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

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