Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

TL;DR

This paper introduces a unified theory using virtual constraints and hybrid zero dynamics to design stable, underactuated bipedal robot walking gaits, bridging physical constraints with control strategies.

Contribution

It develops a comprehensive framework for stable underactuated bipedal locomotion using virtual constraints and hybrid zero dynamics, with practical implementation references.

Findings

Successful implementation on robotic platforms

Stable walking gaits achieved in underactuated models

Framework enhances understanding of physical and virtual constraints

Abstract

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.