Connected and autonomous vehicles (CAVs), unlike conventional cars, will utilise the whole space of intersections and cross in a lane-free order. This paper formulates such a lanefree crossing of intersections as a multi-objective optimal control problem (OCP) that minimises the overall crossing time, as well as the energy consumption due to the acceleration of CAVs. The constraints that avoid collision of vehicles with each other and with road boundaries are smoothed by applying the dual problem theory of convex optimisation. The developed algorithm is capable of finding the lower boundary of the crossing time of a junction which can be used as a benchmark for comparing other intersection crossing algorithms. Simulation results show that the lane-free crossing time is better by an average of 40% as compared to the state-of-the-art reservation-based method, whilst consuming the same amount of energy. Furthermore, it is shown that the lane-free crossing time through intersections is fixed to a constant value regardless of the number of CAVs.
Connected and autonomous vehicles (CAVs) improve the throughput of intersections by crossing in a lane-free order as compared to a signalised crossing. However, it is challenging to quantify such an improvement because the available frameworks to analyse the capacity of the conventional intersections do not apply to the lane-free ones. This paper proposes a novel framework including a measure and an algorithm to calculate the capacity of the lane-free intersections. The results show that a lane-free crossing of CAVs increases the capacity of intersections by 127% and 36% as compared to a signalised crossing of, respectively, human-driven vehicles and CAVs. The paper also provides a sensitivity analysis indicating that, in contrast to the signalised ones, the capacity of the lane-free intersections improves by an increase in the initial speed, maximum permissible speed and acceleration of vehicles.
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 reservationbased 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.
Connected and autonomous vehicles (CAVs), unlike conventional cars, will utilise the whole space of intersections and cross in a lane-free order. This paper formulates such a lane-free crossing of intersections as a multi-objective optimal control problem (OCP) that minimises the overall crossing time, as well as the energy consumption of CAVs. The proposed OCP is convexified by applying the dual problem theory to the constraints that avoid collision of vehicles with each other and with road boundaries. The resulting OCP is smooth and solvable by gradient-based algorithms. Simulation results show that the proposed algorithm reduces the crossing time by an average of 40% and 41% as compared to, respectively, the state-of-theart reservation-based and lane-free methods, whilst consuming the same amount of energy. Furthermore, it is shown that the resulting crossing time of the proposed algorithm is i) fixed to a constant value regardless of the number of CAVs, and ii) very close to its theoretical limit.
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