Coherent Pattern Prediction in Swarms of Delay-Coupled Agents

We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work [Phys. Rev. E 77, 035203(R) (2008)] has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of the coupling amplitude. We extend these results by completely unfolding the bifurcation structure of the mean field approximation. Our analysis reveals a direct correspondence between the different dynamical behaviors found in different regions of the coupling-time delay plane with the different classes of simulated coherent swarm patterns. We derive the spatio-temporal scales of the swarm structures, and also demonstrate how the complicated interplay of coupling strength, time delay, noise intensity, and choice of initial conditions can affect the swarm. In particular, our studies show that for sufficiently large values of the coupling strength and/or the time delay, there is a noise intensity threshold that forces a transition of the swarm from a misaligned state into an aligned state. We show that this alignment transition exhibits hysteresis when the noise intensity is taken to be time dependent

Delays-induced Phase Transitions in Active Matter

We consider the patterns of collective motion emerging when many aligning, self-propelling units move in two dimensions while interacting through a repulsive potential and are also subject to delays and random perturbations. In this approach, delay plays the role analogous to reaction time so that a given particle is influenced by the information about the velocity and the position of the other particles in its vicinity with some time delay. To get insight into the involved complex flows and the transitions between them we use a simple model allowing, by fine-tuning of its few parameters, the observation and analysis of behaviours that are less accessible by experiments or analytic calculations and at the same time make the reproduction of experimental results possible. We report for the first time about a transition from an ordered, polarized collective motion to disorder as a function of the increasing time delay. For a fixed intermediate value of the delay similar transition (from order to disorder) is obtained as the repulsion radius is increased. Our simulations show a transition from total polarization to two kinds of states: fully disordered and a kind of state which is a mixture of patches of fully disordered motion in the background of orderly moving other particles. The transition occurs as the delay time is increased and is sharp, indicating that the nature of this order-disorder transition is either of first-order or is described by a sharply decreasing linear function. Our model is a simplified version of a practical situation of quickly growing interest because time delays are expected to play an increasingly important role when the traffic of many, densely distributed autonomous drones will move around in a quasi-two-dimensional air space

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

An Efficient Multiple-Place Foraging Algorithm for Scalable Robot Swarms

Searching and collecting multiple resources from large unmapped environments is an important challenge. It is particularly difficult given limited time, a large search area and incomplete data about the environment. This search task is an abstraction of many real-world applications such as search and rescue, hazardous material clean-up, and space exploration. The collective foraging behavior of robot swarms is an effective approach for this task. In our work, individual robots have limited sensing and communication range (like ants), but they are organized and work together to complete foraging tasks collectively. An efficient foraging algorithm coordinates robots to search and collect as many resources as possible in the least amount of time. In the foraging algorithms we study, robots act independently with little or no central control. As the swarm size and arena size increase (e.g., thousands of robots searching over the surface of Mars or ocean), the foraging performance per robot decreases. Generally, larger robot swarms produce more inter-robot collisions, and in swarm robot foraging, larger search arenas result in larger travel distances causing the phenomenon of diminishing returns. The foraging performance per robot (measured as a number of collected resources per unit time) is sublinear with the arena size and the swarm size. Our goal is to design a scale-invariant foraging robot swarm. In other words, the foraging performance per robot should be nearly constant as the arena size and the swarm size increase. We address these problems with the Multiple-Place Foraging Algorithm (MPFA), which uses multiple collection zones distributed throughout the search area. Robots start from randomly assigned home collection zones but always return to the closest collection zones with found resources. We simulate the foraging behavior of robot swarms in the robot simulator ARGoS and employ a Genetic Algorithm (GA) to discover different optimized foraging strategies as swarm sizes and the number of resources is scaled up. In our experiments, the MPFA always produces higher foraging rates, fewer collisions, and lower travel and search time than the Central-Place Foraging Algorithm (CPFA). To make the MPFA more adaptable, we introduce dynamic depots that move to the centroid of recently collected resources, minimizing transport times when resources are clustered in heterogeneous distributions. Finally, we extend the MPFA with a bio-inspired hierarchical branching transportation network. We demonstrate a scale-invariant swarm foraging algorithm that ensures that each robot finds and delivers resources to a central collection zone at the same rate, regardless of the size of the swarm or the search area. Dispersed mobile depots aggregate locally foraged resources and transport them to a central place via a hierarchical branching transportation network. This approach is inspired by ubiquitous fractal branching networks such as animal cardiovascular networks that deliver resources to cells and determine the scale and pace of life. The transportation of resources through the cardiovascular system from the heart to dispersed cells is the inverse problem of transportation of dispersed resources to a central collection zone through the hierarchical branching transportation network in robot swarms. We demonstrate that biological scaling laws predict how quickly robots forage in simulations of up to thousands of robots searching over thousands of square meters. We then use biological scaling predictions to determine the capacity of depot robots in order to overcome scaling constraints and produce scale-invariant robot swarms. We verify the predictions using ARGoS simulations. While simulations are useful for initial evaluations of the viability of algorithms, our ultimate goal is predicting how algorithms will perform when physical robots interact in the unpredictable conditions of environments they are placed in. The CPFA and the Distributed Deterministic Spiral Algorithm (DDSA) are compared in physical robots in a large outdoor arena. The physical experiments change our conclusion about which algorithm has the best performance, emphasizing the importance of systematically comparing the performance of swarm robotic algorithms in the real world. We illustrate the feasibility of implementing the MPFA with transportation networks in physical robot swarms. Full implementation of the MPFA in an outdoor environment is the next step to demonstrate truly scalable and robust foraging robot swarms