Collective Motion Patterns Research Articles

Large-Scale Patterns in a Minimal Cognitive Flocking Model: Incidental Leaders, Nematic Patterns, and Aggregates.

We study a minimal cognitive flocking model, which assumes that the moving entities navigate using the available instantaneous visual information exclusively. The model consists of active particles, with no memory, that interact by a short-ranged, position-based, attractive force, which acts inside a vision cone (VC), and lack velocity-velocity alignment. We show that this active system can exhibit-due to the VC that breaks Newton's third law-various complex, large-scale, self-organized patterns. Depending on parameter values, we observe the emergence of aggregates or millinglike patterns, the formation of moving-locally polar-files with particles at the front of these structures acting as effective leaders, and the self-organization of particles into macroscopic nematic structures leading to long-ranged nematic order. Combining simulations and nonlinear field equations, we show that position-based active models, as the one analyzed here, represent a new class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems. The reported results are of prime importance in the study, interpretation, and modeling of collective motion patterns in living and nonliving active systems.

Collaborative Control of Multivehicle Systems in Diverse Motion Patterns

In this brief, a decentralized control algorithm is proposed for a group of vehicles to form diverse collective motion patterns. Without the guidance of a global beacon or a global reference framework, the desired collective behavior occurs provided that the associated network of the multivehicle system is jointly connected. The effectiveness of the approach is verified through theoretical analysis, numerical simulation, and experimental results.

Collective motion patterns of swarms with delay coupling: Theory and experiment.

The formation of coherent patterns in swarms of interacting self-propelled autonomous agents is a subject of great interest in a wide range of application areas, ranging from engineering and physics to biology. In this paper, we model and experimentally realize a mixed-reality large-scale swarm of delay-coupled agents. The coupling term is modeled as a delayed communication relay of position. Our analyses, assuming agents communicating over an Erdös-Renyi network, demonstrate the existence of stable coherent patterns that can be achieved only with delay coupling and that are robust to decreasing network connectivity and heterogeneity in agent dynamics. We also show how the bifurcation structure for emergence of different patterns changes with heterogeneity in agent acceleration capabilities and limited connectivity in the network as a function of coupling strength and delay. Our results are verified through simulation as well as preliminary experimental results of delay-induced pattern formation in a mixed-reality swarm.

Steady and transient states in low-energy swarms: Stability and first-passage times.

We investigate a class of agent-based models of self-propelled particles (SPP) that interact according to a Morse potential in the presence of friction, a class which was able to reproduce many of the intriguing patterns of collective motion observed in nature. Specifically, we compare two closely related SPP models in the literature that differ by their prescription of particle drag and self-propulsion. Writing both models in terms of nondimensional parameters allows us to show that the dynamics in the highly viscous regime is independent of the precise forms of drag and propulsion. In contrast to what is indicated in the literature both models yield the same low-energy self-organized states: the coherent flock and the rigid rotation states which are highly ordered in both the coordinate and the velocity spaces and a velocity-disordered droplet state where particles are confined to rings which pass through the lattice points of the underlying Lagrange configuration. In contrast to the first two states which are stable, the third state is found to be a long-lived transient. In the regime studied, relaxing to one of the ordered steady states is inevitable, but how and when the transition occurs and what is the probability of ending in one state rather than the other are functions of the model parameters. Two types of transitions are characterized and first passage times are computed. Eventually, the evolution of the order parameter is explored in the framework of a Langevin-type equation, and the possible metastability of the random droplet state is discussed.

Collective motion pattern inference via Locally Consistent Latent Dirichlet Allocation

Extracting motion descriptors in crowd videos is highly challenging due to scene clutter and serious occlusions. In this paper, Locally Consistent Latent Dirichlet Allocation (LC-LDA) model is proposed to learn collective motion patterns using tracklets and bag-of-words as low level features. The LC-LDA model implements a graph Laplacian operator to impose neighboring constraints to tracklets on a local manifold, which enforces the spatial–temporal coherence of tracklets in a high dimensional bag-of-word feature space. With initialization of clustering on a manifold, LC-LDA model improves the unsupervised inference capability and compactness of learned collective motion patterns. Experimental results on three public datasets indicate that LC-LDA based motion patterns can improve the trajectory clustering performance effectively.

