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Accurate control of a humanoid robot's global position (i.e., itsthree-dimensional position in the world) is critical to the reliable executionof high-risk tasks such as avoiding collision with pedestrians in a crowdedenvironment. This paper introduces a time-based nonlinear control method thatachieves accurate global-position tracking (GPT) for multi-domain bipedalwalking. Deriving a tracking controller for bipedal robots is challenging dueto the highly complex robot dynamics that are time-varying and hybrid,especially for multi-domain walking that involves multiple phases/domains offull actuation, over actuation, and underactuation. To tackle this challenge,we introduce a continuous-phase GPT control law for multi-domain walking, whichprovably ensures the exponential convergence of the entire error state withinthe full and over actuation domains and that of the directly regulated errorstate within the underactuation domain. We then construct sufficientmultiple-Lyapunov stability conditions for the hybrid multi-domain trackingerror system under the proposed GPT control law. We illustrate the proposedcontroller design through both three-domain walking with all motors activatedand two-domain gait with inactive ankle motors. Simulations of a ROBOTIS OP3bipedal humanoid robot demonstrate the satisfactory accuracy and convergencerate of the proposed control approach under two different cases of multi-domainwalking as well as various walking speeds and desired paths.

Provably Stabilizing Global-Position Tracking Control for Hybrid Models of Multi-Domain Bipedal Walking via Multiple Lyapunov Analysis