Stability Region-Based Analysis of Walking and Push Recovery Control

Abstract

To achieve walking and push recovery successfully, a biped robot must be able to determine if it can maintain its current contact configuration or transition into another one without falling. In this study, the ability of a humanoid robot to maintain single support (SS) or double support (DS) contact and to achieve a step are represented by balanced and steppable regions, respectively, as proposed partitions of an augmented center-of-mass-state space. These regions are constructed with an optimization method that incorporates full-order system dynamics, system properties such as kinematic and actuation limits, and contact interactions with the environment in the two-dimensional sagittal plane. The SS balanced, DS balanced, and steppable regions are obtained for both experimental and simulated walking trajectories of the robot with and without the swing foot velocity constraint to evaluate the contribution of the swing leg momentum. A comparative analysis against one-step capturability, the ability of a biped to come to a stop after one step, demonstrates that the computed steppable region significantly exceeds the one-step capturability of an equivalent reduced-order model. The use of balanced regions to characterize the full balance capability criteria of the system and benchmark controllers is demonstrated with three push recovery controllers. The implemented hip–knee–ankle controller resulted in improved stabilization with respect to decreased foot tipping and time required to balance, relative to an existing hip–ankle controller and a gyro balance feedback controller.