Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to induce a low dimensional system, the zero dynamics, that captures the underactuated aspects of a robot's model, without any approximations. To enhance intuition, the relation between physical constraints and virtual constraints is first established. From here, the hybrid zero dynamics of an underactuated bipedal model is developed, and its fundamental role in the design of asymptotically stable walking motions is established. The chapter includes numerous references to robots on which the highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte

Bipedial Locomotion Up Sandy Slopes: Systematic Experiments Using Zero Moment Point Methods

Bipedal robotic locomotion in granular media presents a unique set of challenges at the intersection of granular physics and robotic locomotion. In this paper, we perform a systematic experimental study in which biped robotic gaits for traversing a sandy slope are empirically designed using Zero Moment Point (ZMP) methods. We are able to implement gaits that allow our 7 degree-of-freedom planar walking robot to ascend slopes with inclines up to 10°. Firstly, we identify a given set of kinematic parameters that meet the ZMP stability criterion for uphill walking at a given angle. We then find that further relating the step lengths and center of mass heights to specific slope angles through an interpolated fit allows for significantly improved success rates when ascending a sandy slope. Our results provide increased insight into the design, sensitivity and robustness of gaits on granular material, and the kinematic changes necessary for stable locomotion on complex media