Stable Walking of Humanoid Robots Using Vertical Center of Mass and Foot Motions by an Evolutionary Optimized Central Pattern Generator

Abstract

This paper proposes a method to produce the stable walking of humanoid robots by incorporating the vertical center of mass (COM) and foot motions, which are generated by the evolutionary optimized central pattern generator (CPG), into the modifiable walking pattern generator (MWPG). The MWPG extends the conventional 3-D linear inverted pendulum model (3-D LIPM) by allowing a zero moment point (ZMP) variation. The disturbance caused by the vertical COM motion is compensated in real time by the sensory feedback in the CPG. In this paper, the vertical foot trajectory of the swinging leg, as well as the vertical COM trajectory of the 3-D LIPM, are generated by the CPG for the effective compensation of the disturbance. Consequently, using the proposed method, the humanoid robot is able to walk with a vertical COM and the foot motions generated by the CPG, while modifying its walking patterns by using the MWPG in real time. The CPG with the sensory feedback is optimized to obtain the desired output signals. The optimization of the CPG is formulated as a constrained optimization problem with equality constraints and is solved by two-phase evolutionary programming (TPEP). The validity of the proposed method is verified through walking experiments for the small-sized humanoid robot, HanSaRam-IX (HSR-IX).