Power laws in the cluster sizes of group-crossing pedestrians: empirical evidence and modelling of causes

.Pedestrian-vehicle mixed traffic at unsignalized crosswalks is a self-organizing system, because of the absence of external control. Consequently, pedestrian group-crossing behaviour may be expected to exhibit the power-law phenomenon, which is often an indicator of self-organized criticality. The assumption that the distribution of cluster sizes may obey power laws was theoretically supported by Xin et al. To test this claim empirically, we observed pedestrian collective motion under natural conditions, using video recordings. These real data confirmed the existence of the power-law phenomenon. A simulation study was then undertaken to uncover the mechanism that generated the observations. The observed patterns could be fully replicated if the behaviour of pedestrians and motorists were modelled, in particular the yielding behaviour of motorists, when approaching crossings and the adaptive behaviour of pedestrians as they increased in number. As well as providing empirical evidence, our findings also provide a deeper understanding of the patterns of the pedestrian collective motion. The results may have implications in the validation of mixed traffic simulation models.

Collective Motions of Heterogeneous Swarms

The emerging collective motions of swarms of interacting agents are a subject of great interest in application areas ranging from biology to physics and robotics. In this paper, we conduct a careful analysis of the collective dynamics of a swarm of self-propelled heterogeneous, delay-coupled agents. We show the emergence of collective motion patterns and segregation of populations of agents with different dynamic properties; both of these behaviors (pattern formation and segregation) emerge naturally in our model, which is based on self-propulsion and attractive pairwise interactions between agents. We derive the bifurcation structure for emergence of different swarming behaviors in the mean field as a function of physical parameters and verify these results through simulation.

Depletion force induced collective motion of microtubules driven by kinesin.

Collective motion is a fascinating example of coordinated behavior of self-propelled objects, which is often associated with the formation of large scale patterns. Nowadays, the in vitro gliding assay is being considered a model system to experimentally investigate various aspects of group behavior and pattern formation by self-propelled objects. In the in vitro gliding assay, cytoskeletal filaments F-actin or microtubules are driven by the surface immobilized associated biomolecular motors myosin or dynein respectively. Although the F-actin/myosin or microtubule/dynein system was found to be promising in understanding the collective motion and pattern formation by self-propelled objects, the most widely used biomolecular motor system microtubule/kinesin could not be successfully employed so far in this regard. Failure in exhibiting collective motion by kinesin driven microtubules is attributed to the intrinsic properties of kinesin, which was speculated to affect the behavior of individual gliding microtubules and mutual interactions among them. In this work, for the first time, we have demonstrated the collective motion of kinesin driven microtubules by regulating the mutual interaction among the gliding microtubules, by employing a depletion force among them. Proper regulation of the mutual interaction among the gliding microtubules through the employment of the depletion force was found to allow the exhibition of collective motion and stream pattern formation by the microtubules. This work offers a universal means for demonstrating the collective motion using the in vitro gliding assay of biomolecular motor systems and will help obtain a meticulous understanding of the fascinating coordinated behavior and pattern formation by self-propelled objects.

Pattern Synchronization of Nonlinear Heterogeneous Multiagent Networks With Jointly Connected Topologies

In this paper, a decentralized control algorithm is proposed for a group of heterogeneous agents with nonlinear dynamics such that it achieves synchronization in diverse collective motion patterns. With the aid of a group of deliberately designed linear homogeneous reference models, the synchronization problem is converted into a class of regulation problem. The regulation problem is hence solved using the nonlinear output feedback control technique. The conversion and, hence, the decentralized synchronization algorithm are valid when the multiagent system is jointly connected in terms of its time-varying network topologies. The effectiveness of the algorithm is verified through theoretical analysis.

Dimensionality reduction of collective motion by principal manifolds

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods is not amenable to the analysis of such manifolds. This is mainly due to the necessary spectral decomposition step, which limits control over the mapping from the original high-dimensional space to the embedding space. Here, we propose an alternative approach that demands a two-dimensional embedding which topologically summarizes the high-dimensional data. In this sense, our approach is closely related to the construction of one-dimensional principal curves that minimize orthogonal error to data points subject to smoothness constraints. Specifically, we construct a two-dimensional principal manifold directly in the high-dimensional space using cubic smoothing splines, and define the embedding coordinates in terms of geodesic distances. Thus, the mapping from the high-dimensional data to the manifold is defined in terms of local coordinates. Through representative examples, we show that compared to existing nonlinear dimensionality reduction methods, the principal manifold retains the original structure even in noisy and sparse datasets. The principal manifold finding algorithm is applied to configurations obtained from a dynamical system of multiple agents simulating a complex maneuver called predator mobbing, and the resulting two-dimensional embedding is compared with that of a well-established nonlinear dimensionality reduction method.

