Modeling and Mathematical Analysis of Swarms of Microscopic Robots

TL;DR

This paper introduces a mathematical framework for modeling swarms of microscopic robots in fluid environments, aiding in understanding their collective behavior and guiding future medical device design.

Contribution

It presents a novel mathematical modeling approach for microscopic robot swarms, focusing on chemical source localization in fluid environments, which is useful for future medical applications.

Findings

Model successfully describes robot behavior in one-dimensional scenarios

Framework helps evaluate design trade-offs for microscopic robots

Potential applications in medical diagnostics and targeted therapy

Abstract

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.