The critical role of locomotion mechanics in decoding sensory systems

Swimming in the "Matrix": VR fish pass the Turing test using a simple control law for collective behavior

Immersive virtual reality reveals that a simple control model from fish schooling can be used to control autonomous vehicles.

Moving in an Uncertain World: Robust and Adaptive Control of Locomotion from Organisms to Machine Intelligence

Whether walking, running, slithering, or flying, organisms display a remarkable ability to move through complex and uncertain environments. In particular, animals have evolved to cope with a host of uncertainties-both of internal and external origin-to maintain adequate performance in an ever-changing world. In this review, we present mathematical methods in engineering to highlight emerging principles of robust and adaptive control of organismal locomotion. Specifically, by drawing on the mathematical framework of control theory, we decompose the robust and adaptive hierarchical structure of locomotor control. We show how this decomposition along the robust-adaptive axis provides testable hypotheses to classify behavioral outcomes to perturbations. With a focus on studies in non-human animals, we contextualize recent findings along the robust-adaptive axis by emphasizing two broad classes of behaviors: (1) compensation to appendage loss and (2) image stabilization and fixation. Next, we attempt to map robust and adaptive control of locomotion across some animal groups and existing bio-inspired robots. Finally, we highlight exciting future directions and interdisciplinary collaborations that are needed to unravel principles of robust and adaptive locomotion.

Sensorimotor adaptation to destabilizing dynamics in weakly electric fish

Humans and other animals can readily learn to compensate for changes in the dynamics of movement. Such changes can result from an injury or changes in the weight of carried objects. These changes in dynamics can lead not only to reduced performance but also to dramatic instabilities. We evaluated the impacts of compensatory changes in control policies in relation to stability and robustness in Eigenmannia virescens, a species of weakly electric fish. We discovered that these fish retune their sensorimotor control system in response to experimentally generated destabilizing dynamics. Specifically, we used an augmented reality system to manipulate sensory feedback during an image stabilization task in which a fish maintained its position within a refuge. The augmented reality system measured the fish's movements in real time. These movements were passed through a high-pass filter and multiplied by a gain factor before being fed back to the refuge motion. We adjusted the gain factor to gradually destabilize the fish's sensorimotor loop. The fish retuned their sensorimotor control system to compensate for the experimentally induced destabilizing dynamics. This retuning was partially maintained when the augmented reality feedback was abruptly removed. The compensatory changes in sensorimotor control improved tracking performance as well as control-theoretic measures of robustness, including reduced sensitivity to disturbances and improved phase margins.

Structural damping renders the hawkmoth exoskeleton mechanically insensitive to non-sinusoidal deformations

Muscles act through elastic and dissipative elements to mediate movement, which can introduce dissipation and filtering which are important for energetics and control. The high power requirements of flapping flight can be reduced by an insect's exoskeleton, which acts as a spring with frequency-independent material properties under purely sinusoidal deformation. However, this purely sinusoidal dynamic regime does not encompass the asymmetric wing strokes of many insects or non-periodic deformations induced by external perturbations. As such, it remains unknown whether a frequency-independent model applies broadly and what implications it has for control. We used a vibration testing system to measure the mechanical properties of isolated Manduca sexta thoraces under symmetric, asymmetric and band-limited white noise deformations. The asymmetric and white noise conditions represent two types of generalized, multi-frequency deformations that may be encountered during steady-state and perturbed flight. Power savings and dissipation were indistinguishable between symmetric and asymmetric conditions, demonstrating that no additional energy is required to deform the thorax non-sinusoidally. Under white noise conditions, stiffness and damping were invariant with frequency, suggesting that the thorax has no frequency-dependent filtering properties. A simple flat frequency response function fits our measured frequency response. This work demonstrates the potential of materials with frequency-independent damping to simplify motor control by eliminating any velocity-dependent filtering that viscoelastic elements usually impose between muscle and wing.

Neuromuscular embodiment of feedback control elements in Drosophila flight

While insects such as Drosophila are flying, aerodynamic instabilities require that they make millisecond time scale adjustments to their wing motion to stay aloft and on course. These stabilization reflexes can be modeled as a proportional-integral (PI) controller; however, it is unclear how such control might be instantiated in insects at the level of muscles and neurons. Here, we show that the b1 and b2 motor units-prominent components of the fly's steering muscle system-modulate specific elements of the PI controller: the angular displacement (integral) and angular velocity (proportional), respectively. Moreover, these effects are observed only during the stabilization of pitch. Our results provide evidence for an organizational principle in which each muscle contributes to a specific functional role in flight control, a finding that highlights the power of using top-down behavioral modeling to guide bottom-up cellular manipulation studies.

Complementary feedback control enables effective gaze stabilization in animals

In visually active animals, eye, head, and body movements are coordinated to direct gaze. Given their distinct mechanics, how does the nervous system weight their contribution? By combining experiments in flying flies with control theory, we show that flies implement an elegant solution to this problem: the lower inertia head is recruited for higher-frequency visual tasks and is sensitive to motion acceleration, whereas the higher inertia body is recruited for lower-frequency visual tasks and is sensitive to motion velocity. This complementary division of labor within the nervous system exhibits two hallmarks of optimality: an increase in task performance accompanied with a decrease in mechanical energy expenditure. Our model recapitulates classic primate head-eye coordination responses, suggesting convergent mechanisms across phyla.

