A new control law for a 3D biped robot based on regulation of the zero moment point and joint path

This paper presents a new controller that can achieve an asymptotically stable, periodic walking gait for a 3D biped robot, which has 14 DOF in the single support phase and 14 actuators. In order to avoid the unexpected rotation of the supporting foot, two positions of the zero moment point or ZMP in the horizontal plane are regulated. For a 3D robot with 14 actuated joints, since the 2 positions of the ZMP are controlled only other 12 outputs should be chosen. The controller is desired to track a parameterized reference trajectory, not the time-variant one. It is defined in such a way that only the kinematic evolution of the robots state is regulated, but not its temporal evolution. In particular, this method allows the computations for the controller design and the periodic orbit to be carried out on a 3 order subsystem of the 14 DOF robot model. The reference motions are adapted at each step in order to create an hybrid zero dynamic system. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincaré map of the hybrid zero dynamics. The effect of controlled outputs selection on the zero dynamics is discussed and some pertinent choices of controlled outputs are proposed, leading to stable walking.