The pursuit strategy of predatory bluefish ( Pomatomus saltatrix).

A predator's ability to capture prey depends critically on how it coordinates its approach in response to a prey's motion. Flying insects, bats and raptors are capable of capturing prey with a strategy known as parallel navigation, which allows a predator to move directly towards the anticipated point of interception. It is unclear if predators using other modes of locomotion are employing this strategy when pursuing evasive prey. Using kinematic measurements and mathematical modelling, we tested whether bluefish ( Pomatomus saltatrix) pursue prey fish ( Fundulus heteroclitus) with parallel navigation. We found that the directional changes of bluefish were not consistent with this strategy, but rather were predicted by a strategy known as deviated pursuit. Although deviated pursuit requires few sensory cues and relatively modest motor coordination, a comparison of mathematical models suggested negligible differences in path length from parallel navigation, largely owing to the acceleration exhibited by bluefish near the end of a pursuit. Therefore, the strategy of bluefish is unlike flying predators, but offers comparable performance with potentially more robust control that may be well suited to the visual system and habitat of fishes. These findings offer a foundation for understanding the sensing and locomotor control of predatory fishes.

Probabilistic information transmission in a network of coupled oscillators reveals speed-accuracy trade-off in responding to threats.

Individuals in a group may obtain information from other group members about the environment, including the location of a food source or the presence of a predator. Here, we model how information spreads in a group using a susceptible-infected-removed epidemic model. We apply this model to a simulated shoal of fish using the motion dynamics of a coupled oscillator model, in order to test the biological hypothesis that polarized or aligned shoaling leads to faster and more accurate escape responses. The contributions of this study are the (i) application of a probabilistic model of epidemics to the study of collective animal behavior; (ii) testing the biological hypothesis that group cohesion improves predator escape; (iii) quantification of the effect of social cues on startle propagation; and (iv) investigation of the variation in response based on network connectivity. We find that when perfectly aligned individuals in a group are startled, there is a rapid escape by individuals that directly detect the threat, as well as by individuals responding to their neighbors. However, individuals that are not startled do not head away from the threat. In startled groups that are randomly oriented, there is a rapid, accurate response by individuals that directly detect the threat, followed by less accurate responses by individuals responding to neighbor cues. Over the simulation duration, however, even unstartled individuals head away from the threat. This study illustrates a potential speed-accuracy trade-off in the startle response of animal groups, in agreement with several previous experimental studies. Additionally, the model can be applied to a variety of group decision-making processes, including those involving higher-dimensional motion.

The dance of male Anopheles gambiae in wild mating swarms.

An important element of mating in the malaria vector Anopheles gambiae Giles in nature is the crepuscular mating aggregation (swarm) composed almost entirely of males, where most coupling and insemination is generally believed to occur. In this study, we mathematically characterize the oscillatory movement of male An. gambiae in terms of an established individual-based mechanistic model that parameterizes the attraction of a mosquito toward the center of the swarm using the natural frequency of oscillation and the resistance to its motion, characterized by the damping ratio. Using three-dimensional trajectory data of ten wild mosquito swarms filmed in Mali, Africa, we show two new results for low and moderate wind conditions, and indicate how these results may vary in high wind. First, we show that in low and moderate wind the vertical component of the mosquito motion has a lower frequency of oscillation and higher damping ratio than horizontal motion. In high wind, the vertical and horizontal motions are similar to one another and the natural frequencies are higher than in low and moderate wind. Second, we show that the predicted average disagreement in the direction of motion of swarming mosquitoes moving randomly is greater than the average disagreement we observed between each mosquito and its three closest neighbors, with the smallest level of disagreement occurring for the nearest neighbor in seven out of 10 swarms. The alignment of the direction of motion between nearest neighbors is the highest in high wind. This result provides evidence for flight-path coordination between swarming male mosquitoes.

A lionfish-inspired predation strategy in planar structured environments.

