Path Planning on SE(2) for Autonomous Vehicles

During my graduate coursework, I took a course called “Group Theory for Optimization and Machine Learning” taught by Prof. Matthew Giamou at McMaster University.
I chose to do my final project on Path Planning for Autonomous Vehicles using group-theoretic concepts.
Below is my final report.

As is typical of graduate students, I do not have much free time to work on side projects, but I hope to revisit this work in the future because it is of great interest to me.