Visually active animals coordinate vision and movement to achieve spectacular tasks. An essential prerequisite to guide agile locomotion is to keep gaze level and stable. Since the eyes, head and body can move independently to control gaze, how does the brain effectively coordinate these distinct motor outputs? Furthermore, since the eyes, head, and body have distinct mechanical constraints (e.g., inertia), how does the nervous system adapt its control to these constraints? To address these questions, we studied gaze control in flying fruit flies (Drosophila) using a paradigm which permitted direct measurement of head and body movements. By combining experiments with mathematical modeling, we show that body movements are sensitive to the speed of visual motion whereas head movements are sensitive to its acceleration. This complementary tuning of the head and body permitted flies to stabilize a broader range of visual motion frequencies. We discovered that flies implement proportional-derivative (PD) control, but unlike classical engineering control systems, relay the proportional and derivative signals in parallel to two distinct motor outputs. This scheme, although derived from flies, recapitulated classic primate vision responses thus suggesting convergent mechanisms across phyla. By applying scaling laws, we quantify that animals as diverse as flies, mice, and humans as well as bio-inspired robots can benefit energetically by having a high ratio between head, body, and eye inertias. Our results provide insights into the mechanical constraints that may have shaped the evolution of active vision and present testable neural control hypotheses for visually guided behavior across phyla.

Honey bees respond to multimodal stimuli following the Principle of Inverse Effectiveness

Multisensory integration is assumed to entail benefits for receivers across multiple ecological contexts. However, signal integration effectiveness is constrained by features of the spatiotemporal and intensity domains. How sensory modalities are integrated during tasks facilitated by learning and memory, such as pollination, remains unsolved. Honey bees use olfactory and visual cues during foraging, making them a good model to study the use of multimodal signals. Here, we examined the effect of stimulus intensity on both learning and memory performance of bees trained using unimodal or bimodal stimuli. We measured the performance and the latency response across planned discrete levels of stimulus intensity. We employed the conditioning of the proboscis extension response protocol in honey bees using an electromechanical setup allowing us to control simultaneously and precisely olfactory and visual stimuli at different intensities. Our results show that the bimodal enhancement during learning and memory was higher as the intensity decreased when the separate individual components were least effective. Still, this effect was not detectable for the latency of response. Remarkably, these results support the principle of inverse effectiveness, traditionally studied in vertebrates, predicting that multisensory stimuli are more effectively integrated when the best unisensory response is relatively weak. Thus, we argue that the performance of the bees while using a bimodal stimulus depends on the interaction and intensity of its individual components. We further hold that the inclusion of findings across all levels of analysis enriches the traditional understanding of the mechanics and reliance of complex signals in honey bees.

Summary: Bimodal enhancement during learning and memory tasks in africanized honey bees increases as the stimulus intensity of its unimodal components decreases; this indicates that learning performance depends on the interaction between the intensity of its components and the nature of the sensory modalities involved, supporting the principle of inverse effectiveness.

Salience of multisensory feedback regulates behavioral variability

Many animal behaviors are robust to dramatic variations in morphophysiological features, both across and within individuals. The control strategies that animals use to achieve such robust behavioral performances are not known. Recent evidence suggests that animals rely on sensory feedback rather than precise tuning of neural controllers for robust control. Here we examine the structure of sensory feedback, including multisensory feedback, for robust control of animal behavior. We re-examined two recent datasets of refuge tracking responses ofEigenmannia virescens, a species of weakly electric fish.Eigenmanniarely on both the visual and electrosensory cues to track the position of a moving refuge. The datasets include experiments that varied the strength of visual and electrosensory signals. Our analyses show that increasing the salience (perceptibility) of visual or electrosensory signals resulted in more robust and precise behavioral responses. Further, we find that robust performance was enhanced by multisensory integration of simultaneous visual and electrosensory cues. These findings suggest that engineers may achieve better system performance by improving the salience of multisensory feedback rather than solely focusing on precisely tuned controllers.

Comparing system identification techniques for identifying human-like walking controllers

While human walking has been well studied, the exact controller is unknown. This paper used human experimental walking data and system identification techniques to infer a human-like controller for a spring-loaded inverted pendulum (SLIP) model. Because the best system identification technique is unknown, three methods were used and compared. First, a linear system was found using ordinary least squares. A second linear system was found that both encoded the linearized SLIP model and matched the first linear system as closely as possible. A third nonlinear system used sparse identification of nonlinear dynamics (SINDY). When directly mapping states from the start to the end of a step, all three methods were accurate, with errors below 10% of the mean experimental values in most cases. When using the controllers in simulation, the errors were significantly higher but remained below 10% for all but one state. Thus, all three system identification methods generated accurate system models. Somewhat surprisingly, the linearized system was the most accurate, followed closely by SINDY. This suggests that nonlinear system identification techniques are not needed when finding a discrete human gait controller, at least for unperturbed walking. It may also suggest that human control of normal, unperturbed walking is approximately linear.

De novo learning versus adaptation of continuous control in a manual tracking task

How do people learn to perform tasks that require continuous adjustments of motor output, like riding a bicycle? People rely heavily on cognitive strategies when learning discrete movement tasks, but such time-consuming strategies are infeasible in continuous control tasks that demand rapid responses to ongoing sensory feedback. To understand how people can learn to perform such tasks without the benefit of cognitive strategies, we imposed a rotation/mirror reversal of visual feedback while participants performed a continuous tracking task. We analyzed behavior using a system identification approach, which revealed two qualitatively different components of learning: adaptation of a baseline controller and formation of a new, task-specific continuous controller. These components exhibited different signatures in the frequency domain and were differentially engaged under the rotation/mirror reversal. Our results demonstrate that people can rapidly build a new continuous controller de novo and can simultaneously deploy this process with adaptation of an existing controller.

Tuning movement for sensing in an uncertain world

While animals track or search for targets, sensory organs make small unexplained movements on top of the primary task-related motions. While multiple theories for these movements exist-in that they support infotaxis, gain adaptation, spectral whitening, and high-pass filtering-predicted trajectories show poor fit to measured trajectories. We propose a new theory for these movements called energy-constrained proportional betting, where the probability of moving to a location is proportional to an expectation of how informative it will be balanced against the movement's predicted energetic cost. Trajectories generated in this way show good agreement with measured trajectories of fish tracking an object using electrosense, a mammal and an insect localizing an odor source, and a moth tracking a flower using vision. Our theory unifies the metabolic cost of motion with information theory. It predicts sense organ movements in animals and can prescribe sensor motion for robots to enhance performance.

