Planar Bipedal Jumping Gaits With Stable Landing

D. Goswami, P. Vadakkepat
2009 IEEE Transactions on robotics  
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
more » ... osed-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. Index Terms-Biped robot, closed-loop dynamics (CLD), critical potential index and critical kinetic index, jumping gaits, landing stability, multiple Lyapunov function (MLF), singular perturbation, switching zero dynamics (ZD ). Periodic trajectories with the specific properties result in stable ZD of a two-link acrobot [9]. The periodic nature of the locomotion/gait is utilized to stabilize the ZD [6], [7], [11], [12]. A Poincaré return map is an effective tool to validate periodicity and orbital stability [6], [7]. Simplified biped models such as Manuscript
doi:10.1109/tro.2009.2026502 fatcat:ymolr2pfarcbzlemswfyjderoy