Bringing the compass-gait bipedal walker to three dimensions

The planar compass-gait biped has been extensively studied in the dynamic walking community, motivated by the gravity-based pendular efficiencies of human walking. These results can be extended to three dimensions using controlled geometric reduction for open-chain robots, by which stable 3-D walking gaits are built from known sagittal-plane limit cycles. We apply this method to the standard and with-torso compass-gait (hipless) bipeds, showing straight-ahead walking gaits (i.e., stable 1-step periodic limit cycles) as well as h-step turning in full circles (i.e., stable h-periodic limit cycles). These constant-curvature maneuvers are composed of stable 1-periodic turning gaits modulo heading change, demonstrating two types of gaits for directional dynamic walking in three dimensions.