Control concepts for walking based on point-mass 3D models

In the field of bipedal locomotion, many researchers use controllers based on simple point mass models to achieve walking balance [1, 2, 3, 4, 5]. In these models, balance is ruled by center of mass (CoM) position and velocity, foot placement and its timing, and pushoff impulses. But is this also true for a more complex, many-DOF, robot? Does upper body motion significantly influence CoM dynamics? Most people cannot balance on stilts without taking a step; the Cornell Ranger robot, designed as a biped, can only move its center of mass by about 2cm by swing leg motions. It appears that walking control, even of a multi-DOF robot, is essentially low-dimensional, and that motion of the CoM is efficiently decoupled from the dynamics of the rest of the body. The latter then can be used to pursue other tasks during locomotion, e.g. energy efficiency. We will justify this idea by considering viability and controllability concepts for an Inverted Pendulum model (IP, [6, 2]) and a Linear Inverted Pendulum model (LIP, [1]). They can be viewed as generalizations of Pratt’s viable and capture regions [4].