Active Sensing: Constancy Requires Change

We constantly generate movements in order to enhance our ability to perceive the external environment. New research on electric fish has used augmented reality to demonstrate that animals dynamically regulate their movements to maintain variability in their sensory input.

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.

Visuomotor error augmentation affects mediolateral head and trunk stabilization during walking

Prior work demonstrates that humans spontaneously synchronize their head and trunk kinematics to a broad range of driving frequencies of perceived mediolateral motion prescribed using optical flow. Using a closed-loop visuomotor error augmentation task in an immersive virtual environment, we sought to understand whether unifying visual with vestibular and somatosensory feedback is a control goal during human walking, at least in the context of head and trunk stabilization. We hypothesized that humans would minimize visual errors during walking - i.e., those between the visual perception of movement and actual movement of the trunk. We found that subjects did not minimize errors between the visual perception of movement and actual movement of the head and trunk. Rather, subjects increased mediolateral trunk range of motion in response to error-augmented optical flow with positive feedback gains. Our results are more consistent with our alternative hypothesis - that visual feedback can override other sensory modalities and independently compel adjustments in head and trunk position. Also, aftereffects following exposure to error-augmented optical flow included longer, narrower steps and reduced mediolateral postural sway, particularly in response to larger amplitude positive feedback gains. Our results allude to a recalibration of head and trunk stabilization toward more tightly regulated postural control following exposure to error-augmented visual feedback. Lasting reductions in mediolateral postural sway may have implications for using error-augmented optical flow to enhance the integrity of walking balance control through training, for example in older adults.

Sensory Cues Modulate Smooth Pursuit and Active Sensing Movements

Animals routinely use autogenous movement to regulate the information encoded by their sensory systems. Weakly electric fish use fore-aft movements to regulate visual and electrosensory feedback as they maintain position within a moving refuge. During refuge tracking, fish produce two categories of movements: smooth pursuit that is approximately linear in its relation to the movement of the refuge and ancillary active sensing movements that are nonlinear. We identified four categories of nonlinear movements which we termed scanning, wiggle, drift, and reset. To examine the relations between sensory cues and production of both linear smooth pursuit and nonlinear active sensing movements, we altered visual and electrosensory cues for refuge tracking and measured the fore-aft movements of the fish. Specifically, we altered the length and structure of the refuge and performed experiments with light and in complete darkness. Linear measures of tracking performance were better for shorter refuges (less than a body length) than longer ones (>1.5 body lengths). The magnitude of nonlinear active sensing movements was strongly modulated by light cues but also increased as a function of both longer refuge length and decreased features. Specifically, fish shifted swimming movements from smooth pursuit to scanning when tracking in dark conditions. Finally, fish appear to use nonlinear movements as an alternate tracking strategy in longer refuges: the fish may use more drifts and resets to avoid exiting the ends of the refuge.

Complementary spatial and timing control in rhythmic arm movements

Volitional rhythmic motor behaviors such as limb cycling and locomotion exhibit spatial and timing regularity. Such rhythmic movements are executed in the presence of exogenous visual and nonvisual cues, and previous studies have shown the pivotal role that vision plays in guiding spatial and temporal regulation. However, the influence of nonvisual information conveyed through auditory or touch sensory pathways, and its effect on control, remains poorly understood. To characterize the function of nonvisual feedback in rhythmic arm control, we designed a paddle juggling task in which volunteers bounced a ball off a rigid elastic surface to a target height in virtual reality by moving a physical handle with the right hand. Feedback was delivered at two key phases of movement: visual feedback at ball peaks only and simultaneous audio and haptic feedback at ball-paddle collisions. In contrast to previous work, we limited visual feedback to the minimum required for jugglers to assess spatial accuracy, and we independently perturbed the spatial dimensions and the timing of feedback. By separately perturbing this information, we evoked dissociable effects on spatial accuracy and timing, confirming that juggling, and potentially other rhythmic tasks, involves two complementary processes with distinct dynamics: spatial error correction and feedback timing synchronization. Moreover, we show evidence that audio and haptic feedback provide sufficient information for the brain to control the timing synchronization process by acting as a metronome-like cue that triggers hand movement. NEW & NOTEWORTHY Vision contains rich information for control of rhythmic arm movements; less is known, however, about the role of nonvisual feedback (touch and sound). Using a virtual ball bouncing task allowing independent real-time manipulation of spatial location and timing of cues, we show their dissociable roles in regulating motor behavior. We confirm that visual feedback is used to correct spatial error and provide new evidence that nonvisual event cues act to reset the timing of arm movements.

Closed-Loop Control of Active Sensing Movements Regulates Sensory Slip

Active sensing involves the production of motor signals for the purpose of acquiring sensory information [1-3]. The most common form of active sensing, found across animal taxa and behaviors, involves the generation of movements-e.g., whisking [4-6], touching [7, 8], sniffing [9, 10], and eye movements [11]. Active sensing movements profoundly affect the information carried by sensory feedback pathways [12-15] and are modulated by both top-down goals (e.g., measuring weight versus texture [1, 16]) and bottom-up stimuli (e.g., lights on or off [12]), but it remains unclear whether and how these movements are controlled in relation to the ongoing feedback they generate. To investigate the control of movements for active sensing, we created an experimental apparatus for freely swimming weakly electric fish, Eigenmannia virescens, that modulates the gain of reafferent feedback by adjusting the position of a refuge based on real-time videographic measurements of fish position. We discovered that fish robustly regulate sensory slip via closed-loop control of active sensing movements. Specifically, as fish performed the task of maintaining position inside the refuge [17-22], they dramatically up- or downregulated fore-aft active sensing movements in relation to a 4-fold change of experimentally modulated reafferent gain. These changes in swimming movements served to maintain a constant magnitude of sensory slip. The magnitude of sensory slip depended on the presence or absence of visual cues. These results indicate that fish use two controllers: one that controls the acquisition of information by regulating feedback from active sensing movements and another that maintains position in the refuge, a control structure that may be ubiquitous in animals [23, 24].

