Bipedal Hopping Pattern Generation for Passively Compliant Humanoids: Exploiting the Resonance

This paper describes a novel technique to analytically generate feasible hopping trajectories that can be applied to passively compliant bipedal humanoid robots. The proposed method is based on exploiting the inherent passive compliance through a reduced model, while the dynamic balance is maintained via the zero moment point (ZMP) criterion. To begin with, a computational resonance frequency analysis and a system identification routine are performed for the actual robot so as to determine the base resonance frequency, which is of special interest. Subsequently, the vertical component of the center of mass trajectory is generated by using a periodic function in which the aforementioned resonance frequency is utilized. The horizontal component of the center of mass trajectory is generated via the ZMP concept to ensure the dynamic balance. Having analytically generated both vertical and horizontal elements of the center of mass trajectory, joint motions are computed through the utilization of translational and angular momentum constraints. Applying the proposed method, a series of periodic forward hopping experiments is conducted on our actual compliant bipedal robot. As a result, we observe repetitive, continuous, and dynamically equilibrated forward hopping cycles with successful landing phases.