We present a decentralized algorithm to achieve segregation into an arbitrary number of groups with swarms of autonomous robots. The distinguishing feature of our approach is in the minimalistic assumptions on which it is based. Specifically, we assume that (i) Each robot is equipped with a ternary sensor capable of detecting the presence of a single nearby robot, and, if that robot is present, whether or not it belongs to the same group as the sensing robot; (ii) The robots move according to a differential drive model; and (iii) The structure of the control system is purely reactive, and it maps directly the sensor readings to the wheel speeds with a simple 'if' statement. We present a thorough analysis of the parameter space that enables this behavior to emerge, along with conditions for guaranteed convergence and a study of non-ideal aspects in the robot design.
Segregation is a common behavior in nature, and it can be observed across scales. For example, cell segregation is a basic building block of embryogeneis in tissue generation processes @cite_3 @cite_0 ; while social insects, such as ants, organize their brood into ring-like structures @cite_14 .
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There are several examples in natural systems that exhibit the self-organizing behavior of segregation when different types of units interact with each other. One of the best examples is a system of biological cells of heterogeneous types that has the ability to self-organize into specific formations, form different types of organs and, ultimately, develop into a living organism. Previous research in this area has indicated that such segregations in biological cells and tissues are made possible because of the differences in adhesivity between various types of cells or tissues. Inspired by this differential adhesivity model, this technical note presents a decentralized approach utilizing differential artificial potential to achieve the segregation behavior in a swarm of heterogeneous robotic agents. The method is based on the proposition that agents experience different magnitudes of potential while interacting with agents of different types. Stability analysis of the system with the proposed approach in the Lyapunov sense is carried out in this technical note. Extensive simulations and analytical investigations suggest that the proposed method would lead a population of two types of agents to a segregated configuration. The establishment and maintenance of precisely organized tissues requires the formation of sharp borders between distinct cell populations. The maintenance of segregated cell populations is also required for tissue homeostasis in the adult, and deficiencies in segregation underlie the metastatic spreading of tumor cells. Three classes of mechanisms that underlie cell segregation and border formation have been uncovered. The first involves differences in cadherin-mediated cell–cell adhesion that establishes interfacial tension at the border between distinct cell populations. A second mechanism involves the induction of actomyosin-mediated contraction by intercellular signaling, such that cortical tension is generated at the border. Third, activation of Eph receptors and ephrins can lead to both decreased adhesion by triggering cleavage of E-cadherin, and to repulsion of cells by regulation of the actin cytoskeleton, thus preventing intermingling between cell populations. These mechanisms play crucial roles at distinct boundaries during development, and alterations in cadherin or Eph ephrin expression have been implicated in tumor metastasis. Aggregation is widespread in invertebrate societies and can appear in response to environmental heterogeneities or by attraction between individuals. We performed experiments with cockroach, Blattella germanica, larvae in a homogeneous environment to investigate the influence of interactions between individuals on aggregations. Different densities were tested. A first phase led to radial dispersion of larvae in relation to wall-following behaviours; the consequence of this process was a homogeneous distribution of larvae around the periphery of the arena. A second phase corresponded to angular reorganization of larvae leading to the formation of aggregates. The phenomenon was analysed both at the individual and collective levels. Individual cockroaches modulated their behaviour depending on the presence of other larvae in their vicinity: probabilities of stopping and resting times were both higher when the numbers of larvae were greater. We then developed an agent-based model implementing individual behavioural rules, all derived from experiments, to explain the aggregation dynamics at the collective level. This study supports evidence that aggregation relies on mechanisms of amplification, supported by interactions between individuals that follow simple rules based on local information and without knowledge of the global structure. Schelling's model of segregation looks to explain the way in which particles or agents of two types may come to arrange themselves spatially into configurations consisting of large homogeneous clusters, i.e. connected regions consisting of only one type. As one of the earliest agent based models studied by economists and perhaps the most famous model of self-organising behaviour, it also has direct links to areas at the interface between computer science and statistical mechanics, such as the Ising model and the study of contagion and cascading phenomena in networks. While the model has been extensively studied it has largely resisted rigorous analysis, prior results from the literature generally pertaining to variants of the model which are tweaked so as to be amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory. In BK , Brandt, Immorlica, Kamath and Kleinberg provided the first rigorous analysis of the unperturbed model, for a specific set of input parameters. Here we provide a rigorous analysis of the model's behaviour much more generally and establish some surprising forms of threshold behaviour, notably the existence of situations where an level of intolerance for neighbouring agents of opposite type leads almost certainly to segregation.