The solution trajectory is the constrained extremum of an objective function that is designed to express dynamic feasibility and comfort. Static and dynamic obstacle constraints are incorporated in the form of polygons. The constraints are carefully designed to ensure that the solution converges to a single, global optimum.
Ziegler, Julius, et al. “Trajectory planning for bertha—a local, continuous method.” 2014 IEEE intelligent vehicles symposium proceedings. IEEE, 2014.