A Feasibility Analysis at Signal-Free Intersections

In this letter, we address the problem of improving the feasible domain of the solution of a control framework for coordinating connected and automated vehicles (CAVs) at signal-free intersections. The framework provides the optimal trajectories of CAVs to cross the intersection safely without stop-and-go driving. However, when traffic volume exceeds a certain level, finding a feasible solution for a CAV may become unattainable. We use concepts from numerical mathematics to identify appropriate polynomials that can serve as alternative trajectories of the CAVs, expanding the domain of the feasible CAV trajectories. We then select the final trajectories through an optimization problem that aims at minimizing jerk. Finally, we demonstrate the efficacy of our approach through numerical simulations.