SUMMARY

Hybrid zero dynamics (HZD) has emerged as a popular framework for dynamic and underactuated bipedal walking, but has significant implementation difficulties when applied to the high degrees of freedom present in humanoid robots. The primary impediment is the process of gait design--it is difficult for optimizers to converge on a viable set of virtual constraints defining a gait. This dissertation presents a methodology that allows for the fast and reliable generation of efficient multi-domain robotic walking gaits through the framework of HZD, even in the presence of underactuation. To achieve this goal, we unify methods from trajectory optimization with the control framework of multi-domain hybrid zero dynamics. We present a novel optimization formulation in the context of direct collocation methods and HZD where we rigorously generate analytic Jacobians for the constraints. Two collocation methods, local collocation and pseudospectral (global) collocation, are developed within an unified framework, and their performance in different circumstances is comparatively studied. As a result, solving the resulting nonlinear program becomes tractable for large-scale NLP solvers, even for systems as high-dimensional as humanoid robots. We experimentally validate our methodology on the spring-legged prototype humanoid, DURUS, showing that the optimization approach yields dynamic and stable walking gaits for different walking configurations, including unrestricted 3D dynamic walking.