  Reference tracking and obstacle avoidance rank among the foremost challenging
aspects of autonomous driving. This paper proposes control designs for solving
reference tracking problems in autonomous driving tasks while considering
static obstacles. We suggest a model predictive control (MPC) strategy that
evades the computational burden of nonlinear nonconvex optimization methods
after embedding the nonlinear model equivalently to a linear parameter-varying
(LPV) formulation using the so-called scheduling parameter. This allows optimal
and fast solutions of the underlying convex optimization scheme as a quadratic
program (QP) at the expense of losing some performance due to the uncertainty
of the future scheduling trajectory over the MPC horizon. Also, to ensure that
the modeling error due to the application of the scheduling parameter
predictions does not become significant, we propose the concept of scheduling
trust region by enforcing further soft constraints on the states and inputs. A
consequence of using the new constraints in the MPC is that we construct a
region in which the scheduling parameter updates in two consecutive time
instants are trusted for computing the system matrices, and therefore, the
feasibility of the MPC optimization problem is retained. We test the method in
different scenarios and compare the results to standard LPVMPC as well as
nonlinear MPC (NMPC) schemes.
