Frenet-Cartesian Model Representations for Automotive Obstacle Avoidance within Nonlinear MPC

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.