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Abstract Robot swarms are generally considered to be composed of cooperative agents that, despite their limited individual capabilities, can perform difficult tasks by working together. However, in open swarms, where different robots can be added to the swarm by different parties with potentially competing interests, cooperation is but one of many strategies. We envision an information market where robots can buy and sell information through transactions stored on a distributed blockchain, and where cooperation is encouraged by the economy itself. As a proof of concept, we study a classical foraging task, where exchanging information with other robots is paramount to accomplish the task efficiently. We illustrate that even a single robot that lies to others—a so-called Byzantine robot—can heavily disrupt the swarm. Hence, we devise two protection mechanisms. Through an individual-level protection mechanism, robots are more sceptical about others’ information and can detect and discard Byzantine information, at the cost of lower efficiency. Through a systemic protection mechanism based on economic rules regulating robot interactions, robots that sell honest information acquire over time more wealth than Byzantines selling false information. Our simulations show that a well-designed robot economy penalises misinformation spreading and protects the swarm from Byzantine behaviour. We believe economics-inspired swarm robotics is a promising research direction that exploits the timely opportunity for decentralised economies offered by blockchain technology.

Abstract Strongly opinionated minorities can have a dramatic impact on the opinion dynamics of a large population. Two factions of inflexible minorities, polarised into two competing opinions, could lead the entire population to persistent indecision. Equivalently, populations can remain undecided when individuals sporadically change their opinion based on individual information rather than social information. Our analysis compares the cross-inhibition model with the voter model for decisions between equally good alternatives, and with the weighted voter model for decisions among alternatives characterised by different qualities. Here we show that cross-inhibition, contrary to the other two models, is a simple mechanism that allows the population to reach a stable majority for one alternative even in the presence of a relatively high amount of asocial behaviour. The results predicted by the mean-field models are confirmed by experiments with swarms of 100 locally interacting robots. This work suggests an answer to the longstanding question of why inhibitory signals are widespread in natural systems of collective decision making, and, at the same time, it proposes an efficient mechanism for designing resilient swarms of minimalistic robots.

Abstract We investigate how reliable movement can emerge in aggregates of highly error-prone individuals. The individuals—robotic modules—move stochastically using vibration motors. By coupling them via elastic links, soft-bodied aggregates can be created. We present distributed algorithms that enable the aggregates to move and deform reliably. The concept and algorithms are validated through formal analysis of the elastic couplings and experiments with aggregates comprising up to 49 physical modules—among the biggest soft-bodied aggregates to date made of autonomous modules. The experiments show that aggregates with elastic couplings can shrink and stretch their bodies, move with a precision that increases with the number of modules, and outperform aggregates with no, or rigid, couplings. Our findings demonstrate that mechanical couplings can play a vital role in reaching coherent motion among individuals with exceedingly limited and error-prone abilities, and may pave the way for low-power, stretchable robots for high-resolution monitoring and manipulation.

It is usually assumed that information cascades are most likely to occur when an early but incorrect opinion spreads through the group. Here, we analyse models of confidence-sharing in groups and reveal the opposite result: simple but plausible models of naive-Bayesian decision-making exhibit information cascades when group decisions are synchronous; however, when group decisions are asynchronous, the early decisions reached by Bayesian decision-makers tend to be correct and dominate the group consensus dynamics. Thus early decisions actually rescue the group from making errors, rather than contribute to it. We explore the likely realism of our assumed decision-making rule with reference to the evolution of mechanisms for aggregating social information, and known psychological and neuroscientific mechanisms.

Recent work has derived the optimal policy for two-alternative value-based decisions, in which decision-makers compare the subjective expected reward of two alternatives. Under specific task assumptions --- such as linear utility, linear cost of time and constant processing noise --- the optimal policy is implemented by a diffusion process in which parallel decision thresholds collapse over time as a function of prior knowledge about average reward across trials. This policy predicts that the decision dynamics of each trial are dominated by the difference in value between alternatives and are insensitive to the magnitude of the alternatives (i.e., their summed values). This prediction clashes with empirical evidence showing magnitude-sensitivity even in the case of equal alternatives, and with ecologically plausible accounts of decision making. Previous work has shown that relaxing assumptions about linear utility or linear time cost can give rise to optimal magnitude-sensitive policies. Here we question the assumption of constant processing noise, in favour of input-dependent noise. The neurally plausible assumption of input-dependent noise during evidence accumulation has received strong support from previous experimental and modelling work. We show that including input-dependent noise in the evidence accumulation process results in a magnitude-sensitive optimal policy for value-based decision-making, even in the case of a linear utility function and a linear cost of time, for both single (i.e., isolated) choices and sequences of choices in which decision-makers maximise reward rate. Compared to explanations that rely on non-linear utility functions and/or non-linear cost of time, our proposed account of magnitude-sensitive optimal decision-making provides a parsimonious explanation that bridges the gap between various task assumptions and between various types of decision making.

Optimality analysis of value-based decisions in binary and multi-alternative choice settings predicts that reaction times should be sensitive only to differences in stimulus magnitudes, but not to overall absolute stimulus magnitude. Yet experimental work in the binary case has shown magnitude sensitive reaction times, and theory shows that this can be explained by switching from linear to multiplicative time costs, but also by nonlinear subjective utility. Thus disentangling explanations for observed magnitude sensitive reaction times is difficult. Here for the first time we extend the theoretical analysis of geometric time-discounting to ternary choices, and present novel experimental evidence for magnitude-sensitivity in such decisions, in both humans and slime moulds. We consider the optimal policies for all possible combinations of linear and geometric time costs, and linear and nonlinear utility; interestingly, geometric discounting emerges as the predominant explanation for magnitude sensitivity.

