Planar bipedal jumping gaits with stable landing

In this paper, landing stability of jumping gaits is studied for a four-link planar biped model. Rotation of the foot during the landing phase leads to underactuation due to the passive degree of freedom at the toe, which results in nontrivial zero dynamics (ZD). Compliance between the foot and ground is modeled as a spring-damper system. Rotation of the foot along with the compliance model introduces switching in the ZD. The stability conditions for the "switching ZD" and closed-loop dynamics (CLD) are established. " Critical potential index" and "critical kinetic index" are introduced as measures of the stability of the CLD of the biped during landing. Landing stability is achieved by utilizing the stability conditions. Stable jumping motion is experimentally realized on a biped robot.