A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on MABEL

The planar bipedal testbed MABEL contains springs in its drivetrain for the purpose of enhancing both energy efficiency and agility of dynamic locomotion. While the potential energetic benefits of springs are well documented in the literature, feedback control designs that effectively realize this potential are lacking. In this paper, we extend and apply the methods of virtual constraints and hybrid zero dynamics, originally developed for rigid robots with a single degree of underactuation, to MABEL, a bipedal walker with a novel compliant transmission and multiple degrees of underactuation. A time-invariant feedback controller is designed such that the closed-loop system respects the natural compliance of the open-loop system and realizes exponentially stable walking gaits. Five experiments are presented that highlight different aspects of MABEL and the feedback design method, ranging from basic elements such as stable walking and robustness under perturbations, to energy efficiency and a walking speed of 1.5 m s-1 (3.4 mph). The experiments also compare two feedback implementations of the virtual constraints, one based on PD control of Westervelt et al., and a second that implements a full hybrid zero dynamics controller. On MABEL, the full hybrid zero dynamics controller yields a much more faithful realization of the desired virtual constraints and was instrumental in achieving more rapid walking.