Lateral oscillations of the center of mass of bipeds as they walk. Inverted pendulum model with two degrees of freedom

The use of inverted pendulum models to study the bio-mechanics of biped walkers is a common practice. In its simplest form, the inverted pendulum consists of a point mass, which models the center of mass of the biped, attached to two straight mass-less legs. Most works using the simplest inverted pendulum model constrain the mass and the legs to the sagittal plane (the plane that contains the direction perpendicular to the ground and the direction toward the biped is walking). In this article, we remove this constrain and use this unconstrained inverted pendulum model to study the oscillations the mass experiences in the direction perpendicular to the sagittal plane as the biped walks. While small, these oscillations are unavoidable and of importance in the understanding of balance and stability of walkers, as well as walkers induced oscillations in pedestrian bridges.