Georgia Institute of Technology College of Sciences

In this talk, we focus on designing computational methods supported by theoretical properties for optimal motion planning and optimal transport (OT). 

Over the past decades, motion planning has attracted large amount of attention in robotics applications. Given certain
configurations in the environment, the objective is to find trajectories which move the robot from one position to the other while satisfying given constraints. We introduce a new method to produce smooth and collision-free trajectories for motion planning task. The proposed model leads to short and smooth trajectories with advantages in numerical computation. We design an efficient algorithm which can be generalized to robotics applications with multiple robots.

The idea of optimal transport naturally arises from many application scenarios and provides powerful tools for comparing probability measures in various types. However, obtaining the optimal plan is generally a computationally-expensive task, sometimes even intractable. We start with the entropy transport problem as a relaxed version of original optimal transport problem with soft marginals, and propose an efficient algorithm to obtain the sample approximation for the optimal plan. We also study an inverse problem of OT and present the computational methods for learning the cost function from the given optimal transport plan.