Serotonin Selectively Increases Detectability of Motion Stimuli in the Electrosensory System

Serotonergic innervation of sensory areas is found ubiquitously across the central nervous system of vertebrates. Here, we used a system's level approach to investigate the role of serotonin on processing motion stimuli in the electrosensory system of the weakly electric fish Apteronotus albifrons. We found that exogenous serotonin application increased the firing activity of pyramidal neural responses to both looming and receding motion. Separating spikes belonging to bursts from those that were isolated revealed that this effect was primarily due to increased burst firing. Moreover, when investigating whether firing activity during stimulation could be discriminated from baseline (i.e., in the absence of stimulation), we found that serotonin increased stimulus discriminability only for some stimuli. This is because increased burst firing was most prominent for these. Further, the effects of serotonin were highly heterogeneous, with some neurons displaying large while others instead displaying minimal changes in responsiveness following serotonin application. Further analysis revealed that serotonin application had the greatest effect on neurons with low baseline firing rates and little to no effect on neurons with high baseline firing rates. Finally, the effects of serotonin on sensory neuron responses were largely independent of object velocity. Our results therefore reveal a novel function for the serotonergic system in selectively enhancing discriminability for motion stimuli.

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.

Entrainment Ranges for Chains of Forced Neural and Phase Oscillators

Sensory input to the lamprey central pattern generator (CPG) for locomotion is known to have a significant role in modulating lamprey swimming. Lamprey CPGs are known to have the ability to entrain to a bending stimulus, that is, in the presence of a rhythmic signal, the CPG will change its frequency to match the stimulus frequency. Bending experiments in which the lamprey spinal cord has been removed and mechanically bent back and forth at a single point have been used to determine the range of frequencies that can entrain the CPG rhythm. First, we model the lamprey locomotor CPG as a chain of neural oscillators with three classes of neurons and sinusoidal forcing representing edge cell input. We derive a phase model using the connections described in the neural model. This results in a simpler model yet maintains some properties of the neural model. For both the neural model and the derived phase model, entrainment ranges are computed for forcing at different points along the chain while varying both intersegmental coupling strength and the coupling strength between the forcer and chain. Entrainment ranges for chains with nonuniform intersegmental coupling asymmetry are larger when forcing is applied to the middle of the chain than when it is applied to either end, a result that is qualitatively similar to the experimental results. In the limit of weak coupling in the chain, the entrainment results of the neural model approach the entrainment results for the derived phase model. Both biological experiments and the robustness of non-monotonic entrainment ranges as a function of the forcing position across different classes of CPG models with nonuniform asymmetric coupling suggest that a specific property of the intersegmental coupling of the CPG is key to entrainment.

Characterization of objects by electrosensing fish based on the first order polarization tensor

Weakly electric fish generate electric current and use hundreds of voltage sensors on the surface of their body to navigate and locate food. Experiments (von der Emde and Fetz 2007 J. Exp. Biol. 210 3082-95) show that they can discriminate between differently shaped conducting or insulating objects by using electrosensing. One approach to electrically identify and characterize the object with a lower computational cost rather than full shape reconstruction is to use the first order polarization tensor (PT) of the object. In this paper, by considering experimental work on Peters' elephantnose fish Gnathonemus petersii, we investigate the possible role of the first order PT in the ability of the fish to discriminate between objects of different shapes. We also suggest some experiments that might be performed to further investigate the role of the first order PT in electrosensing fish. Finally, we speculate on the possibility of electrical cloaking or camouflage in prey of electrosensing fish and what might be learnt from the fish in human remote sensing.

Walking dynamics are symmetric (enough)

Many biological phenomena such as locomotion, circadian cycles and breathing are rhythmic in nature and can be modelled as rhythmic dynamical systems. Dynamical systems modelling often involves neglecting certain characteristics of a physical system as a modelling convenience. For example, human locomotion is frequently treated as symmetric about the sagittal plane. In this work, we test this assumption by examining human walking dynamics around the steady state (limit-cycle). Here, we adapt statistical cross-validation in order to examine whether there are statistically significant asymmetries and, even if so, test the consequences of assuming bilateral symmetry anyway. Indeed, we identify significant asymmetries in the dynamics of human walking, but nevertheless show that ignoring these asymmetries results in a more consistent and predictive model. In general, neglecting evident characteristics of a system can be more than a modelling convenience--it can produce a better model.

Delay-Dependent Response in Weakly Electric Fish under Closed-Loop Pulse Stimulation

In this paper, we apply a real time activity-dependent protocol to study how freely swimming weakly electric fish produce and process the timing of their own electric signals. Specifically, we address this study in the elephant fish, Gnathonemus petersii, an animal that uses weak discharges to locate obstacles or food while navigating, as well as for electro-communication with conspecifics. To investigate how the inter pulse intervals vary in response to external stimuli, we compare the response to a simple closed-loop stimulation protocol and the signals generated without electrical stimulation. The activity-dependent stimulation protocol explores different stimulus delivery delays relative to the fish's own electric discharges. We show that there is a critical time delay in this closed-loop interaction, as the largest changes in inter pulse intervals occur when the stimulation delay is below 100 ms. We also discuss the implications of these findings in the context of information processing in weakly electric fish.

