Optimal Push Recovery for Periodic Walking Motions

We study how humans performing periodic walking motions react to strong perturbations that are applied in form of pushes from behind. We propose a computational method that allows to generate optimal recovery motions based on a dynamic multi-body model of the human walking process. The assumption is that humans in such a situation would aim to pursue the walking motions while at the same time limiting the effort for the motion. For a given position and velocity in the middle of a periodic walking motion and a given pushing force profile, magnitude and contact point we determine the motion of the human model that minimizes a combined criterion joint torques and a deviation from periodicity. The recovery horizon considered in the multiphase optimal control problem is one step. The optimal control problem is solved using a direct boundary value problem approach based on multiple shooting. We present resulting optimal recovery motions for pushing forces between 150 N and 600 N which all look realistic. The proposed method has potential applications in the computation of push recovery motions for humanoid robots or for elderly humans with physical assistive devices, in each case applied to the respective model.