Biomechanics, motor control and dynamic models of the soft limbs of the octopus and other cephalopods

Muscular hydrostats are organs composed entirely of packed arrays of incompressible muscles and lacking any skeletal support. Found in both vertebrates and invertebrates, they are of great interest for comparative biomechanics from engineering and evolutionary perspectives. The arms of cephalopods (e.g. octopus and squid) are particularly interesting muscular hydrostats because of their flexibility and ability to generate complex behaviors exploiting elaborate nervous systems. Several lines of evidence from octopus studies point to the use of both brain and arm-embedded motor control strategies that have evolved to simplify the complexities associated with the control of flexible and hyper-redundant limbs and bodies. Here, we review earlier and more recent experimental studies on octopus arm biomechanics and neural motor control. We review several dynamic models used to predict the kinematic characteristics of several basic motion primitives, noting the shortcomings of the current models in accounting for behavioral observations. We also discuss the significance of impedance (stiffness and viscosity) in controlling the octopus's motor behavior. These factors are considered in light of several new models of muscle biomechanics that could be used in future research to gain a better understanding of motor control in the octopus. There is also a need for updated models that encompass stiffness and viscosity for designing and controlling soft robotic arms. The field of soft robotics has boomed over the past 15 years and would benefit significantly from further progress in biomechanical and motor control studies on octopus and other muscular hydrostats.

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.

Knifefish turning control and hydrodynamics during forward swimming

Rapid turning and swimming contribute to ecologically important behaviors in fishes such as predator avoidance, prey capture, mating, and the navigation of complex environments. For riverine species, such as knifefishes, turning behaviors may also be important for navigating locomotive perturbations caused by turbulent flows. Most research on fish maneuvering focuses on fish with traditional fin and body morphologies, which primarily use body bending and the pectoral fins during turning. However, it is uncertain how fishes with uncommon morphologies, are able to achieve sudden and controllable turns. Here we studied the turning performance and the turning hydrodynamics of the Black ghost knifefish (Apteronotus albifrons, N=6) which has an atypical elongated ribbon fin. Fish were filmed while swimming forward at ∼2 BL s-1 and feeding from a fixed feeder (control) and an oscillating feeder (75 Hz) at two different amplitudes. 3D kinematic analysis of the body revealed the highest pitch angles and lowest body bending coefficients occurred during steady swimming. Low pitch angle, high maximum yaw angles and large body bending coefficients were characteristic of small and large turns. Asynchrony in pectoral fin use was low during turning, however ribbon fin wavelength, frequency, and wave speed were greatest during large turns. Digital particle image velocimetry (DPIV) showed larger counter-rotating vortex pairs produced during turning by the ribbon-fin in comparison to vortices rotating in the same direction during steady swimming. Our results highlight the ribbon fin's role in controlled rapid turning through modulation of wavelength, frequency, and wave speed.

Beyond the Kármán gait: knifefish swimming in periodic and irregular vortex streets

Neotropical freshwater fishes such as knifefishes are commonly faced with navigating intense and highly unsteady streams. However, our knowledge on locomotion in apteronotids comes from laminar flows, where the ribbon fin dominates over the pectoral fins or body bending. Here, we studied the 3D kinematics and swimming control of seven black ghost knifefish (Apteronotus albifrons) moving in laminar flows (flow speed U∞≈1-5 BL s-1) and in periodic vortex streets (U∞≈2-4 BL s-1). Two different cylinders (∼2 and ∼3 cm diameter) were used to generate the latter. Additionally, fish were exposed to an irregular wake produced by a free oscillating cylinder (∼2 cm diameter; U∞≈2 BL s-1). In laminar flows, knifefish mainly used their ribbon fin, with wave frequency, speed and acceleration increasing with U∞. In contrast, knifefish swimming behind a fixed cylinder increased the use of pectoral fins, which resulted in changes in body orientation that mimicked steady backward swimming. Meanwhile, individuals behind the oscillating cylinder presented a combination of body bending and ribbon and pectoral fin movements that counteract the out-of-phase yaw oscillations induced by the irregular shedding of vortices. We corroborated passive out-of-phase oscillations by placing a printed knifefish model just downstream of the moving cylinder, but when placed one cylinder diameter downstream, the model oscillated in phase. Thus, the wake left behind an oscillating body is more challenging than a periodic vortex shedding for an animal located downstream, which may have consequences on inter- and intra-specific interactions.

