  In recent years, nonlinear model predictive control (NMPC) has been
extensively used for solving automotive motion control and planning tasks. In
order to formulate the NMPC problem, different coordinate systems can be used
with different advantages. We propose and compare formulations for the NMPC
related optimization problem, involving a Cartesian and a Frenet coordinate
frame (CCF/ FCF) in a single nonlinear program (NLP). We specify costs and
collision avoidance constraints in the more advantageous coordinate frame,
derive appropriate formulations and compare different obstacle constraints.
With this approach, we exploit the simpler formulation of opponent vehicle
constraints in the CCF, as well as road aligned costs and constraints related
to the FCF. Comparisons to other approaches in a simulation framework highlight
the advantages of the proposed approaches.
