Humanoid Gait Generation on Uneven Ground using Intrinsically Stable MPC

This paper presents a Model Predictive Control (MPC) scheme capable of generating a 3D gait for a humanoid robot. The proposed method starts from an assigned sequence of footsteps and generates online the trajectory of both the Zero Moment Point and Center of Mass. Starting from the moment balance (neglecting rotations) we derive a model characterizing all 3D trajectories that satisfy a linear differential equation along all three axes. Then a solution is found by extending our previously proposed intrinsically stable MPC, which employs a stability constraint for guaranteeing boundedness of the solution. The method is validated using a NAO robot in a simulated dynamic environment.