  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.
