Symmetric virtual constraints for periodic walking of legged robots

Abstract

Dynamic and agile walking or running gaits for legged robots often correspond to periodic orbits in the dynamic model. As the number of degrees of freedom of the models grows, obtaining periodic gaits for these systems through numerical optimization is not always straightforward. In contrast to common numerical search methods for periodic orbits, this paper introduces a class of holonomic constraints, called symmetric virtual constraints, which when enforced by controllers, ensure the existence of periodic orbits. The main advantage of symmetric virtual constraints is that they relax the need for online or offline parameter search for periodic orbits, and at the same time lead directly to feedback controllers that realize a periodic orbit.