SLIP-based and HOPFL Enforced Step Length Control for Stable Body Motions of Realistic SEA Hoppers

In this paper, we consider the problem of precise step length control on underactuated hopping robots, integrating analytical SLIP-based trajectories on a hardware inspired hopper model that includes series-elastic actuation (SEA), leg mass and inertia. Additionally, in the model considered the body center of mass (CoM) is not collocated with the hip joint, and must be stabilized for successful hopping. The majority of recent work with hopping robots is geared towards providing a discrete set of stable limit cycles, and is thus not well suited for non steady-state motions which are required for foothold placement in the real world. Therefore, this work focuses on developing control methods capable of dynamically switching between strides, and thus allowing footholds to be controlled on a step-to-step basis. Building on previous work, we illustrate how high-order partial feedback linearization (HOPFL) can be implemented directly on the leg-length state, and show how to apply these results so that algorithms designed for the SLIP model already widely available in the literature can be accurately implemented as reference trajectories. Furthermore, we develop control laws for the hip torque in order to both stabilize body motions and force the resulting leg angle trajectories to be analytically tractable as following the SLIP model’s dynamics.