Model Predictive Control for Stable Walking Using the Divergent Component of Motion with Footstep Location and Yaw Adaptation

Abstract

This paper presents an extension of previous model predictive control (MPC) schemes for dynamic walking to the stabilization of the time-varying divergent component-of-motion (DCM). In order to address the control authority limitations caused by fixed footholds, the step positions and rotations are treated as control inputs, allowing the generation and execution of stable walking motions, both at high speeds and in the face of disturbances. The use of the time-varying DCM allows consideration of height changes on the DCM dynamics, improving the robustness of the controller over varying terrain. Footstep rotation is included to allow for better modeling of the adjustment effects on reachability for stability and navigation of complex environments. This is done by formulating a quadratically constrained mixed-integer quadratic program (MIQCQP), which, when combined with the use of the time-varying DCM to account for the effects of height changes and use of angular momentum, improves the capabilities of MPC strategies for bipedal walking. While the MIQCQP cannot be solved at the desired control frequency, a method for compensating for the DCM dynamics between solves is presented. Simulation results of fast walking over flat ground and navigating varying-height terrain is presented with the ESCHER humanoid. This is combined with experiments that recover from a variety pushes, which demonstrate the effectiveness of this approach.