Walking Pattern Generation using MPC with minimization of COM Velocity Fluctuation

The center of mass(COM) trajectory obtained through the predetermined Zero Momentum Point(ZMP) reference and Linear Inverted Pendulum Model(LIPM) has been effectively used for the humanoid robot walking. However, a reference in which ZMP is fixed at one point of the support foot during single support(SSP) can cause COM velocity fluctuation and discontinuity of COM acceleration. In order to solve these disadvantages, a moving ZMP trajectory has been used in which the ZMP moves forward from behind the support foot. However, the distance the ZMP moves within the support foot was determined experimentally or proportional to the foot size or stride. This makes it difficult to find a moving ZMP trajectory that can effectively reduce the COM velocity fluctuation. This paper proposes to generate a COM trajectory by directly considering the minimization of COM velocity fluctuation in the cost function of MPC. Through the constraint, the stability of the robot was maintained by keeping the ZMP in the support foot. The proposed method was verified through simulation and experiment.