  Accurate control of a humanoid robot's global position (i.e., its
three-dimensional position in the world) is critical to the reliable execution
of high-risk tasks such as avoiding collision with pedestrians in a crowded
environment. This paper introduces a time-based nonlinear control method that
achieves accurate global-position tracking (GPT) for multi-domain bipedal
walking. Deriving a tracking controller for bipedal robots is challenging due
to the highly complex robot dynamics that are time-varying and hybrid,
especially for multi-domain walking that involves multiple phases/domains of
full actuation, over actuation, and underactuation. To tackle this challenge,
we introduce a continuous-phase GPT control law for multi-domain walking, which
provably ensures the exponential convergence of the entire error state within
the full and over actuation domains and that of the directly regulated error
state within the underactuation domain. We then construct sufficient
multiple-Lyapunov stability conditions for the hybrid multi-domain tracking
error system under the proposed GPT control law. We illustrate the proposed
controller design through both three-domain walking with all motors activated
and two-domain gait with inactive ankle motors. Simulations of a ROBOTIS OP3
bipedal humanoid robot demonstrate the satisfactory accuracy and convergence
rate of the proposed control approach under two different cases of multi-domain
walking as well as various walking speeds and desired paths.
