Research Overview

My research can be mainly classified into two main categories. So far, I have worked on the Covariance Steering Theory and its application in safe and robust trajectory optimization.

Covariance Steering Theory

In this project, we extend the Covariance Steering Theory. Covariance Steering problems are a class of stochastic optimal control problems where the goal is steer a distribution to a desired one while minimizing some cost index.

We solved soft constrained version of this problem in which the condition on the terminal distribution is encoded in the objective function by utilizing squared Wasserstein Distance. We also proposed a new parametrization to these problems to make them more tractable.[1] [2]

In our recent work, we showed that under certain conditions the Covariance Steering with Wasserstein distance problem is convex and convex concave procedure converges to the unique global minimizer. [3]

Covariance Steering in Robust Trajectory Optimization

One implication of covariance control problems is to control the distribution of the state of the agent. We use this interpretation of covariance steering to make model predictive path integral control algorithm more robust against unmodeled disturbances. Furthermore, our approach provides additional safety against bad tuning of running cost functions and algorithm parameters. [4]