Nonlinear stiffness allows passive dynamic hopping for one-legged robots with an upright trunk

Abstract: Template models are frequently used to simplify the control dynamics for robot hopping or running. Passive limit cycles can emerge for such systems and be exploited for energy-efficient control. A grand challenge in locomotion is trunk stabilization when the hip is offset from the center of mass (CoM). The swing phase plays a major role in this process due to the moment of inertia of the leg; however, many template models ignore the leg mass. In this work, the authors consider a robot hopper model (RHM) with a rigid trunk and leg plus a hip that is displaced from the CoM. It has been previously shown that no passive limit cycle exists for such a model given a linear hip spring. In this work, we show that passive limit cycles can be found when a nonlinear hip spring is used instead. To the authors' knowledge, this is the first time that a passive limit cycle has been found for this type of system.