research notes

Emergent homeomorphic curves in swarms This work introduces the concept of geometric embeddings, which permit the application of linear control policies to produce globally-stable emergent curves in swarms of unmanned aerial vehicles. The vehicles make decisions based only on local observations, without knowing their role in the larger group. Below is an animation of the technique being used to produce a lemniscatic arc. Article available here. Code available here. ...

Key Points Built a custom ChatGPT to assist me with my research. Trained it on actual comments from peer-review. Received feedback on my proposed revisions. Overall impressed with its initial performance. Introduction One of my holiday projects this year was to play with some of the special features that come with the OpenAI ChatGPT Plus account. In additon to gaining access to better models and more reliable performance, the Plus account allows you to create your own custom GPTs, tailored to your own needs. ...

I recently conducted a minor survey on potential functions in the context of multi-agent systems. Collective potential functions are a common way to produce desired separation between agents in a swarm. Fig. 1 provides an illustration of one such scenario. Fig. 1: Illustration of potential functions in action. Note that the agents maintain some common distance between eachother, except when navigating around the obstacles in yellow. Potential A common potential function used in molecular dynamics and lattice formation with equilibrium distances is the Lennard-Jones potential function: ...