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 artifi-cial agents. A major difficulty in designing swarms with desired characteristics is understanding the causal relation between individual agent and collective behaviors. Math-ematical analysis of swarm dynamics can address this dif-ficulty to gain insight into system design. This paper pro-poses a framework for mathematical modeling of swarms of microscopic robots that may one day be useful in med-ical applications. While such devices do not yet exist, the modeling approach can be helpful in identifying various de-sign 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 sce-nario in one-dimension and show how results can be used to evaluate certain design decisions. 1