Walking Pattern Generation on Inclined and Uneven Terrains for Humanoid Robots

This paper introduces a walking pattern generation method on an inclined terrain in both pitch and roll directions, and uneven terrain. The walking pattern generation method is based on a modifiable walking pattern generator (MWPG) which allows a zero moment point (ZMP) variation in real-time. As a navigational command set, a 3-D command state (CS) is defined, which consists of single and double support times, sagittal and lateral step lengths, and foot height of the swing leg. In the single support phase, the primary dynamics of the humanoid robot on the inclined terrain is modeled as a 3-D linear inverted pendulum model (LIPM) with constant center of mass (CoM) height, and the dynamic equation of the 3-D LIPM is derived to obtain the sagittal and lateral CoM motions. Using the sagittal and lateral CoM motions, the sagittal and lateral CoM trajectories are generated to satisfy the sagittal and lateral step lengths of the swing leg. The foot trajectories of the swing leg are generated according to the commanded sagittal and lateral step lengths, and foot height. In the double support phase, the vertical CoM trajectory is generated to satisfy the foot height of the swing leg from the single support phase. The walking pattern generation method is implemented on a simulation model of the small-sized humanoid robot, HanSaRam-IX (HSR-IX) and the effectiveness is demonstrated through computer simulations.