On the stability of indirect ZMP controller for biped robot systems

This paper proposes the indirect zero momentum position (ZMP) controller for biped robot systems and proves its disturbance input-to-state stability (ISS). The ZMP control has been used as a standard method for stable walking control of biped robot systems. Since the ZMP information consists of position and acceleration of the center of gravity (COG) for a biped robot system, the ZMP can be indirectly controlled by the motion of COG. In this paper, the reference COG planner is developed by solving the reference ZMP differential equation. The indirect ZMP controller is proposed to derive the desired motion of COG from the reference ZMP trajectory and the COG error (the difference between the reference and real COG). The ISS of the proposed indirect ZMP controller is proved for the simplified biped robot model. The robustness of the proposed indirect ZMP controller is shown in simulation.