Parallel sparse and dense information coding streams in the electrosensory midbrain

Efficient processing of incoming sensory information is critical for an organism's survival. It has been widely observed across systems and species that the representation of sensory information changes across successive brain areas. Indeed, peripheral sensory neurons tend to respond densely to a broad range of sensory stimuli while more central neurons tend to instead respond sparsely to a narrow range of stimuli. Such a transition might be advantageous as sparse neural codes are thought to be metabolically efficient and optimize coding efficiency. Here we investigated whether the neural code transitions from dense to sparse within the midbrain Torus semicircularis (TS) of weakly electric fish. Confirming previous results, we found both dense and sparse coding neurons. However, subsequent histological classification revealed that most dense neurons projected to higher brain areas. Our results thus provide strong evidence against the hypothesis that the neural code transitions from dense to sparse in the electrosensory system. Rather, they support the alternative hypothesis that higher brain areas receive parallel streams of dense and sparse coded information from the electrosensory midbrain. We discuss the implications and possible advantages of such a coding strategy and argue that it is a general feature of sensory processing.

Wing-pitch modulation in maneuvering fruit flies is explained by an interplay between aerodynamics and a torsional spring

While the wing kinematics of many flapping insects have been well characterized, understanding the underlying sensory, neural, and physiological mechanisms that determine these kinematics is still a challenge. Two main difficulties in understanding the physiological mechanisms arise from the complexity of the interaction between a flapping wing and its own unsteady flow, as well as the intricate mechanics of the insect wing hinge, which is among the most complicated joints in the animal kingdom. These difficulties call for the application of reduced-order approaches. Here this strategy is used to model the torques exerted by the wing hinge along the wing-pitch axis of maneuvering fruit flies as a damped torsional spring with elastic and damping coefficients as well as a rest angle. Furthermore, we model the air flows using simplified quasistatic aerodynamics. Our findings suggest that flies take advantage of the passive coupling between aerodynamics and the damped torsional spring to indirectly control their wing-pitch kinematics by modulating the spring parameters. The damped torsional-spring model explains the changes measured in wing-pitch kinematics during roll correction maneuvers through modulation of the spring damping and elastic coefficients. These results, in conjunction with the previous literature, indicate that flies can accurately control their wing-pitch kinematics on a sub-wing-beat time scale by modulating all three effective spring parameters on longer time scales.

Pitch perfect: how fruit flies control their body pitch angle

Flapping insect flight is a complex and beautiful phenomenon that relies on fast, active control mechanisms to counter aerodynamic instability. To directly investigate how freely-flying D. melanogaster control their body pitch angle against such instability, we perturb them using impulsive mechanical torques and film their corrective maneuvers with high-speed video. Combining experimental observations and numerical simulation, we find that flies correct for pitch deflections of up to 40° in 29±8 ms by bilaterally modulating their wings' front-most stroke angle in a manner well-described by a linear proportional-integral (PI) controller. Flies initiate this corrective process only 10±2 ms after the perturbation onset, indicating that pitch stabilization involves a fast reflex response. Remarkably, flies can also correct for very large-amplitude pitch perturbations–greater than 150°–providing a regime in which to probe the limits of the linear-response framework. Together with previous studies regarding yaw and roll control, our results on pitch show that flies' stabilization of each of these body angles is consistent with PI control

Sensory processing within antenna enables rapid implementation of feedback control for high-speed running maneuvers

Animals are remarkably stable during high-speed maneuvers. As the speed of locomotion increases, neural bandwidth and processing delays can limit the ability to achieve and maintain stable control. Processing the information of sensory stimuli into a control signal within the sensor itself could enable rapid implementation of whole-body feedback control during high-speed locomotion. Here, we show that processing in antennal afferents is sufficient to act as control signal for a fast sensorimotor loop. American cockroaches Periplaneta americana use their antennae to mediate escape running by tracking vertical surfaces such as walls. A control theoretic model of wall following predicts that stable control is possible if the animal can compute wall position (P) and velocity, its derivative, (D). Previous whole-nerve recordings from the antenna during simulated turning experiments demonstrated a population response consistent with P and D encoding, and suggested that the response was synchronized with the timing of a turn executed while wall following. Here, we record extracellularly from individual mechanoreceptors distributed along the antenna and show that these receptors encode D and have distinct latencies and filtering properties. When summed, receptors transform the stimulus into a control signal that could control rapid steering maneuvers. The D encoding within the antenna in addition to the temporal filtering properties and P dependence of the population of afferents support a sensory encoding hypothesis from control theory. Our findings support the hypothesis that peripheral sensory processing can enable rapid implementation of whole-body feedback control during rapid running maneuvers.

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.

Motor patterns during active electrosensory acquisition

Motor patterns displayed during active electrosensory acquisition of information seem to be an essential part of a sensory strategy by which weakly electric fish actively generate and shape sensory flow. These active sensing strategies are expected to adaptively optimize ongoing behavior with respect to either motor efficiency or sensory information gained. The tight link between the motor domain and sensory perception in active electrolocation make weakly electric fish like Gnathonemus petersii an ideal system for studying sensory-motor interactions in the form of active sensing strategies. Analyzing the movements and electric signals of solitary fish during unrestrained exploration of objects in the dark, we here present the first formal quantification of motor patterns used by fish during electrolocation. Based on a cluster analysis of the kinematic values we categorized the basic units of motion. These were then analyzed for their associative grouping to identify and extract short coherent chains of behavior. This enabled the description of sensory behavior on different levels of complexity: from single movements, over short behaviors to more complex behavioral sequences during which the kinematics alter between different behaviors. We present detailed data for three classified patterns and provide evidence that these can be considered as motor components of active sensing strategies. In accordance with the idea of active sensing strategies, we found categorical motor patterns to be modified by the sensory context. In addition these motor patterns were linked with changes in the temporal sampling in form of differing electric organ discharge frequencies and differing spatial distributions. The ability to detect such strategies quantitatively will allow future research to investigate the impact of such behaviors on sensing.

