Stabilizing Highly Dynamic Locomotion in Planar Bipedal Robots with Dimension Reducing Control.

Abstract

In the field of robotic locomotion, the method of hybrid zero dynamics (HZD) proposed by Westervelt, Grizzle, and Koditschek provided a new solution to the canonical problem of stabilizing walking in planar bipeds. Original walking experiments on the French biped RABBIT were very successful, with gaits that were robust to external disturbances and to parameter mismatch. Initial running experiments on RABBIT were cut short before a stable gait could be achieved, but helped to identify performance limiting aspects of both the physical hardware of RABBIT and the method of hybrid zero dynamics. To improve upon RABBIT, a new robot called MABEL was designed and constructed in collaboration between the University of Michigan and Carnegie Mellon University.

In light of experiments on RABBIT and in preparation for experiments on MABEL, this thesis provides a theoretical foundation that extends the method of hybrid zero dynamics to address walking in a class of robots with series compliance. Extensive new design tools address two main performance limiting aspects of previous HZD controllers: the dependence on non-Lipschitz finite time convergence and the lack of a constructive procedure for achieving impact invariance when outputs have relative degree greater than two. An analytically rigorous set of solutions - an arbitrarily smooth stabilizing controller and a constructive parameter update scheme - is derived using the method of Poincare sections. Additional contributions of this thesis include the development of sample-based virtual constraints, analysis of walking on a slope, and identification of dynamic singularities that can arise from poorly chosen virtual constraints.