Robust stabilization of hybrid periodic orbits with application to dynamic bipedal walking

Robotic walking has been a topic of interest for a long time and numerous theoretical as well as experimental studies have been conducted so far. However, the area of under-actuated bipedal walking remains open and limited progress has been achieved. This thesis focuses on building a framework for modeling, gait optimization and robust stabilization of periodic bipedal locomotion, especially bipedal walking with more than 1 degree of under-actuation. We make this framework general so that various biped models can be accommodated.; Roughly, two categories of methods in the stabilization of periodic bipedal walking can be identified in the literature: trajectory tracking and Poincare sections. The first category is often too rigid since tracking of phase is typically not desired in practical application, while the methods in the second category are subject to the complexity associated with the computation of Poincare return map, We propose a computational approach that overcomes these drawbacks. In our approach, energy efficient gait is found through optimization; the classic dynamics decomposition is extended to hybrid systems with impulse effects; and finally, an efficient linear matrix inequality (LMI) based synthesis approach is developed to provide robust controllers for the system. We demonstrate that the approach works for both planar and spatial under-actuated biped robots. No other case of successful control of under-actuated spatial bipeds has been reported to date.