Time-Projection control on 3LP, a simple idea to deal with intermittent pushes online

In this article, we propose a new controller for recovering intermittent pushes during bipedal locomotion. We use 3LP as a template model which can provide closed-form solutions for state evolution. The idea behind our controller is to project the perturbed state of current time-step back to the beginning of the hybrid phase, use the expertise of a discrete controller and then apply the resulting optimal policy to the system at the current time-step. Linear properties of 3LP makes such calculation very fast and effective. By optimizing a certain cost function, we find the most robust and generic projecting configuration which outperforms the discrete controller itself.