Sensory processing and corollary discharge effects in posterior caudal lobe Purkinje cells in a weakly electric mormyrid fish

Although it has been suggested that the cerebellum functions to predict the sensory consequences of motor commands, how such predictions are implemented in cerebellar circuitry remains largely unknown. A detailed and relatively complete account of predictive mechanisms has emerged from studies of cerebellum-like sensory structures in fish, suggesting that comparisons of the cerebellum and cerebellum-like structures may be useful. Here we characterize electrophysiological response properties of Purkinje cells in a region of the cerebellum proper of weakly electric mormyrid fish, the posterior caudal lobe (LCp), which receives the same mossy fiber inputs and projects to the same target structures as the electrosensory lobe (ELL), a well-studied cerebellum-like structure. We describe patterns of simple spike and climbing fiber activation in LCp Purkinje cells in response to motor corollary discharge, electrosensory, and proprioceptive inputs and provide evidence for two functionally distinct Purkinje cell subtypes within LCp. Protocols that induce rapid associative plasticity in ELL fail to induce plasticity in LCp, suggesting differences in the adaptive functions of the two structures. Similarities and differences between LCp and ELL are discussed in light of these results.

Motion processing across multiple topographic maps in the electrosensory system

Animals can efficiently process sensory stimuli whose attributes vary over orders of magnitude by devoting specific neural pathways to process specific features in parallel. Weakly electric fish offer an attractive model system as electrosensory pyramidal neurons responding to amplitude modulations of their self‐generated electric field are organized into three parallel maps of the body surface. While previous studies have shown that these fish use parallel pathways to process stationary stimuli, whether a similar strategy is used to process motion stimuli remains unknown to this day. We recorded from electrosensory pyramidal neurons in the weakly electric fish Apteronotus leptorhynchus across parallel maps of the body surface (centromedial, centrolateral, and lateral) in response to objects moving at velocities spanning the natural range. Contrary to previous observations made with stationary stimuli, we found that all cells responded in a similar fashion to moving objects. Indeed, all cells showed a stronger directionally nonselective response when the object moved at a larger velocity. In order to explain these results, we built a mathematical model incorporating the known antagonistic center–surround receptive field organization of these neurons. We found that this simple model could quantitatively account for our experimentally observed differences seen across E and I‐type cells across all three maps. Our results thus provide strong evidence against the hypothesis that weakly electric fish use parallel neural pathways to process motion stimuli and we discuss their implications for sensory processing in general.

Haptic feedback enhances rhythmic motor control by reducing variability, not improving convergence rate

Stability and performance during rhythmic motor behaviors such as locomotion are critical for survival across taxa: falling down would bode well for neither cheetah nor gazelle. Little is known about how haptic feedback, particularly during discrete events such as the heel-strike event during walking, enhances rhythmic behavior. To determine the effect of haptic cues on rhythmic motor performance, we investigated a virtual paddle juggling behavior, analogous to bouncing a table tennis ball on a paddle. Here, we show that a force impulse to the hand at the moment of ball-paddle collision categorically improves performance over visual feedback alone, not by regulating the rate of convergence to steady state (e.g., via higher gain feedback or modifying the steady-state hand motion), but rather by reducing cycle-to-cycle variability. This suggests that the timing and state cues afforded by haptic feedback decrease the nervous system's uncertainty of the state of the ball to enable more accurate control but that the feedback gain itself is unaltered. This decrease in variability leads to a substantial increase in the mean first passage time, a measure of the long-term metastability of a stochastic dynamical system. Rhythmic tasks such as locomotion and juggling involve intermittent contact with the environment (i.e., hybrid transitions), and the timing of such transitions is generally easy to sense via haptic feedback. This timing information may improve metastability, equating to less frequent falls or other failures depending on the task.

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.

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.

Self-motion effects on hydrodynamic pressure sensing: part I. forward-backward motion

In underwater locomotion, extracting meaningful information from local flows is as desirable as it is challenging, due to complex fluid-structure interaction. Sensing and motion are tightly interconnected; hydrodynamic signals generated by the external stimuli are modified by the self-generated flow signals. Given that very little is known about self-generated signals, we used onboard pressure sensors to measure the pressure profiles over the head of a fusiform-shape craft while moving forward and backward harmonically. From these measurements we obtained a second-order polynomial model which incorporates the velocity and acceleration of the craft to estimate the surface pressure within the swimming range up to one body length/second (L s(-1)). The analysis of the model reveals valuable insights into the temporal and spatial changes of the pressure intensity as a function of craft's velocity. At low swimming velocities (<0.2 L s(-1)) the pressure signals are more sensitive to the acceleration of the craft than its velocity. However, the inertial effects gradually become less important as the velocity increases. The sensors on the front part of the craft are more sensitive to its movements than the sensors on the sides. With respect to the hydrostatic pressure measured in still water, the pressure detected by the foremost sensor reaches values up to 300 Pa at 1 L s(-1) swimming velocity, whereas the pressure difference between the foremost sensor and the next one is less than 50 Pa. Our results suggest that distributed pressure sensing can be used in a bimodal sensing strategy. The first mode detects external hydrodynamic events taking place around the craft, which requires minimal sensitivity to the self-motion of the craft. This can be accomplished by moving slowly with a constant velocity and by analyzing the pressure gradient as opposed to absolute pressure recordings. The second mode monitors the self-motion of the craft. It is shown here that distributed pressure sensing can be used as a speedometer to measure the craft's velocity.

