Towards Swarm Calculus: Urn Models of Collective Decisions and Universal Properties of Swarm Performance

Methods of general applicability are searched for in swarm intelligence with the aim of gaining new insights about natural swarms and to develop design methodologies for artificial swarms. An ideal solution could be a `swarm calculus' that allows to calculate key features of swarms such as expected swarm performance and robustness based on only a few parameters. To work towards this ideal, one needs to find methods and models with high degrees of generality. In this paper, we report two models that might be examples of exceptional generality. First, an abstract model is presented that describes swarm performance depending on swarm density based on the dichotomy between cooperation and interference. Typical swarm experiments are given as examples to show how the model fits to several different results. Second, we give an abstract model of collective decision making that is inspired by urn models. The effects of positive feedback probability, that is increasing over time in a decision making system, are understood by the help of a parameter that controls the feedback based on the swarm's current consensus. Several applicable methods, such as the description as Markov process, calculation of splitting probabilities, mean first passage times, and measurements of positive feedback, are discussed and applications to artificial and natural swarms are reported

Modulating interaction times in an artificial society of robots

In a collaborative society, sharing information is advantageous for each individual as well as for the whole community. Maximizing the number of agent-to-agent interactions per time becomes an appealing behavior due to fast information spreading that maximizes the overall amount of shared information. However, if malicious agents are part of society, then the risk of interacting with one of them increases with an increasing number of interactions. In this paper, we investigate the roles of interaction rates and times (aka edge life) in artificial societies of simulated robot swarms. We adapt their social networks to form proper trust sub-networks and to contain attackers. Instead of sophisticated algorithms to build and administrate trust networks, we focus on simple control algorithms that locally adapt interaction times by changing only the robots' motion patterns. We successfully validate these algorithms in collective decision-making showing improved time to convergence and energy-efficient motion patterns, besides impeding the spread of undesired opinions

A Reductionist Approach to Hypothesis-Catching for the Analysis of Self-Organizing Decision-Making Systems

A difficulty in analyzing self-organizing decision-making systems is their high dimension-ality which needs to be reduced to allow for deep insights. Following the hypothesis that such a dimensionality reduction can only be usefully determined in an act of a low-scale scientific discovery, a recipe for a data-driven, iterative process for determining, testing, and refining hypotheses about how the system operates is presented. This recipe relies on the definition of Markov chains and their analysis based on an urn model. Positive and negative feedback loops operating on global features of the system are detected by this analysis. The workflow of this analysis process is shown in two case studies investigating the BEECLUST algorithm and collective motion in locusts. The reported recipe has the potential to be generally applicable to self-organizing collective systems and is efficient due to an incremental approach.

Space-Time Continuous Models of Swarm Robotic Systems: Supporting Global-to-Local Programming

A generic model in as far as possible mathematical closed-form was developed that predicts the behavior of large self-organizing robot groups (robot swarms) based on their control algorithm. In addition, an extensive subsumption of the relatively young and distinctive interdisciplinary research field of swarm robotics is emphasized. The connection to many related fields is highlighted and the concepts and methods borrowed from these fields are described shortly

The impact of agent density on scalability in collective systems : noise-induced versus majority-based bistability

In this paper, we show that non-uniform distributions in swarms of agents have an impact on the scalability of collective decision-making. In particular, we highlight the relevance of noise-induced bistability in very sparse swarm systems and the failure of these systems to scale. Our work is based on three decision models. In the first model, each agent can change its decision after being recruited by a nearby agent. The second model captures the dynamics of dense swarms controlled by the majority rule (i.e., agents switch their opinion to comply with that of the majority of their neighbors). The third model combines the first two, with the aim of studying the role of non-uniform swarm density in the performance of collective decision-making. Based on the three models, we formulate a set of requirements for convergence and scalability in collective decision-making

Individuality in Swarm Robots with the Case Study of Kilobots: Noise, Bug, or Feature?

Inter-individual differences are studied in natural systems, such as fish, bees, and humans, as they contribute to the complexity of both individual and collective behaviors. However, individuality in artificial systems, such as robotic swarms, is undervalued or even overlooked. Agent-specific deviations from the norm in swarm robotics are usually understood as mere noise that can be minimized, for example, by calibration. We observe that robots have consistent deviations and argue that awareness and knowledge of these can be exploited to serve a task. We measure heterogeneity in robot swarms caused by individual differences in how robots act, sense, and oscillate. Our use case is Kilobots and we provide example behaviors where the performance of robots varies depending on individual differences. We show a non-intuitive example of phototaxis with Kilobots where the non-calibrated Kilobots show better performance than the calibrated supposedly ``ideal" one. We measure the inter-individual variations for heterogeneity in sensing and oscillation, too. We briefly discuss how these variations can enhance the complexity of collective behaviors. We suggest that by recognizing and exploring this new perspective on individuality, and hence diversity, in robotic swarms, we can gain a deeper understanding of these systems and potentially unlock new possibilities for their design and implementation of applications.Comment: Accepted at the 2023 Conference on Artificial Life (ALife). To see the 9 Figures in large check this repo: https://github.com/mohsen-raoufi/Kilobots-Individuality-ALife-23/tree/main/Figure

Pick, Pack, & Survive: Charging Robots in a Modern Warehouse based on Online Connected Dominating Sets

The modern warehouse is partially automated by robots. Instead of letting human workers walk into shelfs and pick up the required stock, big groups of autonomous mobile robots transport the inventory to the workers. Typically, these robots have an electric drive and need to recharge frequently during the day. When we scale this approach up, it is essential to place recharging stations strategically and as soon as needed so that all robots can survive. In this work, we represent a warehouse topology by a graph and address this challenge with the Online Connected Dominating Set problem (OCDS), an online variant of the classical Connected Dominating Set problem [Guha and Khuller, 1998]. We are given an undirected connected graph G = (V, E) and a sequence of subsets of V arriving over time. The goal is to grow a connected subgraph that dominates all arriving nodes and contains as few nodes as possible. We propose an O(log^2 n)-competitive randomized algorithm for OCDS in general graphs, where n is the number of nodes in the input graph. This is the best one can achieve due to Korman\u27s randomized lower bound of Omega(log n log m) [Korman, 2005] for the related Online Set Cover problem [Alon et al., 2003], where n is the number of elements and m is the number of subsets. We also run extensive simulations to show that our algorithm performs well in a simulated warehouse, where the topology of a warehouse is modeled as a randomly generated geometric graph