Turning Behavior of Running Systems induced by Leg Placement

Abstract

Compared to legged robots, animals and humans can perform much faster and larger turns, even when they run at high speeds. Such rapid turns require the body of a runner to reorient dynamically and in synchrony with its redirection during stance. While it is clear that foot placement affects both direction and orientation, the functional relationship between the three is not well understood. Understanding this relationship could lead to more advanced controllers for turning maneuvers in legged robots as well as to deeper insights into the turning behavior of animals including humans. To develop this relationship, we build on the established spring-mass model for running, replacing its point mass with a rigid body and off-center hip joints. Generalizing ideas from the theory of spring-mass running, we develop controllers for the rigid body version of this model that execute stable running at high speed (5m/s) and synchronous turning between -25° and 45° in deadbeat fashion, on terrain with large uncertainties up to 20% of the rest leg length. We also develop an analytical model for turning dynamics of legged running systems using a simplified and empirical model of forces and kinematics, that qualitatively approximates turning behaviors without the need for the full order dynamics. Our work not only provides a holistic analysis of turning behaviors of running systems with integrated rotational dynamics but also presents a terrain agnostic leg placement strategy for these systems to achieve synchronous turning at high speeds.