Turning Motions in the Simplest Passive Walking Model

Turning Motions in the Simplest Passive Walking Model

The ability to move along curved paths is an essential feature for biped walkers to move around obstacles. This study is aimed at extending passive walking concept for curved walking and turning to generate more natural and effective motion. Hence threedimensional (3D) motion of a rimless spoked-wheel about a general vertical fixed coordinate system has been derived as the simplest walking model. Then, two types of stable passive turning (i.e. limited and circular continuous) have been introduced and discussed. It was shown that the first type can be implemented on a straight slope surface, while the second novel category is applicable on a special surface profile that has been introduced as “helical slope”. Such new passive periodic motions can be interpreted as 2D and 3D fixed points of the Poincare return map, respectively. Their stability was evaluated numerically by Jacobian analysis, as well as demonstrated through several simulation runs. Results show asymptotical stability of such motions and their considerable basin of attraction with respect to initial states. In addition, the characteristic of passive turning is shown to be strictly concerned to the value of the initial perturbed condition, for instance, to the initial inclination of the wheel.