  In this study, we are concerned with autonomous driving missions when a
static obstacle blocks a given reference trajectory. To provide a realistic
control design, we employ a model predictive control (MPC) utilizing nonlinear
state-space dynamic models of a car with linear tire forces, allowing for
optimal path planning and tracking to overtake the obstacle. We provide
solutions with two different methodologies. Firstly, we solve a nonlinear MPC
(NMPC) problem with a nonlinear optimization framework, capable of considering
the nonlinear constraints. Secondly, by introducing scheduling signals, we
embed the nonlinear dynamics in a linear parameter varying (LPV) representation
with adaptive linear constraints for realizing the nonlinear constraints
associated with the obstacle. Consequently, an LPVMPC optimization problem can
be solved efficiently as a quadratic programming (QP) that constitutes the main
novelty of this work. We test the two methods for a challenging obstacle
avoidance task and provide qualitative comparisons. The LPVMPC shows a
significant reduction in terms of the computational burden at the expense of a
slight loss of performance.

Systems and Control;Systems and Control