Variability in locomotor dynamics reveals the critical role of feedback in task control

Animals vary considerably in size, shape, and physiological features across individuals, but yet achieve remarkably similar behavioral performances. We examined how animals compensate for morphophysiological variation by measuring the system dynamics of individual knifefish (Eigenmannia virescens) in a refuge tracking task. Kinematic measurements of Eigenmannia were used to generate individualized estimates of each fish’s locomotor plant and controller, revealing substantial variability between fish. To test the impact of this variability on behavioral performance, these models were used to perform simulated ‘brain transplants’—computationally swapping controllers and plants between individuals. We found that simulated closed-loop performance was robust to mismatch between plant and controller. This suggests that animals rely on feedback rather than precisely tuned neural controllers to compensate for morphophysiological variability.

People come in different shapes and sizes, but most will perform similarly well if asked to complete a task requiring fine manual dexterity – such as holding a pen or picking up a single grape. How can different individuals, with different sized hands and muscles, produce such similar movements? One explanation is that an individual’s brain and nervous system become precisely tuned to mechanics of the body’s muscles and skeleton. An alternative explanation is that brain and nervous system use a more “robust” control policy that can compensate for differences in the body by relying on feedback from the senses to guide the movements.

To distinguish between these two explanations, Uyanik et al. turned to weakly electric freshwater fish known as glass knifefish. These fish seek refuge within root systems, reed grass and among other objects in the water. They swim backwards and forwards to stay hidden despite constantly changing currents. Each fish shuttles back and forth by moving a long ribbon-like fin on the underside of its body. Uyanik et al. measured the movements of the ribbon fin under controlled conditions in the laboratory, and then used the data to create computer models of the brain and body of each fish. The models of each fish’s brain and body were quite different.

To study how the brain interacts with the body, Uyanik et al. then conducted experiments reminiscent of those described in the story of Frankenstein and transplanted the brain from each computer model into the body of different model fish. These “brain swaps” had almost no effect on the model’s simulated swimming behavior. Instead, these “Frankenfish” used sensory feedback to compensate for any mismatch between their brain and body.

This suggests that, for some behaviors, an animal’s brain does not need to be precisely tuned to the specific characteristics of its body. Instead, robust control of movement relies on many seemingly redundant systems that provide sensory feedback. This has implications for the field of robotics. It further suggests that when designing robots, engineers should prioritize enabling the robots to use sensory feedback to cope with unexpected events, a well-known idea in control engineering.

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.

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.

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.

Benthic walking, bounding, and maneuvering in flatfishes (Pleuronectiformes: Pleuronectidae): New vertebrate gaits

Video-based observations of voluntary movements reveal that six species of pleuronectid flatfishes use sequential portions of long-based dorsal and anal fins as "feet" (hereafter, fin-feet) to move on the substrate. All six species used a gait that we term "walking," which produced constant forward movement, and several of these species also used a second gait that we call "bounding" for intermittent movements over the substrate. We selected Pacific Sand Sole, Psettichthys melanostictus, and English Sole, Parophrys vetulus, for kinematic analyses of these two gaits. Psettichthys melanostictus consistently used walking for benthic locomotion; Parophrys vetulus primarily used a bounding gait. During forward walking, a fin ray swings up off the substrate, protracts and converges with neighboring fin rays to contribute to a fin-foot. The fin-foot pushes down on the substrate and rotates posteriorly by sequential recruitment of fin rays, a pattern known as a metachronal wave. As one fin-foot passes off the posterior end of the fin, a new fin-foot forms anteriorly. During bounding, undulations of the body and tail assist one or two waves of fin-feet, producing rapid but intermittent forward acceleration of the body. Flatfishes also use fin-feet to maneuver on the substrate. The Starry Flounder, Platichthys stellatus, performs near zero displacement rotation by running waves of fin-feet in opposing directions along the dorsal and anal fins. Although other teleosts use specialized pectoral fin rays for bottom walking (e.g., Sea Robins: Triglidae), the duplication of structures and patterns of movement in the median fins of flatfishes more closely resembles metachronal motions of millipede feet or the parapodia of polychaete worms. Sequential use of median fin rays in flatfishes resembles that of other teleosts that swim with elongate median fins, including Amiiformes, Gymnotiformes, and some Tetraodontiformes, but flatfishes offer a novel form of substrate locomotion based on dorsal and anal fins.

