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:\[\ddot{r}_i=(1-\lvert\dot{r}_i\rvert^2)\dot{r}_i-(r_i-R)\] where \(R\) is the center of mass of the system, given by\[R=\sum_{i=1}^Nr_i\] Expected limit behavior is pictured below:

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.

In the summer of 2017, I worked at Naval Research Laboratory in Washington, DC with Dr. Ira Schwartz. Primarily, I researched swarm collisions in systems subject to delay. We summarized our findings in a report, titled "The Dynamics of Interacting Swarms". It is available on the ArXiv.

Mathematica, ROS, and Gazebo Integration

In the course of my work on swarming, I have looked at applications to UAVs. 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: