Partial Feedback Linearization and Control of the SLIP Model Via Two-Element Leg Actuation Strategy

The Spring Loaded Inverted Pendulum (SLIP) has been extensively studied and used as an inspiration to research on 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 added series actuation. In particular, we propose a two-element control strategy for actuator displacement to add/remove energy from the system, and analytically solve part of its dynamics. In addition, we develop two control strategies for online computation of actuator displacement and leg positioning: one to drive the system to a desired state, even in the presence of terrain perturbation; the other to control the system to hop on a desired set of terrain footholds. Furthermore, we propose an adaptive control technique for steady-state locomotion on flat terrain to reduce approximation errors by the use of an approximation of the leg-angle dynamics during the stance phase.