Lane-Free Crossing of CAVs through Intersections as a Minimum-Time Optimal Control Problem

TL;DR

This paper formulates a minimum-time optimal control problem for connected autonomous vehicles at intersections, enabling lane-free crossing and significantly reducing crossing times through a convexified, gradient-based solution.

Contribution

It introduces a novel convex optimization framework for lane-free intersection crossing that achieves fixed, minimal crossing times regardless of vehicle count.

Findings

Reduces intersection crossing time by over 50% compared to existing methods.

Provides a convex formulation solvable by gradient-based algorithms.

Achieves constant crossing time independent of vehicle number.

Abstract

Unlike conventional cars, connected and autonomous vehicles (CAVs) can cross intersections in a lane-free order and utilise the whole area of intersections. This paper presents a minimum-time optimal control problem to centrally control the CAVs to simultaneously cross an intersection in the shortest possible time. Dual problem theory is employed to convexify the constraints of CAVs to avoid collision with each other and with road boundaries. The developed formulation is smooth and solvable by gradient-based algorithms. Simulation results show that the proposed strategy reduces the crossing time of intersections by an average of 52% and 54% as compared to, respectively, the state-of-the-art reservation-based and lane-free methods. Furthermore, the crossing time by the proposed strategy is fixed to a constant value for an intersection regardless of the number of CAVs.