Resilience and Controllability of Dynamic Collective Behaviors

Abstract

The network paradigm is used to gain insight into the structural root causes of the resilience of consensus in dynamic collective behaviors, and to analyze the controllability of the swarm dynamics. Here we devise the dynamic signaling network which is the information transfer channel underpinning the swarm dynamics of the directed interagent connectivity based on a topological neighborhood of interactions. The study of the connectedness of the swarm signaling network reveals the profound relationship between group size and number of interacting neighbors, which is found to be in good agreement with field observations on flock of starlings [Ballerini et al. (2008) Proc. Natl. Acad. Sci. USA, 105: 1232]. Using a dynamical model, we generate dynamic collective behaviors enabling us to uncover that the swarm signaling network is a homogeneous clustered small-world network, thus facilitating emergent outcomes if connectedness is maintained. Resilience of the emergent consensus is tested by introducing exogenous environmental noise, which ultimately stresses how deeply intertwined are the swarm dynamics in the physical and network spaces. The availability of the signaling network allows us to analytically establish for the first time the number of driver agents necessary to fully control the swarm dynamics.

Influence of the number of topologically interacting neighbors on swarm dynamics

“…Two noise levels were considered—moderate η = 0.1 π and low η = 0.01 π —following the study by Komareji & Bouffanais22. The results, shown in Fig.…”

The Best-of-n Problem in Robot Swarms: Formalization, State of the Art, and Novel Perspectives

“…Continuous consensus achievement problems have been also studied in the context of wireless sensor networks with the aim of developing algorithms for distributed estimation of signals (Schizas et al, 2008a,b). More recently, continuous consensus achievement has been investigated using a network-theoretic perspective, which focuses on the signaling network emerging between interacting agents (Komareji and Bouffanais, 2013;Shang and Bouffanais, 2014).…”

Swarm-Enabling Technology for Multi-Robot Systems

“…Recently, studies of such signaling networks in swarms have revealed the need for specific structural properties of the network-in terms of degree distribution, shortest path, and clustering coefficient-in order to achieve effective consensusreaching dynamics (Shang and Bouffanais, 2014;Sekunda et al, 2016) and high dynamic controllability of the swarm by a given subset of driving agents (Komareji and Bouffanais, 2013).…”

“…Recently, studies of such temporal networks (Holme and Saramäki, 2012) in swarms have revealed the need for specific structural properties of the network-in terms of degree distribution, shortest path, and clustering coefficient-in order to achieve effective consensusreaching dynamics (Shang and Bouffanais, 2014;Sekunda et al, 2016) and high dynamic control of the swarm by a given subset of driving agents (Komareji and Bouffanais, 2013). With a mesh network, all agents are identical (from the network viewpoint) and can exchange information with a specific set of neighbors (e.g., metric, topological, Voronoi neighborhoods) directly without involving a third agent or going through a central hub or router.…”