A Feasibility Analysis at Signal-Free Intersections

In this letter, we address the problem of improving the feasible domain of the solution of a decentralized control framework for coordinating connected and automated vehicles (CAVs) at signal-free intersections as the traffic volume increases. The framework provides the optimal trajectories of CAVs to cross the intersection safely without stop-and-go driving. However, as the traffic volume increases, the domain of the feasible trajectories decreases. We use concepts of numerical interpolation to identify appropriate polynomials that can serve as alternative trajectories of the CAVs, expanding the domain of the feasible CAV trajectories. We provide the conditions under which such polynomials exist. Finally, we demonstrate the efficacy of our approach through numerical simulations.