Joint Colloquium Distinguished Lecture Series
Feedback Motion Planning with Sum-of-Squares Verification
(w/ applications to Walking Robots and Robotic Birds)
Wednesday, November 10, 2010
In this talk, I will present a nonlinear feedback control synthesis algorithm which combines randomized motion planning algorithms, popular in robotics, with sum of squares optimization. In order to drive the system to a goal state or limit cycle, the algorithm systematically populates the controllable subset of state space with a sparse set of trajectories which are locally stabilized with linear feedback and verified with sums of squares; we have now developed efficient methods for performing this verification along trajectories and around limit cycles, on systems with hybrid dynamics, and on systems with mixed polynomial/trigonometric nonlinearities. Under mild assumptions, the planning algorithm probabilistically converges to a controller which stabilizes the entire controllable set; in initial experiments this coverage occurs relatively quickly.
By virtue of the randomized planning component, the algorithm has potential for implementation on "hopelessly nonconvex" problems. I'll describe the application of these ideas to bipedal locomotion, quadrupedal locomotion over rough terrain, and small unmanned airplanes that land on a perch.
Russ Tedrake is an Associate Professor of Electrical Engineering and Computer Science at Massachusetts Institute of Technology (USA), and a member of the Computer Science and Artificial Intelligence Lab. He received his B.S.E. in Computer Engineering from the University of Michigan, Ann Arbor, in 1999, his Ph.D. in Electrical Engineering and Computer Science from MIT in 2004, and was a Postdoctoral Associate in Brain and Cognitive Sciences at MIT before joining the faculty in EECS in 2005. He has received an NSF CAREER award, the MIT Jerome Saltzer award for undergraduate teaching, the DARPA Young Faculty Award, and was named a Microsoft Research New Faculty Fellow. The goal of his research is to build robots which exploit their natural dynamics to achieve extraordinary agility and efficiency.
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