Design of reference trajectory to stabilize desired nominal cyclic gait of a biped

The paper presents the design of a reference trajectory to stabilize a desired nominal motion of a planar biped. It consists of five rigid links, with no feet; only the hip and knee joints are actuated. The gait is composed of alternating phases of single and double support. Biped is under actuated during single support motion. Instantaneous double support is modeled by passive impact equations. We choose the inter-link angles for four actuated articulations as polynomials depending on the angle of supporting leg shin relative to the vertical position. Final inter-link angular velocities and accelerations are assumed zeros. The configuration of our biped does not change before an impact and the biped rotates as a rigid body around the ankle joint. The nominal cyclic motion of the biped is obtained numerically. We design the Poincare map and show that this nominal motion is asymptotically stable. We then improve the stability of the nominal regime by changing the inclination of the torso during the single support phase