Stability of an underactuated bipedal gait

A self-excited biped walking mechanism consisting of two legs that are connected in series at the hip joint through a servomotor is studied as a cyclic system with collisions. A torque proportional to angle between the shank of the swinging leg and the vertical is seen to sustain a gait. Each leg has a thigh and a shank connected at a passive knee joint that has a knee stopper restricting hyperextension similar to the human knee. A mathematical model for the dynamics of the system including the impact equations is used to analyse the stability of the system through examination of phase plane plots. Attractor lines along which the system approaches stability have been identified. A leg length for optimal stability has been identified. The biological basis for the proposed system has been identified by comparison with human gait.