Robust walking control based on the extended variable stiffness SLIP model

The spring-loaded inverted pendulum (SLIP) model is commonly used as a template model to control the walking gait of bipedal robots. However, this model has two major deficiencies: it ignores the swing foot dynamics and it lacks robustness against disturbances. These issues have been separately addressed in a couple of studies. The robustness issue of the SLIP was addressed by swapping the leg springs with variable stiffness ones in the variable SLIP (V-SLIP) model. The SLIP model with swing leg (SLIP-SL) introduced swing leg dynamics to the SLIP by adding a massed leg and foot, and springs to move them. In this paper, we first propose a template model that combines the swing leg dynamics and robustness solutions in a new model called "the variable stiffness SLIP model with swing leg dynamics" (VSLIP-SL). Then, we go on to propose a controller for a 5-link fully actuated bipedal robot model that is based on the VSLIP-SL. The challenge of the controller is to translate the variable stiffness responses of the VSLIP-SL to the 5-link model, which does not have any compliant elements. We achieve this through an encoderdecoder scheme and feedback linearization. It is shown by numerical simulations that we are able to tackle the robustness issue on a template level.