This paper investigates a pursuit-evasion game with a single pursuer and evader in a bounded environment, inspired by observations of predation attempts by lionfish (Pterois sp.). The pursuer tracks the evader with a pure pursuit strategy while using an additional bioinspired tactic to trap the evader, i.e. minimize the evader's escape routes. Specifically, the pursuer employs symmetric appendages inspired by the large pectoral fins of lionfish, but this expansion increases its drag and therefore its work to capture the evader. The evader employs a bioinspired randomly-directed escape strategy to avoid capture and collisions with the boundary. Here we investigate the trade-off between minimizing the work to capture the evader and minimizing the evader's escape routes. By using the pursuer's expected work to capture as a cost function, we determine when the pursuer should expand its appendages as a function of the relative distance to the evader and the evader's proximity to the boundary. Visualizing the pursuer's expected work to capture everywhere in the bounded domain, yields additional insights about optimal pursuit trajectories and illustrates the role of the boundary in predator-prey interactions.

A 3D underwater robotic collective called Blueswarm.

A swarm of agile fish-robots uses vision-based implicit coordination to demonstrate self-organizing behaviors in a laboratory tank.

Bioinspired pursuit with a swimming robot using feedback control of an internal rotor.

Theoretical guarantees of capture become complicated in the case of a swimming fish or fish robot because of the oscillatory nature of the fish heading. Building on the connection between a swimming fish and the canonical Chaplygin sleigh, a novel state feedback control law is shown to result in closed-loop dynamics that exhibit a limit cycle resulting in steady forward-swimming motion in a desired heading. Analysis of this limit cycle reveals boundaries on the size of the oscillations around the desired heading, which are then used to specify under what conditions (e.g. prey speed, predator speed, control gains) capture is guaranteed. By changing the desired swimming direction in response to prey movements, the control law is shown to be capable of pure pursuit, deviated pure pursuit, intercept, and parallel navigation in simulation. An experimental demonstration of pure pursuit by a flexible fish-inspired robot actuated with an internal reaction wheel is described.

Probabilistic analytical modelling of predator-prey interactions in fishes.

Predation is a fundamental interaction between species, yet it is largely unclear what tactics are successful for the survival or capture of prey. One challenge in this area comes with how to test theoretical ideas about strategy with experimental measurements of features such as speed, flush distance and escape angles. Tactics may be articulated with an analytical model that predicts the motion of predator or prey as they interact. However, it may be difficult to recognize how the predictions of such models relate to behavioural measurements that are inherently variable. Here, we present an alternative approach for modelling predator-prey interactions that uses deterministic dynamics, yet incorporates experimental kinematic measurements of natural variation to predict the outcome of biological events. This technique, called probabilistic analytical modelling (PAM), is illustrated by the interactions between predator and prey fish in two case studies that draw on recent experiments. In the first case, we use PAM to model the tactics of predatory bluefish ( Pomatomus saltatrix) as they prey upon smaller fish ( Fundulus heteroclitus). We find that bluefish perform deviated pure pursuit with a variable pursuit angle that is suboptimal for the time to capture. In the second case, we model the escape tactics of zebrafish larvae ( Danio rerio) when approached by adult predators of the same species. Our model successfully predicts the measured patterns of survivorship using measured probability density functions as parameters. As these results demonstrate, PAM is a data-driven modelling approach that can be predictive, offers analytical transparency, and does not require numerical simulations of system dynamics. Though predator-prey interactions demonstrate the use of this technique, PAM is not limited to studying biological systems and has broad utility that may be applied towards understanding a wide variety of natural and engineered dynamical systems where data-driven modelling is beneficial.

On Planar Discrete Elastic Rod Models for the Locomotion of Soft Robots.

Modeling soft robots that move on surfaces is challenging from a variety of perspectives. A recent formulation by Bergou et al. of a rod theory that exploits new developments in discrete differential geometry offers an attractive, numerically efficient avenue to help overcome some of these challenges. Their formulation is an example of a discrete elastic rod theory. In this article, we consider a planar version of Bergou et al.'s theory and, with the help of recent works on Lagrange's equations of motion for constrained systems of particles, show how it can be used to model soft robots that are composed of segments of soft material folded and bonded together. We then use our formulation to examine the dynamics of a caterpillar-inspired soft robot that is actuated using shape memory alloys and exploits stick-slip friction to achieve locomotion. After developing and implementing procedures to prescribe the parameters for components of the soft robot, we compare our calibrated model to the experimental behavior of the caterpillar-inspired soft robot.

Model-based observer and feedback control design for a rigid Joukowski foil in a Kármán vortex street.

