EECS Colloquium: Feedback Motion Planning with Sum-of-Squares Verification

EECS Colloquium: Feedback Motion Planning with Sum-of-Squares Verification

Colloquium | November 10 | 4-5 p.m. | Soda Hall, HP Auditorium (306)

Russ Tedrake, Professor, Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT)

Electrical Engineering and Computer Sciences (EECS), CiBER-IGERT

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.