Autonomous Biped Stepping Control Based on the LIPM Potential

This paper proposes a novel biped stepping control which does not depend on the time-defined trajectory. The up-down motion of the foot is determined by referring to the LIPM potential, which is defined in the paper, based on the phase-space analysis of the center of mass (COM). The motion rate of the COM relative to the Zero-Moment Point (ZMP) is represented as the gradient of the potential, and the potential monotonously decreases from positive to negative during one step. The dominant component of the COM movement turns from convergent mode to divergent mode at the zero potential, and thus, the positive potential encourages the lifting-up and the negative potential alerts the necessity of touch-down. This emerges a stable alternate stepping of the feet by combining with a self-exciting oscillation of the COM and the ZMP, which was also proposed by one of the authors. The controller provides robots with flexibility against disturbances since it does not rely on any pre-defined referential motion trajectory. Computer simulations show that this idea is valid for a bipedal foot controller.