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From Schooling to Shoaling: Patterns of Collective Motion in Zebrafish (Danio rerio)

Animal groups on the move can take different configurations. For example, groups of fish can either be ‘shoals’ or ‘schools’: shoals are simply aggregations of individuals; schools are shoals exhibiting polarized, synchronized motion. Here we demonstrate that polarization distributions of groups of zebrafish (Danio rerio) are bimodal, showing two distinct modes of collective motion corresponding to the definitions of shoaling and schooling. Other features of the group's motion also vary consistently between the two modes: zebrafish schools are faster and less dense than zebrafish shoals. Habituation to an environment can also alter the proportion of time zebrafish groups spend schooling or shoaling. Models of collective motion suggest that the degree and stability of group polarization increases with the group's density. Examining zebrafish groups of different sizes from 5 to 50, we show that larger groups are less polarized than smaller groups. Decreased fearfulness in larger groups may function similarly to habituation, causing them to spend more time shoaling than schooling, contrary to most models' predictions.

Statistical Interaction Modeling of Bovine Herd Behaviors

While there has been interest in modeling the group behavior of herds or flocks, much of this work has focused on simulating their collective spatial motion patterns, which have not accounted for individuality in the herd and instead assume a homogenized role for all members or subgroups of the herd. Animal behavior experts have noted that domestic animals exhibit behaviors that are indicative of social hierarchy: leader/follower type behaviors are present as well as dominance and subordination, aggression and rank order, and specific social affiliations may also exist. Both wild and domestic cattle are social species, and group behaviors are likely to be influenced by the expression of specific social interactions. In this paper, global positioning system coordinate fixes gathered from a herd of beef cows tracked in open fields over several days at a time are utilized to learn a model that focuses on the interactions within the herd as well as its overall movement. Using these data, in this way, explores the validity of existing group behavior models against actual herding behaviors. Domain knowledge, location geography, and human observations are utilized to explain the causes of these deviations from this idealized behavior.

Emergence of coherent motion in aggregates of motile coupled maps

In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are able to swing along the route to chaos. Thereby, each motile can display different types of behavior, i.e. from ordered to fully erratic motion, accordingly with its surrounding conditions. The appearance of patterns of collective motion is shown to be related to the emergence of interparticle synchronization and the degree of coherence of motion is quantified by means of a graph representation. The effects related to the density of particles and to interparticle distances are explored. It is shown that the higher degrees of coherence and group cohesion are attained when the system elements display a combination of ordered and chaotic behaviors, which emerges from a collective self-organization process.

Co-ordinated collective motion patterns in a discrete-time setting with experiments

In this study, the authors co-ordinated collective motion patterns for a group of autonomous vehicles with Cartesian co-ordinate coupling in a discrete-time setting and present experimental results to validate the theoretical results. The collective motion patterns include rendezvous, circular patterns and logarithmic spiral patterns. The authors first study the collective motion patterns for a group of autonomous vehicles with single-integrator kinematics in a discrete-time setting when there exists time delay. The conditions on the network topology, the sampling period, the time delay and the Euler angle are presented such that different collective motion patterns can be achieved. The collective motion patterns for a group of autonomous vehicles with double-integrator dynamics in a discrete-time setting in the presence of relative damping are studied. The conditions on the network topology, the sampling period, the damping factor and the Euler angle are presented such that different collective patterns can be achieved. Finally, the theoretical results are experimentally validated on a multi-robot platform.

Coordinated control of an underwater glider fleet in an adaptive ocean sampling field experiment in Monterey Bay

AbstractA full‐scale adaptive ocean sampling network was deployed throughout the month‐long 2006 Adaptive Sampling and Prediction (ASAP) field experiment in Monterey Bay, California. One of the central goals of the field experiment was to test and demonstrate newly developed techniques for coordinated motion control of autonomous vehicles carrying environmental sensors to efficiently sample the ocean. We describe the field results for the heterogeneous fleet of autonomous underwater gliders that collected data continuously throughout the month‐long experiment. Six of these gliders were coordinated autonomously for 24 days straight using feedback laws that scale with the number of vehicles. These feedback laws were systematically computed using recently developed methodology to produce desired collective motion patterns, tuned to the spatial and temporal scales in the sampled fields for the purpose of reducing statistical uncertainty in field estimates. The implementation was designed to allow for adaptation of coordinated sampling patterns using human‐in‐the‐loop decision making, guided by optimization and prediction tools. The results demonstrate an innovative tool for ocean sampling and provide a proof of concept for an important field robotics endeavor that integrates coordinated motion control with adaptive sampling. © 2010 Wiley Periodicals, Inc.