Modeling and Mathematical Analysis of Swarms of Microscopic Robots
  The biologically-inspired swarm paradigm is being used to design self-organizing systems of locally interacting artificial agents. A major difficulty in designing swarms with desired characteristics is understanding the causal relation between individual agent and collective behaviors. Mathematical analysis of swarm dynamics can address this difficulty to gain insight into system design. This paper proposes a framework for mathematical modeling of swarms of microscopic robots that may one day be useful in medical applications. While such devices do not yet exist, the modeling approach can be helpful in identifying various design trade-offs for the robots and be a useful guide for their eventual fabrication. Specifically, we examine microscopic robots that reside in a fluid, for example, a bloodstream, and are able to detect and respond to different chemicals. We present the general mathematical model of a scenario in which robots locate a chemical source. We solve the scenario in one-dimension and show how results can be used to evaluate certain design decisions. 
Aram Galstyan, Tad Hogg, Kristina Lerman