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Motion Planning Around Obstacles with Convex Optimization

Wednesday, January 18th, 4:10pm Tel Aviv time (3:10pm CET, 9:10am NY time)


Russ Tedrake, MIT and Toyota Research Institute


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.


Russ Tedrake is the Toyota Professor at the Massachusetts Institute of Technology (MIT) in the Department of Electrical Engineering and Computer Science, Mechanical Engineering, and Aero/Astro, and he is a member of MIT’s Computer Science and Artificial Intelligence Lab (CSAIL). He is also the Vice President of Robotics Research at Toyota Research Institute (TRI). He received a B.S.E. in Computer Engineering from the University of Michigan in 1999, and a Ph.D. in Electrical Engineering and Computer Science from MIT in 2004. Dr. Tedrake is the Director of the MIT CSAIL Center for Robotics and was the leader of MIT's entry in the DARPA Robotics Challenge. He is a recipient of 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. His research has been recognized with numerous conference best paper awards, including ICRA, Robotics: Science and Systems, Humanoids, Hybrid Systems: Computation and Control, as well as the inaugural best paper award from the IEEE RAS Technical Committee on Whole-Body Control.
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