  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.
