Omnidirectional Walking with a Compliant Inverted Pendulum Model

In this paper, we propose a novel omnidirectional walking engine that achieves energy efficient, human like, stable and fast walking. We augment the 3D inverted pendulum with a spring model to implement a height change in the robot’s center of mass trajectory. This model is used as simplified model of the robot and the zero moment point (ZMP) criterion is used as the stability indicator. The presented walking engine consists of 5 main modules including the “next posture generator” module, the “foot trajectory generator” module, the “center of mass (CoM) trajectory generator” module, the “robot posture controller” module and “Inverse kinematics (IK) solver” module. The focus of the paper is the generation of the position of the next step and the CoM trajectory generation. For the trajectory generator, we extend the 3D-IPM with an undamped spring to implement height changes of the CoM. With this model we can implement active compliance for the robot’s gait, resulting in a more energy efficient movement. We present a modified method for solving ZMP equations which derivation is based on the new proposed model for omnidirectional walking. The walk engine is tested on simulated and a real NAO robot. We use policy search to optimize the parameters of the walking engines for the standard 3D-LIPM and our proposed model to compare the performance of both models each with their optimal parameters. We optimize the policy parameters in terms of energy efficiency for a fixed walking speed. The experimental results show the advantages of our proposed model over 3D-LIPM.