  This paper proposes a novel real-time affordable solution to the trajectory
tracking control problem for self-driving cars subject to longitudinal and
steering angular velocity constraints. To this end, we develop a dual-mode
Model Predictive Control (MPC) solution starting from an input-output feedback
linearized description of the vehicle kinematics. First, we derive the
state-dependent input constraints acting on the linearized model and
characterize their worst-case time-invariant inner approximation. Then, a
dual-mode MPC is derived to be real-time affordable and ensuring, by design,
constraints fulfillment, recursive feasibility, and uniformly ultimate
boundedness of the tracking error in an ad-hoc built robust control invariant
region. The approach's effectiveness and performance are experimentally
validated via laboratory experiments on a Quanser Qcar. The obtained results
show that the proposed solution is computationally affordable and with tracking
capabilities that outperform two alternative control schemes.
