Approximation and Control of the SLIP Model Dynamics via Partial Feedback Linearization and Two-Element Leg Actuation Strategy

Abstract

The spring loaded inverted pendulum (SLIP) has been extensively studied and used as a model capturing general aspects of legged locomotion. Biological data suggest that legs regulate energy production and removal via muscle activation; 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 nonconservative version of the SLIP model with added series actuation. In particular, we propose a partial feedback linearization action for actuator displacement to analytically solve part of its dynamics, thereby reducing computational time and increasing the practicality of performing online control actions. This is then paired with a two-part control action to add/remove energy to/from the system and modify the upcoming apex state to span an open set within the reachable apex states. 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, and the other to control the system to hop on a desired set of terrain footholds. Furthermore, we demonstrate the proposed strategy on a more dynamically sophisticated planar hopper model.