Trajectory tracking in an underactuated, non-minimum phase two-link multibody system through model predictive control with embedded reference dynamics

This paper proposes a novel formulation of Model Predictive Control (MPC), based on linearized models, for tip trajectory tracking of time-varying references in an underactuated, non-minimum phase, two-link multibody system. Indeed, tip trajectory tracking in such systems is challenging due to the unstable internal dynamics. Additionally, when traditional MPC is used, the reference is usually tracked with delay, since MPC is intrinsically devoted to regulation or to step tracking. To overcome these issues, the proposed approach embeds an autonomous state-space model of the time-varying reference into the constrained optimization process of MPC. The controller is therefore named MPC with Embedded Reference Dynamics, MPC-ERD. By embedding the reference in the controller design, tracking with negligible error and delay is achieved, and no feedforward control is required, thus overcoming the difficulties in model inversion. The MPC-ERD is experimentally validated and the results are compared with those provided by standard MPC with embedded integrator (also including output error constraints). Besides inheriting the benefits of standard MPC, MPC-ERD ensures precise tracking of the tip time-varying reference, with negligible delay and error.