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

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.

ULT-model: Towards a one-legged unified locomotion template model for forward hopping with an upright trunk

While many advancements have been made in the development of template models for describing upright-trunk locomotion, the majority of the effort has been focused on the stance phase. In this paper, we develop a new compact dynamic model as a first step toward a fully unified locomotion template model (ULT-model) of an upright-trunk forward hopping system, which will also require a unified control law in the next step. We demonstrate that all locomotion subfunctions are enabled by adding just a point foot mass and a parallel leg actuator to the well-known trunk SLIP model and that a stable limit cycle can be achieved. This brings us closer toward the ultimate goal of enabling closed-loop dynamics for anchor matching and thus achieving simple, efficient, robust and stable upright-trunk gait control, as observed in biological systems.