In 2017, I received the Trident Scholarship from the Naval Academy. The Trident Scholarship allowed me to devote 24 credit-hours (total) towards research. My advisor, Prof Kostya Medynets, and I chose to look at mathematical swarm models. In particular, we were interested in the parabolic potential model, a model for swarms based on spring-like attraction. In a system of \(N\) agents, each of which has position vector \(r_i\), the parabolic potential model has the following equation of motion:

where \(R\) is the center of mass of the system, given by

\[R=\sum_{i=1}^Nr_i\]

Expected limit behavior is pictured below:

Typical limit behavior of the parabolic potential model.

Over the course of a year, we proved several new results about the stability of this system. We were fortunate to observe some behavior that has never been seen before.

Previously unobserved limit behavior in the parabolic potential model.

In summer 2017, I interned at the Naval Research Laboratory in Washington, DC, advised by Dr. Ira Schwartz. I researched swarm collisions in systems subject to delay. We summarized our findings in a report, titled The Dynamics of Interacting Swarms, published by the Defense Technical Information Center.

Mathematica, ROS, and Gazebo Integration

In the course of my work on swarming, I researched applications to unmanned systems. I spent some time getting differential equation models (simulated in Wolfram Mathematica) to drive virtual drones (simulated in Gazebo) using ROS, the Robot Operating System to interface between the two. A video of my work is available on Youtube: