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We present an optimization based real-time walking controller for a full size humanoid robot. The controller consists of two levels of optimization, a high level trajectory optimizer that reasons about center of mass and swing foot trajectories, and a low level controller that tracks those trajectories by solving a floating base full body inverse dynamics problem using Quadratic Programming. Our controller is capable of walking on rough terrain, and also achieves longer foot steps, faster walking speed, heel-strike and toe push-off. Results are demonstrated with Boston Dynamics' Atlas robot in simulation.
Feng et al. (2013) studied this question.