Mathematics and Learning for Agile and Dynamic Bipedal Locomotion

Abstract

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!