Exploiting ankle torque for orbital stabilization in biped robots; a hybrid zero dynamics approach

This paper investigates the rule of ankle torque in stabilization of periodic motions in planar biped with feet. In order to illustrate the main concepts, the walking is considered to be consist of two phases; A fully actuated phase, where the stance foot is flat on the ground, and an instantaneous double support phase. It is shown how the ankle torque can be used effectively within hybrid zero dynamics framework to stabilize the system around a target periodic orbit. This control torque which is designed as an internal command to the swing phase zero dynamics is further exploited to switch among different orbits in one transition step. For the former goal, the Lagrangian property of the swing phase zero dynamics is employed and the ankle torque is applied to regulate the corresponding energy level of the target orbit. For the switching problem, this command is used to steer the trajectory of the system within connecting zero dynamics manifold. The proposed methods are verified through several simulations on a seven-link planar biped robot.