Obstacles and swimming fish in flow create a wake with an alternating left/right vortex pattern known as a Kármán vortex street and reverse Kármán vortex street, respectively. An energy-efficient fish behavior resembling slaloming through the vortex street is called Kármán gaiting. This paper describes the use of a bioinspired array of pressure sensors on a Joukowski foil to estimate and control flow-relative position in a Kármán vortex street using potential flow theory, recursive Bayesian filtering, and trajectory-tracking feedback control. The Joukowski foil is fixed in downstream position in a flowing water channel and free to move on air bearings in the cross-stream direction by controlling its angle of attack to generate lift. Inspired by the lateral-line neuromasts found in fish, the sensing and control scheme is validated using off-the-shelf pressure sensors in an experimental testbed that includes a flapping device to create vortices. We derive a potential flow model that describes the flow over a Joukowski foil in a Kármán vortex street and identify an optimal path through a Kármán vortex street using empirical observability. The optimally observable trajectory is one that passes through each vortex in the street. The estimated vorticity and location of the Kármán vortex street are used in a closed-loop control to track either the optimally observable path or the energetically efficient gait exhibited by fish. Results from the closed-loop control experiments in the flow tank show that the artificial lateral line in conjunction with a potential flow model and Bayesian estimator allow the robot to perform fish-like slaloming behavior in a Kármán vortex street. This work is a precursor to an autonomous robotic fish sensing the wake of another fish and/or performing pursuit and schooling behavior.

Distributed flow sensing for closed-loop speed control of a flexible fish robot.

Flexibility plays an important role in fish behavior by enabling high maneuverability for predator avoidance and swimming in turbulent flow. This paper presents a novel flexible fish robot equipped with distributed pressure sensors for flow sensing. The body of the robot is molded from soft, hyperelastic material, which provides flexibility. Its Joukowski-foil shape is conducive to modeling the fluid analytically. A quasi-steady potential-flow model is adopted for real-time flow estimation, whereas a discrete-time vortex-shedding flow model is used for higher-fidelity simulation. The dynamics for the flexible fish robot yield a reduced model for one-dimensional swimming. A recursive Bayesian filter assimilates pressure measurements to estimate flow speed, angle of attack, and foil camber. The closed-loop speed-control strategy combines an inverse-mapping feedforward controller based on an average model derived for periodic actuation of angle-of-attack and a proportional-integral feedback controller utilizing the estimated flow information. Simulation and experimental results are presented to show the effectiveness of the estimation and control strategy. The paper provides a systematic approach to distributed flow sensing for closed-loop speed control of a flexible fish robot by regulating the flapping amplitude.

Distributed flow estimation and closed-loop control of an underwater vehicle with a multi-modal artificial lateral line.

Bio-inspired sensing modalities enhance the ability of autonomous vehicles to characterize and respond to their environment. This paper concerns the lateral line of cartilaginous and bony fish, which is sensitive to fluid motion and allows fish to sense oncoming flow and the presence of walls or obstacles. The lateral line consists of two types of sensing modalities: canal neuromasts measure approximate pressure gradients, whereas superficial neuromasts measure local flow velocities. By employing an artificial lateral line, the performance of underwater sensing and navigation strategies is improved in dark, cluttered, or murky environments where traditional sensing modalities may be hindered. This paper presents estimation and control strategies enabling an airfoil-shaped unmanned underwater vehicle to assimilate measurements from a bio-inspired, multi-modal artificial lateral line and estimate flow properties for feedback control. We utilize potential flow theory to model the fluid flow past a foil in a uniform flow and in the presence of an upstream obstacle. We derive theoretically justified nonlinear estimation strategies to estimate the free stream flowspeed, angle of attack, and the relative position of an upstream obstacle. The feedback control strategy uses the estimated flow properties to execute bio-inspired behaviors including rheotaxis (the tendency of fish to orient upstream) and station-holding (the tendency of fish to position behind an upstream obstacle). A robotic prototype outfitted with a multi-modal artificial lateral line composed of ionic polymer metal composite and embedded pressure sensors experimentally demonstrates the distributed flow sensing and closed-loop control strategies.

Male motion coordination in anopheline mating swarms.

