Humanoid gait generation for walk-to locomotion using single-stage MPC

We consider the problem of gait generation for a humanoid robot that must walk to an assigned Cartesian goal. As a first solution, we consider a rather straightforward adaptation of our previous work: an external block produces high-level velocities, which are then tracked by a double-stage intrinsically stable MPC scheme where the orientation of the footsteps is chosen before determining their location and the CoM trajectory. The second solution, which represents the main contribution of the paper, is conceptually different: no high-level velocity is generated, and footstep orientations are chosen at the same time of the other decision variables in a singlestage MPC. This is made possible by carefully redesigning the motion constraints so as to preserve linearity. Preliminary results on a simulated NAO confirm that the single-stage method outperforms the conventional double-stage scheme.