Abstract
In this chapter we consider a double-integrator model of an agent. As in the last chapter, we characterize swarm cohesiveness as a stability property and use a Lyapunov approach to develop conditions under which local agent actions lead to cohesive foraging. The conditions here allow for the presence of “noise” characterized by uncertainty on sensing other agent’s position and velocity, and in sensing nutrients (a resource profile) that each agent is foraging for. The results quantify claims in biology 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 at the end of the chapter show that very complicated but orderly group behaviors, reminiscent of those seen in biology, emerge in the presence of noise.
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