On the equivalence of the three-link to the almost linear form*

Abstract

The almost linear form that is state and feedback equivalent to the dynamics of the so-called three-link (aka biped with torso) is derived and proved here. This result is then applied to the walking design with downward torso movement imitating balancing role of a hand. This motivates a challenging idea: the balancing role of hands in two-dimensional walking consists in synchronizing the hand angle with the hip angle in such a way that the resulting restricted dynamics is exact feedback linearizable. Results are demonstrated by the simulations of a single step including walking animations.