Lane-free crossing of connected and autonomous vehicles through intersections

Unlike conventional cars, connected and autonomous vehicles (CAVs) can cross intersections in a lane-free order. Lane-free crossing allows CAVs to make use of all segments of roads and intersections which is hypothesised to improve energy consumption and traffic throughput. However, controlling CAVs to pass through intersections in a lane-free order is a challenging minimum-time optimal control problem (OCP) with non-differentiable collision avoidance constraints and is difficult to be formulated and solved. This thesis addresses this challenge by proposing: i) a control strategy that incorporates differentiable collision avoidance constraints to cross CAVs through lane-free intersections; ii) a framework to evaluate the capacity of intersections when CAVs are crossing in a lane-free order. The proposed control strategy is formulated as a multi-objective OCP that minimises a combination of the crossing time and the energy consumption of CAVs due to their accelerations. The non-differentiable constraints that avoid collisions of vehicles with each other and with road boundaries are smoothed by applying the dual problem theory. It is shown that the solution of the formulated OCP when the crossing time is the only objective provides a lower bound of the crossing time of a junction which is exceptionally close to the theoretical limit. The calculated lower bound is a feasible benchmark to evaluate the performance of other intersection crossing algorithms. Considering the energy consumption as well, the results show that the proposed lane-free strategy reduces the crossing time of vehicles 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 crossing time through a lane-free intersection is fixed to a constant value regardless of the number of the crossing CAVs. This work also proposes a novel framework including a measure and an algorithm to quantify the capacity of the lane-free intersections. The available measures to assess capacity of the conventional intersections are not applicable to the lane-free ones because the conventional roads restrain vehicles to travel within lanes. The results of this thesis show that a lane-free crossing of CAVs increases the capacity of intersections by, respectively, 127% and 36% as compared to the signalised crossing by human-drivers and by CAVs. A sensitivity analysis indicates that, in contrast to the signalised intersections, the capacity of the lane-free ones is improved by an increase in the initial speed and the maximum permissible speed and acceleration of the vehicles.