Stable Social Foraging Swarms in a Noisy Environment

Abstract

Abstract-Bacteria, bees, and birds often work together in groups to find food. A group of robots can be designed to coordinate their activities to search for and collect objects. Networked cooperative uninhabited autonomous vehicles are being developed for commercial and military applications. Suppose that we refer to all such groups of entities as "social foraging swarms." In order for such multiagent systems to succeed it is often critical that they can both maintain cohesive behaviors and appropriately respond to environmental stimuli (e.g., by optimizing the acquisition of nutrients in foraging for food). In this paper, we characterize swarm cohesiveness as a stability property and use a Lyapunov approach to develop conditions under which local agent actions will lead to cohesive foraging even in the presence of "noise" characterized by uncertainty on sensing other agent's position and velocity, and in sensing nutrients that each agent is foraging for. The results quantify earlier claims that social foraging is in a certain sense superior to individual foraging when noise is present, and provide clear connections between local agent-agent interactions and emergent group behavior. Moreover, the simulations show that very complicated but orderly group behaviors, reminiscent of those seen in biology, emerge in the presence of noise.

Modeling and Cohesiveness Analysis of Midge Swarms

“…Boundedness of discrete-time swarms was first studied in (Liu and Passino, 2004b), with corresponding continuous-time results given in (Liu and Passino, 2004a). In both these studies, however, the work was entirely mathematical, with no connection to a biological swarm.…”

Distributed Consensus in Networks of Dynamic Agents

“…Symmetric argument holds if the second condition occurs. Initially, we show thatt > 0 sincet = 0 is contradictory with the fact that, since max j∈Γ {x j (0)} < ∞, all the components of u(0) are bounded by definition (7). Next, we observe that all x i (t) are continuous and differentiable with bounded derivatives, for 0 ≤ t ≤t, since both max j∈Γ {x j (t)} and min j∈Γ {x j (t)} are bounded and then all the components u(t) are bounded too.…”

“…(7) Initially, we study the stability of the system under protocol (7). To this aim, we consider the space of the edge variables η ji = ϑ(x j ) − ϑ(x i ).…”

“…To complete the prove note that the above arguments hold for any value of ε > 0. It is left to show that any statẽ x i within the above range is reachable under protocol (7). But this is easy to see sincex i can be expressed as convex combination of x j (0) for all j ∈ Γ.…”

“…Agents implement a consensus protocol to reach consensus, that is to (make their states) converge to a same value, called consensus-value, or group decision value [1]. Coordination of agents/vehicles is an important task in several applications including autonomous formation flight [2], [3], cooperative search of unmanned air-vehicles (UAVs) [4], [5], swarms of autonomous vehicles or robots [6], [7], multi-retailer inventory control [8], [9] and congestion/flow control in communication networks [10]. Actually, a central point in consensus problems is the connection between the graph structure, defined by the Laplacian Matrix, and delays or distortions in communication links [11].…”