Controlled Reduction of a Five-Link 3D Biped with Unactuated Yaw

This paper presents a formulation of controlled geometric reduction with one degree of underactuation for mechanical systems with an unactuated cyclic variable subject to passive damping. We show that the first control term in the fully actuated case reduces to passive joint-velocity feedback, which can be equivalently provided by viscous friction. The underactuated control strategy is applied to a five-link 3D biped with a hip, torso, knees, and unactuated yaw at the foot contact point. We show asymptotically stable walking in the presence of passive yawing for realistic friction coefficients.