1Embedding Active Force Control within the Compliant Hybrid Zero Dynamics to Achieve Stable, Fast Running on MABEL

Abstract—A mathematical formalism for designing run-ning gaits in bipedal robots with compliance is introduced and subsequently validated experimentally on MABEL, a planar biped that contains springs in its drivetrain. The methods of virtual constraints and hybrid zero dynamics are used to design a time-invariant feedback controller that respects the natural compliance of the open-loop system. In addition, it also enables active force control within the compliant hybrid zero dynamics allowing within-stride adjustments of the effective stance leg stiffness. The proposed control strategy was implemented on MABEL and resulted in a kneed-biped running record of 3.06 m/s (10.9 kph or 6.8 mph)