Humanoid Push Recovery with Robust Convex Synthesis

We address the problem of dynamic stabilization and push recovery for humanoid robots using robust control through convex optimization. By formulating the simultaneous search for a controller and the associated domain of attraction as a single problem, we provide a unified framework in which full-body push recovery controllers can be designed and their performance analyzed. The resulting controller explicitly models external disturbances in the system dynamics and guarantees stabilization under bounded disturbances as well as physical constraints on the robot. Through numerical simulations, we demonstrate full-body push recovery for a planar, three-link, bipedal humanoid in the sagittal plane.