"Motion Planning Around Obstacles with Convex Optimization"

Thursday, May 12th @ 11am PDT

This is a hybrid seminar with in-person presentation in EBU-1 Qualcomm Large Conference Room (first floor) and

Zoom Linkhttps://ucsd.zoom.us/j/96958677518

Speaker:  Russ Tedrake

Seminar Abstract

In this talk, I'll describe a new approach to planning that strongly leverages both continuous and discrete/combinatorial optimization.  The framework is fairly general, but I will focus on a particular application of the framework to planning continuous curves around obstacles. Traditionally, these sort of motion planning problems have either been solved by trajectory optimization approaches, which suffer with local minima in the presence of obstacles, or by sampling-based motion planning algorithms, which can struggle with derivative constraints and in very high dimensions.  In the proposed framework, called Graph of Convex Sets (GCS), we can recast the trajectory optimization problem over a parametric class of continuous curves into a problem combining convex optimization formulations for graph search and for motion planning.  The result is a non-convex optimization problem whose convex relaxation is very tight — to the point that we can very often solve very complex motion planning problems to global optimality using the convex relaxation plus a cheap rounding strategy.  I will describe numerical experiments of GCS applied to a quadrotor flying through buildings and robotic arms moving through confined spaces.  On a seven-degree-of-freedom manipulator, GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time, and in 14 dimensions (or more) it can solve problems to global optimality which are hard to approach with sampling-based techniques.

Joint work with Tobia Marcucci, Mark Petersen, David von Wrangel, and Pablo Parrilo


Russ is the Toyota Professor of Electrical Engineering and Computer ScienceAeronautics and Astronautics, and Mechanical Engineering at MIT, the Director of the Center for Robotics at the Computer Science and Artificial Intelligence Lab, and the leader of Team MIT's entry in the DARPA Robotics Challenge. Russ is also the Vice President of Robotics Research at the Toyota Research Institute. He is a recipient of the 2021 Jamieson Teaching Award, the NSF CAREER Award, the MIT Jerome Saltzer Award for undergraduate teaching, the DARPA Young Faculty Award in Mathematics, the 2012 Ruth and Joel Spira Teaching Award, and was named a Microsoft Research New Faculty Fellow.

Russ received his B.S.E. in Computer Engineering from the University of Michigan, Ann Arbor, in 1999, and his Ph.D. in Electrical Engineering and Computer Science from MIT in 2004, working with Sebastian Seung. After graduation, he joined the MIT Brain and Cognitive Sciences Department as a Postdoctoral Associate. During his education, he has also spent time at Microsoft, Microsoft Research, and the Santa Fe Institute.