Georgia Institute of Technology College of Sciences

Optimal transport is a thoroughly studied field in mathematics and introduces the concept of Wasserstein distance, which has been widely used in various applications in computational mathematics, machine learning as well as many areas in engineering. Meanwhile, control theory and path planning is an active branch in mathematics and robotics, focusing on algorithms that calculates feasible or optimal paths for robotic systems. In this defense, we use the properties of the gradient flows in Wasserstein metric to design algorithms to handle different types of path planning and control problems as well as the K-means problems defined on graphs.