Analytical control parameters of the swing leg retraction method using an instantaneous SLIP model

The Spring-Loaded Inverted Pendulum (SLIP) is a widely used model for the description of humans and animals running motion. The SLIP model is, however, sensitive to impact angle for various terrain heights. One known method for increasing the model's robustness to terrain changes is the Swing Leg Retraction (SLR) method. Despite its popularity, an analytic formulation of this method has yet been provided. In this work, using an instantaneous stance phase assumption, we present the increase in robustness of the swing method. This analysis provides a way to isolate the optimal parameters of the SLR. We validate these optimal parameters in simulations and proof-of-concept experiments in a planar environment.