Post-impact adaptive compliance for humanoid falls using predictive control of a reduced model

We consider control of a humanoid robot in active compliance just after the impact consecutive to a fall. The goal of this post-impact braking is to absorb undesired linear momentum accumulated during the fall, using a limited supply of time and actuation power. The gist of our method is an optimal distribution of undesired momentum between the robot's hand and foot contact points, followed by the parallel resolution of Linear Model Predictive Control (LMPC) at each contact. This distribution is made possible thanks to torque-limited friction polytopes, an extension of friction cones that takes actuation limits into account. Individual LMPC results are finally combined back into a feasible CoM trajectory sent to the robot's whole-body controller. We validate the solution in full-body dynamics simulation of an HRP-4 humanoid falling on a wall.