Abstract
The purpose of our research is to analyze stability of a geometrically controlled biped. The biped is planar and is composed of five links. Telescopic knee joints are employed to avoid the foot clearance problem. The ankle is not actuated then the robot is underactuated in single support phase. A geometric evolution of the biped configuration is controlled, instead of a temporal evolution. The input-output linearization with a PD control law and a feed forward compensation is used for geometric tracking. The temporal evolution is analyzed using Poincare map. The map is given by an analytic expression based on the angular momentum around the contact point. As a result, the radius of the circular arc foot affects to stability of walking, and speed of convergence decreases when the radius increases. Moreover a basin of attraction is broadened by choosing larger radius among the stable cyclic motion. Finally we discuss relationships of stability properties between the controlled system and passive dynamic walking.
