Simultaneous Optimization of ZMP and Footsteps Based on the Analytical Solution of Divergent Component of Motion

Abstract

Real-time planning of footsteps has been a big challenge for bipedal research. A large number of methods have been proposed over the last several years. In addition, divergent component of motion (DCM) of linear inverted pendulum (LIP) has been applied to solve this problem thus attracting a great deal of attention. In this paper, we derive an analytical solution of DCM for an arbitrary input function and propose a novel quadratic programming (QP) problem for the simultaneous optimization of zero moment point (ZMP) and foot placements based on the analytical solution. To validate the method, we conducted a push recovery experiment on real hardware. The result of the experiment shows that our new algorithm realizes a hierarchical strategy for disturbance compensation.