Postural control of a feet-less biped vertical posture using limited torques

We consider the problem of the stabilization in single support of the vertical posture of a two-link, a three-link, and a five-link planar biped without feet. The control torques are applied in the inter-link joints only. Thus, our objects are under actuated systems. The control laws are designed, using the biped linear models and their associated Jordan forms. The feedback is synthesized to suppress the unstable modes. The limits imposed on the torques are taken into account explicitly. Thus, the feedback laws with saturation are designed. The numerical investigations of the nonlinear models with designed control laws are presented