Dynamic modulation of visual and electrosensory gains for locomotor control

Animal nervous systems resolve sensory conflict for the control of movement. For example, the glass knifefish, Eigenmannia virescens, relies on visual and electrosensory feedback as it swims to maintain position within a moving refuge. To study how signals from these two parallel sensory streams are used in refuge tracking, we constructed a novel augmented reality apparatus that enables the independent manipulation of visual and electrosensory cues to freely swimming fish (n = 5). We evaluated the linearity of multisensory integration, the change to the relative perceptual weights given to vision and electrosense in relation to sensory salience, and the effect of the magnitude of sensory conflict on sensorimotor gain. First, we found that tracking behaviour obeys superposition of the sensory inputs, suggesting linear sensorimotor integration. In addition, fish rely more on vision when electrosensory salience is reduced, suggesting that fish dynamically alter sensorimotor gains in a manner consistent with Bayesian integration. However, the magnitude of sensory conflict did not significantly affect sensorimotor gain. These studies lay the theoretical and experimental groundwork for future work investigating multisensory control of locomotion.

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.

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.

Stability versus Maneuvering: Challenges for Stability during Swimming by Fishes

Fishes are well known for their remarkable maneuverability and agility. Less visible is the continuous control of stability essential for the exploitation of the full range of aquatic resources. Perturbations to posture and trajectory arise from hydrostatic and hydrodynamic forces centered in a fish (intrinsic) and from the environment (extrinsic). Hydrostatic instabilities arise from vertical and horizontal separation of the centers of mass (CM) and of buoyancy, thereby creating perturbations in roll, yaw, and pitch, with largely neglected implications for behavioral ecology. Among various forms of hydrodynamic stability, the need for stability in the face of recoil forces from propulsors is close to universal. Destabilizing torques in body-caudal fin swimming is created by inertial and viscous forces through a propulsor beat. The recoil component is reduced, damped, and corrected in various ways, including kinematics, shape of the body and fins, and deployment of the fins. We postulate that control of the angle of orientation, θ, of the trailing edge is especially important in the evolution and lifestyles of fishes, but studies are few. Control of stability and maneuvering are reflected in accelerations around the CM. Accelerations for such motions may give insight into time-behavior patterns in the wild but cannot be used to determine the expenditure of energy by free-swimming fishes.

Predicting propulsive forces using distributed sensors in a compliant, high DOF, robotic fin

Engineered robotic fins have adapted principles of propulsion from bony-finned fish, using spatially-varying compliance and complex kinematics to produce and control the fin's propulsive force through time. While methods of force production are well understood, few models exist to predict the propulsive forces of a compliant, high degree of freedom, robotic fin as it moves through fluid. Inspired by evidence that the bluegill sunfish (Lepomis macrochirus) has bending sensation in its pectoral fins, the objective of this study is to understand how sensors distributed within a compliant robotic fin can be used to estimate and predict the fin's propulsive force. A biorobotic model of a bluegill sunfish pectoral fin was instrumented with pressure and bending sensors at multiple locations. Experiments with the robotic fin were executed that varied the swimming gait, flapping frequency, stroke phase, and fin stiffness to understand the forces and sensory measures that occur during swimming. A convolution-based, multi-input-single-output (MISO) model was selected to model and study the relationships between sensory data and propulsive force. Subsets of sensory data were studied to determine which sensor modalities and sensor placement locations resulted in the best force predictions. The propulsive forces of the fin were accurately predicted using the linear MISO model on intrinsic sensory data. Bending sensation was more effective than pressure sensation for predicting propulsive forces, and the importance of bending sensation was consistent with several results in biology and engineering studies. It was important to have a spatial distribution of sensors and multiple sensory modalities in order to predict forces across large changes to dynamics. The relationship between propulsive forces and intrinsic sensory measures is complex, and good models should allow for temporal lags between forces and sensory data, changes to the model within a fin stroke, and changes to the model through gait transitions.