Discriminating external and internal causes for heading changes in freely flying Drosophila

As animals move through the world in search of resources, they change course in reaction to both external sensory cues and internally-generated programs. Elucidating the functional logic of complex search algorithms is challenging because the observable actions of the animal cannot be unambiguously assigned to externally- or internally-triggered events. We present a technique that addresses this challenge by assessing quantitatively the contribution of external stimuli and internal processes. We apply this technique to the analysis of rapid turns (“saccades”) of freely flying Drosophila melanogaster. We show that a single scalar feature computed from the visual stimulus experienced by the animal is sufficient to explain a majority (93%) of the turning decisions. We automatically estimate this scalar value from the observable trajectory, without any assumption regarding the sensory processing. A posteriori, we show that the estimated feature field is consistent with previous results measured in other experimental conditions. The remaining turning decisions, not explained by this feature of the visual input, may be attributed to a combination of deterministic processes based on unobservable internal states and purely stochastic behavior. We cannot distinguish these contributions using external observations alone, but we are able to provide a quantitative bound of their relative importance with respect to stimulus-triggered decisions. Our results suggest that comparatively few saccades in free-flying conditions are a result of an intrinsic spontaneous process, contrary to previous suggestions. We discuss how this technique could be generalized for use in other systems and employed as a tool for classifying effects into sensory, decision, and motor categories when used to analyze data from genetic behavioral screens.

Researchers have spent considerable effort studying how specific sensory stimuli elicit behavioral responses and how other behaviors may arise independent of external inputs in conditions of sensory deprivation. Yet an animal in its natural context, such as searching for food or mates, turns both in response to external stimuli and intrinsic, possibly stochastic, decisions. We show how to estimate the contribution of vision and internal causes on the observable behavior of freely flying Drosophila. We developed a dimensionality reduction scheme that finds a one-dimensional feature of the visual stimulus that best predicts turning decisions. This visual feature extraction is consistent with previous literature on visually elicited fly turning and predicts a large majority of turns in the tested environment. The rarity of stimulus-independent events suggests that fly behavior is more deterministic than previously suggested and that, more generally, animal search strategies may be dominated by responses to stimuli with only modest contributions from internal causes.

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.

Using computational and mechanical models to study animal locomotion

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms' performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures. Despite the large body of recent work in this area, the application of mathematical and numerical methods to improve our understanding of organisms in the context of their environment and physiology has remained relatively unexplored. Nature has evolved a wide variety of fascinating mechanisms of locomotion that exploit the properties of complex materials and fluids, but only recently are the mathematical, computational, and robotic tools available to rigorously compare the relative advantages and disadvantages of different methods of locomotion in variable environments. Similarly, advances in computational physiology have only recently allowed investigators to explore how changes at the molecular, cellular, and tissue levels might lead to changes in performance at the organismal level. In this article, we highlight recent examples of how computational, mathematical, and experimental tools can be combined to ultimately answer the questions posed in one of the grand challenges in organismal biology: "Integrating living and physical systems."

Neuromuscular control of free-flight yaw turns in the hawkmoth Manduca sexta

The biomechanical properties of an animal's locomotor structures profoundly influence the relationship between neuromuscular inputs and body movements. In particular, passive stability properties are of interest as they may offer a non-neural mechanism for simplifying control of locomotion. Here, we hypothesized that a passive stability property of animal flight, flapping counter-torque (FCT), allows hawkmoths to control planar yaw turns in a damping-dominated framework that makes rotational velocity directly proportional to neuromuscular activity. This contrasts with a more familiar inertia-dominated framework where acceleration is proportional to force and neuromuscular activity. To test our hypothesis, we collected flight muscle activation timing, yaw velocity and acceleration data from freely flying hawkmoths engaged in planar yaw turns. Statistical models built from these data then allowed us to infer the degree to which the moths inhabit either damping- or inertia-dominated control domains. Contrary to our hypothesis, a combined model corresponding to inertia-dominated control of yaw but including substantial damping effects best linked the neuromuscular and kinematic data. This result shows the importance of including passive stability properties in neuromechanical models of flight control and reveals possible trade-offs between manoeuvrability and stability derived from damping.

Active sensing via movement shapes spatiotemporal patterns of sensory feedback

Previous work has shown that animals alter their locomotor behavior to increase sensing volumes. However, an animal's own movement also determines the spatial and temporal dynamics of sensory feedback. Because each sensory modality has unique spatiotemporal properties, movement has differential and potentially independent effects on each sensory system. Here we show that weakly electric fish dramatically adjust their locomotor behavior in relation to changes of modality-specific information in a task in which increasing sensory volume is irrelevant. We varied sensory information during a refuge-tracking task by changing illumination (vision) and conductivity (electroreception). The gain between refuge movement stimuli and fish tracking responses was functionally identical across all sensory conditions. However, there was a significant increase in the tracking error in the dark (no visual cues). This was a result of spontaneous whole-body oscillations (0.1 to 1 Hz) produced by the fish. These movements were costly: in the dark, fish swam over three times further when tracking and produced more net positive mechanical work. The magnitudes of these oscillations increased as electrosensory salience was degraded via increases in conductivity. In addition, tail bending (1.5 to 2.35 Hz), which has been reported to enhance electrosensory perception, occurred only during trials in the dark. These data show that both categories of movements - whole-body oscillations and tail bends - actively shape the spatiotemporal dynamics of electrosensory feedback.

