Two-element control for the active SLIP model

The Spring Loaded Inverted Pendulum has been extensively studied and used as an inspiration to the study of legged locomotion. Biological data suggest that legs regulate energy production and removal via muscle activation, and therefore the conservative SLIP model cannot fully explain the robustness of many legged animals during running and hopping gaits. In this work we consider the active SLIP model, an energetically non-conservative version of the SLIP model with series actuation. In particular, we propose a strategy for actuator displacement to add/remove energy from the system, and to analytically solve part of its dynamics. Additionally, we develop a control strategy for online actuator displacement to drive the system to a desired state, even in the presence of terrain perturbation.