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.

Fish locomotion: recent advances and new directions

Research on fish locomotion has expanded greatly in recent years as new approaches have been brought to bear on a classical field of study. Detailed analyses of patterns of body and fin motion and the effects of these movements on water flow patterns have helped scientists understand the causes and effects of hydrodynamic patterns produced by swimming fish. Recent developments include the study of the center-of-mass motion of swimming fish and the use of volumetric imaging systems that allow three-dimensional instantaneous snapshots of wake flow patterns. The large numbers of swimming fish in the oceans and the vorticity present in fin and body wakes support the hypothesis that fish contribute significantly to the mixing of ocean waters. New developments in fish robotics have enhanced understanding of the physical principles underlying aquatic propulsion and allowed intriguing biological features, such as the structure of shark skin, to be studied in detail.

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.

Feedback control as a framework for understanding tradeoffs in biology

Control theory arose from a need to control synthetic systems. From regulating steam engines to tuning radios to devices capable of autonomous movement, it provided a formal mathematical basis for understanding the role of feedback in the stability (or change) of dynamical systems. It provides a framework for understanding any system with regulation via feedback, including biological ones such as regulatory gene networks, cellular metabolic systems, sensorimotor dynamics of moving animals, and even ecological or evolutionary dynamics of organisms and populations. Here, we focus on four case studies of the sensorimotor dynamics of animals, each of which involves the application of principles from control theory to probe stability and feedback in an organism's response to perturbations. We use examples from aquatic (two behaviors performed by electric fish), terrestrial (following of walls by cockroaches), and aerial environments (flight control by moths) to highlight how one can use control theory to understand the way feedback mechanisms interact with the physical dynamics of animals to determine their stability and response to sensory inputs and perturbations. Each case study is cast as a control problem with sensory input, neural processing, and motor dynamics, the output of which feeds back to the sensory inputs. Collectively, the interaction of these systems in a closed loop determines the behavior of the entire system.

Mutually opposing forces during locomotion can eliminate the tradeoff between maneuverability and stability

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.

Kinematics of ribbon-fin locomotion in the bowfin, Amia calva

An elongated dorsal and/or anal ribbon-fin to produce forward and backward propulsion has independently evolved in several groups of fishes. In these fishes, fin ray movements along the fin generate a series of waves that drive propulsion. There are no published data on the use of the dorsal ribbon-fin in the basal freshwater bowfin, Amia calva. In this study, frequency, amplitude, wavelength, and wave speed along the fin were measured in Amia swimming at different speeds (up to 1.0 body length/sec) to understand how the ribbon-fin generates propulsion. These wave properties were analyzed to (1) determine whether regional specialization occurs along the ribbon-fin, and (2) to reveal how the undulatory waves are used to control swimming speed. Wave properties were also compared between swimming with sole use of the ribbon-fin, and swimming with simultaneous use of the ribbon and pectoral fins. Statistical analysis of ribbon-fin kinematics revealed no differences in kinematic patterns along the ribbon-fin, and that forward propulsive speed in Amia is controlled by the frequency of the wave in the ribbon-fin, irrespective of the contribution of the pectoral fin. This study is the first kinematic analysis of the ribbon-fin in a basal fish and the model species for Amiiform locomotion, providing a basis for understanding ribbon-fin locomotion among a broad range of teleosts.

Biomimetic and bio-inspired robotics in electric fish research

Weakly 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.

Undulating fins produce off-axis thrust and flow structures

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 high-fidelity 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 as well as a virtual rendering of our robot. Our results indicate 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 due to the undulatory kinematics of the elongated fin.