The Anopheles gambiae species complex comprises the primary vectors of malaria in much of sub-Saharan Africa. Most of the mating in these species occurs in swarms composed almost entirely of males. Intermittent, organized patterns in such swarms have been observed, but a detailed description of male-male interactions has not previously been available. We identify frequent, time-varying interactions characterized by periods of parallel flight in data from 8 swarms of Anopheles gambiae and 3 swarms of Anopheles coluzzii filmed in 2010 and 2011 in the village of Donéguébogou, Mali. We use the cross correlation of flight direction to quantify these interactions and to induce interaction graphs, which show that males form synchronized subgroups whose size and membership change rapidly. A swarming model with damped springs between each male and the swarm centroid shows good agreement with the correlation data, provided that local interactions represented by damping of relative velocity between males are included.

Stereoscopic video analysis of Anopheles gambiae behavior in the field: challenges and opportunities.

Advances in our ability to localize and track individual swarming mosquitoes in the field via stereoscopic image analysis have enabled us to test long-standing ideas about individual male behavior and directly observe coupling. These studies further our fundamental understanding of the reproductive biology of mosquitoes. In addition, our analyses using stereoscopic video of swarms of the African malaria vector Anopheles gambiae have produced results that should be relevant to any "release-based" method of control including Sterile Insect Technique (SIT) and genetically modified male mosquitoes (GMM). The relevance of the results is primarily due to the fact that any mosquito vectors released for control are almost certainly going to be males; further, for SIT, GMM or similar approaches to be successful, the released males will have to successfully locate swarms and then mate with wild females. Thus, understanding and potentially manipulating the mating process could play a key role in future control programs. Our experience points to special challenges created by stereoscopic video of swarms. These include the expected technical difficulties of capturing usable images of mosquitoes in the field, and creating an automated tracking system to enable generation of large numbers of three dimensional tracks over many seconds of footage. Once the data are collected, visualization and application of appropriate statistical and analytic methods also are required. We discuss our recent progress on these problems, give an example of a statistical approach to quantify individual male movement in a swarm with some novel results, and suggest further studies incorporating experimental manipulation and three dimensional localization and tracking of individual mosquitoes in wild swarms.

Three-dimensional reconstruction of the fast-start swimming kinematics of densely schooling fish.

Information transmission via non-verbal cues such as a fright response can be quantified in a fish school by reconstructing individual fish motion in three dimensions. In this paper, we describe an automated tracking framework to reconstruct the full-body trajectories of densely schooling fish using two-dimensional silhouettes in multiple cameras. We model the shape of each fish as a series of elliptical cross sections along a flexible midline. We estimate the size of each ellipse using an iterated extended Kalman filter. The shape model is used in a model-based tracking framework in which simulated annealing is applied at each step to estimate the midline. Results are presented for eight fish with occlusions. The tracking system is currently being used to investigate fast-start behaviour of schooling fish in response to looming stimuli.

Reconstructing the flight kinematics of swarming and mating in wild mosquitoes.

We describe a novel tracking system for reconstructing three-dimensional tracks of individual mosquitoes in wild swarms and present the results of validating the system by filming swarms and mating events of the malaria mosquito Anopheles gambiae in Mali. The tracking system is designed to address noisy, low frame-rate (25 frames per second) video streams from a stereo camera system. Because flying A. gambiae move at 1-4 m s(-1), they appear as faded streaks in the images or sometimes do not appear at all. We provide an adaptive algorithm to search for missing streaks and a likelihood function that uses streak endpoints to extract velocity information. A modified multi-hypothesis tracker probabilistically addresses occlusions and a particle filter estimates the trajectories. The output of the tracking algorithm is a set of track segments with an average length of 0.6-1 s. The segments are verified and combined under human supervision to create individual tracks up to the duration of the video (90 s). We evaluate tracking performance using an established metric for multi-target tracking and validate the accuracy using independent stereo measurements of a single swarm. Three-dimensional reconstructions of A. gambiae swarming and mating events are presented.

3D tracking of mating events in wild swarms of the malaria mosquito Anopheles gambiae.

We describe an automated tracking system that allows us to reconstruct the 3D kinematics of individual mosquitoes in swarms of Anopheles gambiae. The inputs to the tracking system are video streams recorded from a stereo camera system. The tracker uses a two-pass procedure to automatically localize and track mosquitoes within the swarm. A human-in-the-loop step verifies the estimates and connects broken tracks. The tracker performance is illustrated using footage of mating events filmed in Mali in August 2010.