcarangiform) that demonstrate differences in the wakes and in swimming performance. The swimming of mackerel and lamprey was also simulated computationally with realistic body shapes and both swimming modes: the normal carangiform mackerel and anguilliform lamprey, then an anguilliform mackerel and carangiform lamprey. The gross structure of simulated wakes (single versus double vortex row) depended strongly on Strouhal number, while body shape influenced the complexity of the vortex row, and the swimming mode had the weakest effect. Performance was affected even by small differences in the wakes: both experimental and computational results indicate that anguilliform swimmers are more efficient at lower swimming speeds, while carangiform swimmers are more efficient at high speed. At high Reynolds number, the lamprey-shaped swimmer produced a more complex wake than the mackerel-shaped swimmer, similar to the experimental results. Finally, we show results from a simple physical model of a flapping fin, using fins of different flexural stiffness. When actuated in the same way, fins of different stiffnesses propel themselves at different speeds with different kinematics. Future experimental and computational work will need to consider the mechanisms underlying production of the anguilliform and carangiform swimming modes, because anguilliform swimmers tend to be less stiff, in general, than are carangiform swimmers.

Robotic Models for Studying Undulatory Locomotion in Fishes

Many fish swim using body undulations to generate thrust and maneuver in threedimensions.Thepatternofbodybendingduringsteadyrectilinearlocomotion has similar general characteristics in many fishes and involves a wave of increasing amplitude passing from the head region toward the tail. While great progress has been made in understanding the mechanics of undulatory propulsion in fishes, the inability to control and precisely alter individual parameters such as oscillation frequency, body shape, and body stiffness, and the difficulty of measuring forces on freely swimming fishes have greatly hampered our ability to understand the fundamental mechanics of the undulatory mode of locomotion in aquatic systems. In this paper, we present the use of a robotic flapping foil apparatus that allows these parameters to be individually altered and forces measured on self-propelling flapping flexible foils that produce a wave-like motion very similar to that of freely swimming fishes. We use this robotic device to explore the effects of changing swimming speed, foil length, and foil-trailing edge shape on locomotor hydrodynamics, the cost of transport, and the shape of the undulating foil during locomotion. We also examine the passive swimming capabilities of a freshly dead fish body. Finally, wemodel fin-fininteractionsin fishesusingdual-flappingfoilsandshowthatthrust can be enhanced under correct conditions of foil phasing and spacing as a result of the downstream foil making use of vortical energy released by the upstream foil.

Ontogenetic changes in larval swimming and orientation of pre-competent sea urchin Arbacia punctulata in turbulence

ABSTRACT Many marine organisms have complex life histories, having sessile adults and relying on the planktonic larvae for dispersal. Larvae swim and disperse in a complex fluid environment and the effect of ambient flow on larval behavior could in turn impact their survival and transport. However, to date, most studies on larvae–flow interactions have focused on competent larvae near settlement. We examined the importance of flow on early larval stages by studying how local flow and ontogeny influence swimming behavior in pre-competent larval sea urchins, Arbacia punctulata. We exposed larval urchins to grid-stirred turbulence and recorded their behavior at two stages (4- and 6-armed plutei) in three turbulence regimes. Using particle image velocimetry to quantify and subtract local flow, we tested the hypothesis that larvae respond to turbulence by increasing swimming speed, and that the increase varies with ontogeny. Swimming speed increased with turbulence for both 4- and 6-armed larvae, but their responses differed in terms of vertical swimming velocity. 4-Armed larvae swam most strongly upward in the unforced flow regime, while 6-armed larvae swam most strongly upward in weakly forced flow. Increased turbulence intensity also decreased the relative time that larvae spent in their typical upright orientation. 6-Armed larvae were tilted more frequently in turbulence compared with 4-armed larvae. This observation suggests that as larvae increase in size and add pairs of arms, they are more likely to be passively re-oriented by moving water, rather than being stabilized (by mechanisms associated with increased mass), potentially leading to differential transport. The positive relationship between swimming speed and larval orientation angle suggests that there was also an active response to tilting in turbulence. Our results highlight the importance of turbulence to planktonic larvae, not just during settlement but also in earlier stages through morphology–flow interactions. Highlighted Article: Pre-competent, 6-armed larval urchins swim faster and are less stable in experimental turbulent flow than younger 4-armed larvae, suggesting a potential age/morphology-driven differential transport mechanism in ambient flow conditions.

Theoretical and computational fluid dynamics of an attached remora (Echeneis naucrates).

Remora fishes have a unique dorsal suction pad that allows them to form robust, reliable, and reversible attachment to a wide variety of host organisms and marine vessels. Although investigations of the suction pad have been performed, the primary force that remoras must resist, namely fluid drag, has received little attention. This work provides a theoretical estimate of the drag experienced by an attached remora using computational fluid dynamics informed by geometry obtained from micro-computed tomography. Here, simulated flows are compared to measured flow fields of a euthanized specimen in a flow tank. Additionally, the influence of the hosts boundary layer is investigated, and scaling relationships between remora features are inferred from the digitized geometry. The results suggest the drag on an attached remora is similar to that of a streamlined body, and is minimally influenced by the hosts viscous boundary layer. Consequently, this evidence does not support the hypothesis that remoras discriminate between attachment locations based on hydrodynamic considerations. Comparison of the simulated drag with experimental friction tests show that even at elevated swimming speeds it is unlikely that remoras are dislodged by drag alone, and furthermore that larger remoras may be more difficult to dislodge than smaller remoras indicating that they become more suited to attachment as they mature.

From the track to the ocean : using flow control to improve marine bio-logging tags for cetaceans

Bio-logging tags are an important tool for the study of cetaceans, but superficial tags inevitably increase hydrodynamic loading. Substantial forces can be generated by tags on fast-swimming animals, potentially affecting behavior and energetics or promoting early tag removal. Streamlined forms have been used to reduce loading, but these designs can accelerate flow over the top of the tag. This non-axisymmetric flow results in large lift forces (normal to the animal) that become the dominant force component at high speeds. In order to reduce lift and minimize total hydrodynamic loading this work presents a new tag design (Model A) that incorporates a hydrodynamic body, a channel to reduce fluid speed differences above and below the housing and wing to redirect flow to counter lift. Additionally, three derivatives of the Model A design were used to examine the contribution of individual flow control features to overall performance. Hydrodynamic loadings of four models were compared using computational fluid dynamics (CFD). The Model A design eliminated all lift force and generated up to ~30 N of downward force in simulated 6 m/s aligned flow. The simulations were validated using particle image velocimetry (PIV) to experimentally characterize the flow around the tag design. The results of these experiments confirm the trends predicted by the simulations and demonstrate the potential benefit of flow control elements for the reduction of tag induced forces on the animal.