A surprising feature of animal locomotion is that organisms typically produce substantial forces in directions other than what is necessary to move the animal through its environment, such as perpendicular to, or counter to, the direction of travel. The effect of these forces has been difficult to observe because they are often mutually opposing and therefore cancel out. Indeed, it is likely that these forces do not contribute directly to movement but may serve an equally important role: to simplify and enhance the control of locomotion. To test this hypothesis, we examined a well-suited model system, the glass knifefish Eigenmannia virescens, which produces mutually opposing forces during a hovering behavior that is analogous to a hummingbird feeding from a moving flower. Our results and analyses, which include kinematic data from the fish, a mathematical model of its swimming dynamics, and experiments with a biomimetic robot, demonstrate that the production and differential control of mutually opposing forces is a strategy that generates passive stabilization while simultaneously enhancing maneuverability. Mutually opposing forces during locomotion are widespread across animal taxa, and these results indicate that such forces can eliminate the tradeoff between stability and maneuverability, thereby simplifying neural control.bioinspired robotics | biomechanics

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.

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.

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.

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.

Weakly electric knifefish, Eigenmannia, are highly maneuverable swimmers. The animals rely on a long, undulating ribbon fin to generate propulsive force. During closed-loop control of hovering and station keeping, knifefish partition their fin to produce two inward counter-propagating waves, enabling them to hover and rapidly change direction. In response to moving objects or changes in ambient flow speed, the fish can actively modulate the nodal point where the two waves meet. During hovering, this nodal point is somewhere in the middle, but it can be moved forward or backward changing the relative force generated by the front and back portions of the fin. Although this strategy for thrust generation may be energetically inefficient, we show here that it enables rapid switching of swimming direction and produces a linear drag-like force that confers passive stability. Robotic results and simple computational simulations reveal that the net force generated by counter-propagating waves changes linearly with respect to the nodal position. Another strategy for reversing swim direction would be to completely reverse the direction of a single traveling wave. We show why full wave reversal (and similar strategies) may be ineffective for low-speed swimming-a regime where counter-propagating waves may simplify control.

Weakly electric fish emit an AC electric field into the water and use thousands of sensors on the skin to detect field perturbations due to surrounding objects. The fish's active electrosensory system allows them to navigate and hunt, using separate neural pathways and receptors for resistive and capacitive perturbations. We have previously developed a sensing method inspired by the weakly electric fish to detect resistive perturbations and now report on an extension of this system to detect capacitive perturbations as well. In our method, an external object is probed by an AC field over multiple frequencies. We present a quantitative framework that relates the response of a capacitive object at multiple frequencies to the object's composition and internal structure, and we validate this framework with an electrosense robot that implements our capacitive sensing method. We define a metric for comparing the electrosensory range of different underwater electrosense systems. For detecting non-conductive objects, we show that capacitive sensing performs better than resistive sensing by almost an order of magnitude using this measure, while for conductive objects there is a four-fold increase in performance. Capacitive sensing could therefore provide electric fish with extended sensing range for capacitive objects such as prey, and gives artificial electrolocation systems enhanced range for targets that are capacitive.

Tracking the position of moving objects requires tight coordination of sensing and movement, in both biological contexts such as prey pursuit and capture, and in target localization by mobile robots. Algorithms for target tracking often use a probabilistic map, or information map, of the domain to guide active search. Though it is reasonable to expect that the best approach would be to choose control actions driving the robot toward the maximum of this information map, we show improved performance in simulation by using a simple heuristic incorporating the time history of robot movement into the map. Furthermore, our results indicate that as the distribution of robot positions approaches the distribution of the density of information, the variance of the estimate is decreased and tracking improves. We conclude that control actions based solely on information maximization may underperform in information orientated tasks, such as the estimation of moving target positions.