Mathematics and Learning for Agile and Dynamic Bipedal Locomotion

March 09, 2018, Webb 1100

Jessy Grizzle

University of Michigan, Electrical and Computer Engineering


Is it great fortune or a curse to do legged robotics on a University campus that has Maya Lin’s earthen sculpture, The Wave Field? Come to the talk and find out! Our work on model-based feedback control for highly dynamic locomotion in bipedal robots will be amply illustrated through images, videos, and math. The core technical portion of the presentation is a method to overcome the obstructions imposed by high-dimensional bipedal models by embedding a stable walking motion in an attractive low-dimensional surface of the system's state space. The process begins with trajectory optimization to design an open-loop periodic walking motion of the high-dimensional model and then adding to this solution, a carefully selected set of additional open-loop trajectories of the model that steer toward the nominal motion. A drawback of trajectories is that they provide little information on how to respond to a disturbance. To address this shortcoming, Supervised Machine Learning is used to extract a low-dimensional state-variable realization of the open-loop trajectories. The periodic orbit is now an attractor of a low-dimensional state-variable model but is not attractive in the full-order system. We then use the special structure of mechanical models associated with bipedal robots to embed the low-dimensional model in the original model in such a manner that the desired walking motions are locally exponentially stable. When combined with robot vision, we hope this approach to control design will allow the full complexity of the Wave Field to be conquered. In any case, as Jovanotti points out, “Non c'è scommessa più persa di quella che non giocherò”. The speaker for one will keep trying!

Speaker's Bio

Jessy W. Grizzle received the Ph.D. in electrical engineering from The University of Texas at Austin in 1983. He is currently a Professor of Electrical Engineering and Computer Science at the University of Michigan, where he holds the titles of the Elmer Gilbert Distinguished University Professor and the Jerry and Carol Levin Professor of Engineering. He jointly holds sixteen patents dealing with emissions reduction in passenger vehicles through improved control system design. Professor Grizzle is a Fellow of the IEEE and IFAC. He received the Paper of the Year Award from the IEEE Vehicular Technology Society in 1993, the George S. Axelby Award in 2002, the Control Systems Technology Award in 2003, the Bode Prize in 2012 and the IEEE Transactions on Control Systems Technology Outstanding Paper Award in 2014. His work on bipedal locomotion has been the object of numerous plenary lectures and has been featured on CNN, ESPN, Discovery Channel, The Economist, Wired Magazine, Discover Magazine, Scientific American and Popular Mechanics.

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