Hybrid Invariance in Bipedal Robots with Series Compliant Actuators

Stable walking motions in bipedal robots can be modeled as asymptotically stable periodic orbits in nonlinear systems with impulse effects. The method of hybrid zero dynamics, previously used to analyze planar walking in bipeds with one degree of underactuation, is extended to address the increased degrees of underactuation and the additional impact invariance conditions that arise when actuator dynamics are explicitly modeled. The resultant controller is parameterized and includes a discrete feedback in the parameters that is active only in the instantaneous double support phase. The controller design method is illustrated on a five-link planar walker with series compliant actuation, that is, a robot where a compliant element has been deliberately inserted between each actuated joint and its corresponding motor in order to increase the overall energy efficiency of locomotion