Passive turning motion of 3D rimless wheel: novel periodic gaits for bipedal curved walking

Passive dynamic walking originally was introduced to describe some natural stable periodic gaits in straight walking. However, in this research, we have extended this notion to curved walking, wherein some novel three-dimensional (3D) periodic gaits with natural stability have been realized. For this aim, the simplest bipedal walking model, i.e. a rimless spoked-wheel, in its general 3D form, has been considered on a straight slope surface. Then, two kinds of stable passive turning, i.e. limited and circular continuous have been discussed. The first kind is actually a transfer among two-dimensional (2D) periodic motions and can be implemented on such straight slope surface. It is shown that the second kind is related to novel 3D periodic motions and can be just recognized on a special surface profile namely ‘helical slope’. The latter are interpreted as 3D fixed points of a Poincare return map. Results not only show asymptotical stability of such periodic motions, but also surprisingly indicate that the stability of a 3D periodic gait (turning) is higher than 2D one (straight walking). Furthermore, the characteristics of passive turning are shown to be firmly connected with the value of the state variables such as the lean angle in each case. Graphical abstract

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