Nonlinear model predictive control for constrained mechanical systems with state jump

In this paper, a nonlinear model predictive control (MPC) scheme for constrained mechanical systems with state discontinuity, or state jump, is examined. The proposed control method extends a fast numerical algorithm based on continuation and GMRES methods, allowing online implementation for mechanical systems possible. The validity of the strategy is demonstrated through numerical simulations, applying the method to landing control of a simplified humanoid model. The system is constrained to restrict the position of the zero moment point (ZMP) of the robot and state discontinuity exists at the landing instant.