Trajectory planning methodologies, for example using Mixed Integer Linear Programming (MILP), are used to determine globally optimal trajectories for vehicles. Many trajectory planning methodologies constrain vehicle trajectories with a linear approximation of the vehicle's dynamics.
Typically, a linear approximation of the vehicle's dynamics does not contain a notion of vehicle heading. This is typically because the introduction a heading angle introduces non-linearities. As a result, a determined trajectory may feature motion that cannot be achieved by conventional wheeled or tracked vehicles.