Parameterization Approach of the Frenet Transformation for Model Predictive Control of Autonomous Vehicles

Model predictive control (MPC) and nonlinear optimization-based planning for autonomous vehicles are often formulated in a transformed coordinate frame, namely the curvilinear Frenet frame. Mostly the center line of the road is used as a transformation curve, but the choice of the transformation curve might have properties which make the optimization problem hard or even infeasible to solve in the whole search space. This paper proposes an optimization-based parameterization approach to establish an alternative transformation curve which yields favorable numerical properties for the consecutive use of numerical optimization approaches such as MPC. The optimization objective minimizes the change of curvature and pushes the evolute (i.e. singular region) of the transformation curve outside the feasible region. The convergence improvement of the proposed parameterization approach in terms of integrator precision, optimization time and iteration counts is compared in simulation examples, using a time-optimal nonlinear optimization formulation.