Geometry is everywhere, and the representation and manipulation of geometric data is critical in applications including scientific simulation, robot planning, and entertainment systems. Drawing from ideas in differential geometry and elsewhere, our research seeks to develop new algorithms which are more efficient and more effective for computing with geometry.
Optimal trajectory control computes control inputs which will transition a dynamical system from an initial state to a final state minimizing some cost metric. Analytical methods can significantly constrain the solution space, but rarely give direct solutions. I'm interested in the algorithms that "close the gap", searching the restricted solution space to find optimal solutions in real-world dynamical systems.
Recently, I've developed a new front-propagation method to extend set-based control for navigation in current fields to 3D.
I work on a variety of algorithmic problems in systems biology, specifically graph algorithms for protein interaction networks. My primary efforts have been in the prediction of signaling pathways from interaction databases. Recent work has investigated the value of hypergraphs in this system.
One significant contribution is a new augmentation to Yen's k-shortest paths which improves performance on protein networks by a factor of 40 or more. We have found that using this method to compute tens of thousands of shortest paths can yield significant prediction improvements.
Biomimetic robotics investigates the value of robots inspired by natural mechanisms. In my senior design project with the Virginia Tech Engineering Science and Mechanics Department, my team studied undulatory batoid robots, which have wings like a manta ray. Our analysis included both computational methods and building a prototype, BURT (Batoid Underwater Robotics Testbed). We won the departmental award for overall best project! The project is now being continued in its second year by two new teams of students.