A feasibility-driven MPC scheme for robust gait generation in humanoids

We present a Robust Intrinsically Stable Model Predictive Control (RIS-MPC) framework for humanoid gait generation, which realizes as closely as possible a predefined sequence of footsteps in the presence of both persistent and impulsive perturbations. The MPC-based controller has two modes of operations, each involving a Quadratic Program. Since perturbations act by modifying the state, as well as the feasibility region itself, the fundamental idea is to select in real time the operation mode based on the feasibility properties of the current state. In standard mode, footsteps are regarded as fixed and the MPC computes a Center of Mass (CoM) and a Zero Moment Point (ZMP) trajectory. Robustness is ensured by a robust stability constraint which uses a disturbance estimate and by restricted ZMP constraints along the control horizon. In the presence of strong perturbations, that violate the aforementioned conditions, the system switches to recovery mode, in which footsteps positions and timings can be modified in order to recover feasibility. We analyze the feasibility of both modes of operation and provide conditions for recursive feasibility of the standard mode. Simulations on an HRP-4 robot as well as experiments on NAO and OP3 are provided to validate the scheme.