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

SUMMARYWeakly electric fish are extraordinarily maneuverable swimmers, able to swim as easily forward as backward and rapidly switch swim direction, among other maneuvers. The primary propulsor of gymnotid electric fish is an elongated ribbon-like anal fin. To understand the mechanical basis of their maneuverability, we examine the hydrodynamics of a non-translating ribbon fin in stationary water using computational fluid dynamics and digital particle image velocimetry (DPIV) of the flow fields around a robotic ribbon fin. Computed forces are compared with drag measurements from towing a cast of the fish and with thrust estimates for measured swim-direction reversals. We idealize the movement of the fin as a traveling sinusoidal wave, and derive scaling relationships for how thrust varies with the wavelength, frequency, amplitude of the traveling wave and fin height. We compare these scaling relationships with prior theoretical work. The primary mechanism of thrust production is the generation of a streamwise central jet and the associated attached vortex rings. Under certain traveling wave regimes, the ribbon fin also generates a heave force, which pushes the body up in the body-fixed frame. In one such regime, we show that as the number of waves along the fin decreases to approximately two-thirds, the heave force surpasses the surge force. This switch from undulatory parallel thrust to oscillatory normal thrust may be important in understanding how the orientation of median fins may vary with fin length and number of waves along them. Our results will be useful for understanding the neural basis of control in the weakly electric knifefish as well as for engineering bio-inspired vehicles with undulatory thrusters. Supplementary material available online at

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

Five unique soft robotic jellyfish were manufactured with eight pneumatic network tentacle actuators extending radially from their centers. These jellyfish robots were able to freely swim untethered in the ocean, to steer from side to side, and to swim through orifices more narrow than the nominal diameter of the jellyfish. Each of the five jellyfish robots were manufactured with a different composition of body and tentacle actuator Shore hardness. A three-factor study was performed with these five jellyfish robots to determine the impact that actuator material Shore hardness, actuation frequency, and tentacle stroke actuation amplitude had upon the measured thrust force. It was found that all three of these factors significantly impacted mean thrust force generation, which peaked with a half-stroke actuation amplitude at a frequency of 0.8 Hz.

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

, N=1000 for all other cases). . A single wave travels caudally during forward swimming, while two waves traveling towards each other are observed while hovering. Grayscale is used to enhance amplitude information. The rostral end of the fin is at 0% on the fin length axis.Two errors appeared in J. Exp. Biol. 216,[823][824][825][826][827][828][829][830][831][832][833][834] During data processing, the wrong scaling factor was used when converting the fin amplitude from pixels on the video to linear displacement in millimetres [term y(x) in Eqn 1]. This error caused the angular displacement to be underestimated by a factor that varied between 2.9 and 3.6 (mean ± s.d. = 3.28 ± 0.27) for the different data sets.The error is found in Figs 2, 4, 9 and 10. In the right panels of Fig. 2, both panels of Fig. 4, Fig. 9C and the color bar in Fig. 10, the range of the y-axis is approximately three times smaller than it should have been.In the Results and Discussion, we comment on the direction of the change in amplitude at different swimming speeds. The error does not affect these comments because the amplitude at all swimming speeds was scaled by approximately the same factor.A second error was introduced when calculating the ratio of the fin length to the fin base length. The measurement of the fin base length was performed only on the first frame of every data set, instead of averaging the length across all the frames as was done for the fin length. This caused the ratio of fin length to fin base length to be larger in the hovering condition and smaller when swimming at 6 cm s −1. After the correction, the ratio is more constant than before. 3766

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

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