Social insect colonies use negative as well as positive feedback signals to regulate foraging behaviour. In ants and bees individual foragers have been observed to use negative pheromones or mechano-auditory signals to indicate that forage sources are not ideal, for example being unrewarded, crowded, or dangerous. Here we propose an additional function for negative feedback signals during foraging, variance reduction. We show that while on average populations will converge to desired distributions over forage patches both with and without negative feedback signals, in small populations negative feedback reduces variation around the target distribution compared to the use of positive feedback alone. Our results are independent of the nature of the target distribution, providing it can be achieved by foragers collecting only local information. Since robustness is a key aim for biological systems, and deviation from target foraging distributions may be costly, we argue that this could be a further important and hitherto overlooked reason that negative feedback signals are used by foraging social insects.

Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor networks. Thus several stochastic and naïve deterministic algorithms for distributed graph size estimation or calculation have been provided. Here we present a deterministic and distributed algorithm that allows every node of a connected graph to determine the graph size in finite time, if an upper bound on the graph size is provided. The algorithm consists in the iterative aggregation of information in local hubs which then broadcast it throughout the whole graph. The proposed node-counting algorithm is on average more efficient in terms of node memory and communication cost than its previous deterministic counterpart for node counting, and appears comparable or more efficient in terms of average-case time complexity. As well as node counting, the algorithm is more broadly applicable to problems such as summation over graphs, quorum sensing, and spontaneous hierarchy creation.

Collective behaviour is of fundamental importance in the life sciences, where it appears at levels of biological complexity from single cells to superorganisms, in demography and the social sciences, where it describes the behaviour of populations, and in the physical and engineering sciences, where it describes physical phenomena and can be used to design distributed systems. Reasoning about collective behaviour is inherently difficult, as the non-linear interactions between individuals give rise to complex emergent dynamics. Mathematical techniques have been developed to analyse systematically collective behaviour in such systems, yet these frequently require extensive formal training and technical ability to apply. Even for those with the requisite training and ability, analysis using these techniques can be laborious, time-consuming and error-prone. Together these difficulties raise a barrier-to-entry for practitioners wishing to analyse models of collective behaviour. However, rigorous modelling of collective behaviour is required to make progress in understanding and applying it. Here we present an accessible tool which aims to automate the process of modelling and analysing collective behaviour, as far as possible. We focus our attention on the general class of systems described by reaction kinetics, involving interactions between components that change state as a result, as these are easily understood and extracted from data by natural, physical and social scientists, and correspond to algorithms for component-level controllers in engineering applications. By providing simple automated access to advanced mathematical techniques from statistical physics, nonlinear dynamical systems analysis, and computational simulation, we hope to advance standards in modelling collective behaviour. At the same time, by providing expert users with access to the results of automated analyses, sophisticated investigations that could take significant effort are substantially facilitated. Our tool can be accessed online without installing software, uses a simple programmatic interface, and provides interactive graphical plots for users to develop understanding of their models.

The engineering of large-scale decentralised systems requires sound methodologies to guarantee the attainment of the desired macroscopic system-level behaviour given the microscopic individual-level implementation. While a general-purpose methodology is currently out of reach, specific solutions can be given to broad classes of problems by means of well-conceived design patterns. We propose a design pattern for collective decision making grounded on experimental/theoretical studies of the nest-site selection behaviour observed in honeybee swarms (Apis mellifera). The way in which honeybee swarms arrive at consensus is fairly well-understood at the macroscopic level. We provide formal guidelines for the microscopic implementation of collective decisions to quantitatively match the macroscopic predictions. We discuss implementation strategies based on both homogeneous and heterogeneous multiagent systems, and we provide means to deal with spatial and topological factors that have a bearing on the micro-macro link. Finally, we exploit the design pattern in two case studies that showcase the viability of the approach. Besides engineering, such a design pattern can prove useful for a deeper understanding of decision making in natural systems thanks to the inclusion of individual heterogeneities and spatial factors, which are often disregarded in theoretical modelling.

We introduce zePPeLIN, a distributed system designed to address the challenges of path planning in large, cluttered, dynamic environments. The objective is to define a sequence of instructions to precisely move a ground object (e.g., a mobile robot) from an initial to a final configuration in an environment. zePPeLIN is based on a set of wirelessly networked overhead cameras. While each camera only covers a limited environment portion, the camera set fully covers the environment through the union of its fields of view. Path planning is performed in a fully distributed and cooperative way, based on potential diffusion over local Voronoi skeletons and local message exchanging. Additionally, the control of the moving object is fully distributed: it receives movement instructions from each camera when it enters that camera's field of view. The overall task is made particularly challenging by intrinsic errors in the overlap in cameras' fields of view. We study the performance of the system as a function of these errors, as well as its scalability for the size and density of the camera network. We also propose a few heuristics to improve performance and computational and communication efficiency. The reported results include both extensive simulation experiments and validation using a real camera network planning for a two-robot system.