m.r Sabaapour - School of Mechanical Engineering, University of Tehran, Iran
m.r Hairi Yazdi - School of Mechanical Engineering, University of Tehran, Iran
b Beigzadeh - Department of Mechanical Engineering, Iran University of Science and Technology, Iran

Dynamically stable biped robots mimicking human locomotion have received significant attention over the last few decades. Formerly, the existence of stable periodic gaits for straight walking of passive biped walkers was well known and investigated as the notion of passive dynamic walking. This study is aimed to elaborate this notion in the case of three dimensional (3D) walking and extend it for other maneuvers, specifically curved walking or turning. For this purpose, the motion of a general 3D compass gait model on a ramp has been analyzed theoretically in detail. A comprehensive dynamic modeling with respect to the vertical fixed frame is used based on Lagrangian and augmented methods. In addition to 3D passive straight walking, the results confirm the existence of some passive turning motions for the biped walker towards the steepest decent of the ramp. It was shown that the value of passive turning is strictly concerned to the value of initial perturbed condition of the walker, especially to the value of heading angle. A parameter analysis was also accompanied to examine the change in the characteristics of such passive motions caused by the change in model parameters.

3D Biped Robot, Passive walking, Curved walking, Turning, Steering, Asymptotical Stability