Human Crowds as Social Networks: Collective Dynamics of Consensus and Polarization.

A ubiquitous type of collective behavior and decision-making is the coordinated motion of bird flocks, fish schools, and human crowds. Collective decisions to move in the same direction, turn right or left, or split into subgroups arise in a self-organized fashion from local interactions between individuals without central plans or designated leaders. Strikingly similar phenomena of consensus (collective motion), clustering (subgroup formation), and bipolarization (splitting into extreme groups) are also observed in opinion formation. As we developed models of crowd dynamics and analyzed crowd networks, we found ourselves going down the same path as models of opinion dynamics in social networks. In this article, we draw out the parallels between human crowds and social networks. We show that models of crowd dynamics and opinion dynamics have a similar mathematical form and generate analogous phenomena in multiagent simulations. We suggest that they can be unified by a common collective dynamics, which may be extended to other psychological collectives. Models of collective dynamics thus offer a means to account for collective behavior and collective decisions without appealing to a priori mental structures.

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.

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.

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.