Modeling object pursuit for desktop virtual reality

Models of interaction tasks are quantitative descriptions of relationships between human temporal performance and the spatial characteristics of the interactive tasks. Examples include Fitts' law for modeling the pointing task and Accot and Zhai's steering law for the path steering task. Interaction models can be used as guidelines to design efficient user interfaces and quantitatively evaluate interaction techniques and input devices. In this paper, we introduce and experimentally verify an interaction model for a 3D object-pursuit interaction task. Object pursuit requires that a user continuously tracks an object that moves with constant velocities in a desktop virtual environment. For modeling purposes, we divide the total object-pursuit movement into a tracking phase and a correction phase. Following a two-step modeling methodology that is originally proposed in this paper, the time for the correction phase is modeled as a function of path length, path curvature, target width, and target velocity. The object-pursuit model can be used to quantitatively evaluate the efficiency of user interfaces that involve 3D interaction with moving objects.

Bursts and isolated spikes code for opposite movement directions in midbrain electrosensory neurons

Directional selectivity, in which neurons respond strongly to an object moving in a given direction but weakly or not at all to the same object moving in the opposite direction, is a crucial computation that is thought to provide a neural correlate of motion perception. However, directional selectivity has been traditionally quantified by using the full spike train, which does not take into account particular action potential patterns. We investigated how different action potential patterns, namely bursts (i.e. packets of action potentials followed by quiescence) and isolated spikes, contribute to movement direction coding in a mathematical model of midbrain electrosensory neurons. We found that bursts and isolated spikes could be selectively elicited when the same object moved in opposite directions. In particular, it was possible to find parameter values for which our model neuron did not display directional selectivity when the full spike train was considered but displayed strong directional selectivity when bursts or isolated spikes were instead considered. Further analysis of our model revealed that an intrinsic burst mechanism based on subthreshold T-type calcium channels was not required to observe parameter regimes for which bursts and isolated spikes code for opposite movement directions. However, this burst mechanism enhanced the range of parameter values for which such regimes were observed. Experimental recordings from midbrain neurons confirmed our modeling prediction that bursts and isolated spikes can indeed code for opposite movement directions. Finally, we quantified the performance of a plausible neural circuit and found that it could respond more or less selectively to isolated spikes for a wide range of parameter values when compared with an interspike interval threshold. Our results thus show for the first time that different action potential patterns can differentially encode movement and that traditional measures of directional selectivity need to be revised in such cases.

Proprioceptive feedback reinforces centrally generated stepping patterns in the cockroach

The relative importance of sensory input for the production of centrally generated motor patterns is crucial to our understanding of how animals coordinate their body segments to locomote. In legged locomotion, where terrain heterogeneity may require stride-by-stride changes in leg placement, evidence suggests that sensory information is essential for the timing of leg movement. In a previous study we showed that in cockroaches, renowned for rapid and stable running, a coordinated pattern can be elicited from the motor centres driving the different legs in the absence of sensory feedback. In the present paper, we assess the role of movement-related sensory inputs in modifying this central pattern. We studied the effect of spontaneous steps as well as imposed transient and periodic movements of a single intact leg, and demonstrate that, depending on the movement properties, the resulting proprioceptive feedback can significantly modify phase relationships among segmental oscillators of other legs. Our analysis suggests that feedback from front legs is weaker but more phasically precise than from hind legs, selectively transferring movement-related information in a manner that strengthens the inherent rhythmic pattern and modulates local perturbations.

Kinematics of the ribbon fin in hovering and swimming of the electric ghost knifefish

Weakly electric knifefish are exceptionally maneuverable swimmers. In prior work, we have shown that they are able to move their entire body omnidirectionally so that they can rapidly reach prey up to several centimeters away. Consequently, in addition to being a focus of efforts to understand the neural basis of sensory signal processing in vertebrates, knifefish are increasingly the subject of biomechanical analysis to understand the coupling of signal acquisition and biomechanics. Here, we focus on a key subset of the knifefish's omnidirectional mechanical abilities: hovering in place, and swimming forward at variable speed. Using high speed video and a markerless motion capture system to capture fin position, we show that hovering is achieved by generating two traveling waves, one from the caudal edge of the fin, and one from the rostral edge, moving toward each other. These two traveling waves overlap at a nodal point near the center of the fin, cancelling fore-aft propulsion. During forward swimming at low velocities, the caudal region of the fin continues to have counter-propagating waves, directly retarding forward movement. The gait transition from hovering to forward swimming is accompanied by a shift in the nodal point toward the caudal end of the fin. While frequency varies significantly to increase speed at low velocities, beyond about one body length per second, the frequency stays near 10~Hz, and amplitude modulation becomes more prominent despite its higher energetic costs. A coupled central pattern generator model is able to reproduce qualitative features of fin motion and suggest hypotheses regarding the fin's neural control.

Damping in flapping flight and its implications for manoeuvring, scaling and evolution

Flying animals exhibit remarkable degrees of both stability and manoeuvrability. Our understanding of these capabilities has recently been improved by the identification of a source of passive damping specific to flapping flight. Examining how this damping effect scales among different species and how it affects active manoeuvres as well as recovery from perturbations provides general insights into the flight of insects, birds and bats. These new damping models offer a means to predict manoeuvrability and stability for a wide variety of flying animals using prior reports of the morphology and flapping motions of these species. Furthermore, the presence of passive damping is likely to have facilitated the evolution of powered flight in animals by providing a stability benefit associated with flapping.

Spikes alone do not behavior make: why neuroscience needs biomechanics

Neural circuits do not function in isolation; they interact with the physical world, accepting sensory inputs and producing outputs via muscles. Since both these pathways are constrained by physics, the activity of neural circuits can only be understood by considering biomechanics of muscles, bodies, and the exterior world. We discuss how animal bodies have natural stable motions that require relatively little activation or control from the nervous system. The nervous system can substantially alter these motions, by subtly changing mechanical properties such as body or leg stiffness. Mechanics can also provide robustness to perturbations without sensory reflexes. By considering a complete neuromechanical system, neuroscientists and biomechanicians together can provide a more integrated view of neural circuitry and behavior.