Hopping at the resonance frequency: A trajectory generation technique for bipedal robots with elastic joints

It is known that bipedal robots with passive compliant structures have obvious advantages over stiff robots, as they are able to handle the potential energy management. Therefore, this paper is aimed at presenting a jumping pattern generation method that takes advantage of this property via the utilization of the base resonance frequency, which is of special importance. To begin with, the resonance frequency is determined through a system identification procedure on our actual robot. Consequentially, the vertical component of the CoM is generated via a periodic function in which the resonance frequency is employed. The horizontal component of the CoM is obtained using the ZMP criterion to guarantee the dynamic balance. Having obtained the necessary elements of the CoM trajectory within an analytical manner, joint motions are computed with the help of translational and angular momenta constraints. In order to validate the method, two legged jumping experiments are conducted on our actual compliant robot. In conclusion, we observed repetitive, continuous, and dynamically equilibrated jumping cycles with feasible landing phases.