Mar 11 (Mon) @ 9:00am: "Graphs of Convex Sets and their Applications in Robotics and Control," Tobia Marcucci, PhD Student, MIT

Abstract

In this talk we introduce a novel modeling and computational framework for joint discrete and continuous decision making. We consider graphs where each vertex is associated with a convex optimization problem, and each edge couples two problems through additional convex costs and constraints. We call these Graphs of Convex Sets (GCS). Many classical problems in graph theory are naturally generalized to GCS, yielding a new class of problems at the interface of combinatorial and convex optimization with a wide variety of applications. For the solution of these problems, we present a unified technique that leverages perspective operators to formulate tight convex relaxations and strong mixed-integer formulations. Our main focus will be the shortest-path problem in GCS and its applications in robot motion planning and optimal control. We will show that, in these two areas, our optimization techniques generalize or significantly improve upon algorithms that have been developed for decades and are widely used in academia and industry.

Bio

Tobia Marcucci is a PhD student in Computer Science at the Massachusetts Institute of Technology (MIT), under the supervision of Russ Tedrake and Pablo Parrilo. During his PhD, Tobia has also spent one year at Stanford University as a graduate visiting researcher in Stephen Boyd’s group. Before MIT, Tobia was at the University of Pisa, where he graduated cum laude in mechanical engineering and where he started a PhD in robotics at the Research Center E. Piaggio and the Italian Institute of Technology (IIT). His research lies at the intersection of convex and combinatorial optimization, with applications to robotics, motion planning, and optimal control.

Hosted by: ECE Department

Submitted by: Alexa Pazell <apazell@ece.ucsb.edu>