Constraint mapping in a feedback linearization/MPC scheme for trajectory tracking of underactuated multibody systems

In this work, a nonlinear control scheme consisting of an exact feedback linearization and a model predictive controller is presented in order to track reference trajectories for an end-effector of an underactuated multibody system. In the case of minimum-phase systems, designing a feedback linearization results in an exactly linearized system, which can be used for model predictive control design. A method is proposed in detail how to handle mechanical constraints like restricted inputs through the nonlinear mapping of the feedback linearization in the optimization problem. A predictive controller combined with an exact input-output linearization is applied to a serial manipulator with a passive joint, which enables both accurate trajectory tracking and compliance of the constraints.