Perfect tracking of ZMP trajectory for humanoid locomotion using repetitive control

Abstract

In this paper, the tracking of the zero moment point (ZMP) trajectory for humanoid locomotion is addressed. For that, a combination of a repetitive controller (RC) and a linear quadratic regulator (LQR) is proposed. The RC controller achieves a zero steady state tracking error for any periodic desired output with a fixed period. Here, the robot model is simplified as a cart table model. In the first stage, a walking pattern with constant gait is considered to allow the use of a repetitive controller. The results are then compared to a classical PD control. In the second part, the proposed controller is applied to track a desired ZMP profile generated using a central pattern generator (CPG). Here, the speed of the oscillator is adjusted via a proper selection of the parameters of the CPG and the RC design is simultaneously updated to assure the perfect tracking of the ZMP.