Monopedal running control: SLIP embedding and virtual constraint controllers

Two feedback controllers that induce stable running gaits on a three-degree-of-freedom asymmetric hopper, termed the asymmetric spring loaded inverted pendulum (ASLIP), see Fig. 1, are compared in terms of their steady-state and transient behaviors. In each case, feedback is used to create a lower-dimensional hybrid subsystem that determines the existence and stability properties of periodic motions of the full-dimensional closed-loop system. The first controller creates a one degree-of-freedom subsystem through imposing two suitably selected (virtual) holonomic constraints on the configuration variables of the ASLIP. The second controller asymptotically imposes a single (virtual) holonomic constraint to create a two-degree-of-freedom subsystem that is diffeomorphic to a standard spring loaded inverted pendulum (SLIP). The two controllers induce identical steady-state behaviors. Under transient conditions, however, the underlying compliant nature of the SLIP allows significantly larger disturbances to be accommodated, with less actuator effort, and without violation of the unilateral constraints between the leg end and the ground.