Embedding reference dynamics in model predictive control for trajectory tracking of multi-input multi-output non-minimum phase underactuated multibody systems

This paper proposes a feedback control technique for path and trajectory tracking on multi-input, multi-output nonminimum phase underactuated multibody systems and applies it to a spatial gantry crane moving a double pendulum. The two links forming the double pendulum are connected in series and the desired output of the system is the tip of the second link. This output selection yields to a nonminimum phase system, which is a class of dynamical systems that are particularly challenging from the control design perspective. In this paper, an enhanced formulation of Model Predictive Control is proposed to solve the output trajectory tracking problem by embedding the dynamics of the spatial reference trajectory within the optimization process performed at each time step. The proposed control technique is formulated considering two different scenarios: the case of torque-controlled (i.e., current-controlled) actuators, and the case of position-controlled actuators. The latter is unusual in the field of MPC and is suitable for industrial applications where proprietary controllers are adopted. Numerical validations show negligible contour and tracking errors during the execution of the desired trajectories, with low computational effort.