  Trajectory planning and coordination for connected and automated vehicles
(CAVs) have been studied at isolated ``signal-free'' intersections and in
``signal-free'' corridors under the fully CAV environment in the literature.
Most of the existing studies are based on the definition of approaching and
exit lanes. The route a vehicle takes to pass through an intersection is
determined from its movement. That is, only the origin and destination arms are
included. This study proposes a mixed-integer linear programming (MILP) model
to optimize vehicle trajectories at an isolated ``signal-free'' intersection
without lane allocation, which is denoted as ``lane-allocation-free'' (LAF)
control. Each lane can be used as both approaching and exit lanes for all
vehicle movements including left-turn, through, and right-turn. A vehicle can
take a flexible route by way of multiple arms to pass through the intersection.
In this way, the spatial-temporal resources are expected to be fully utilized.
The interactions between vehicle trajectories are modeled explicitly at the
microscopic level. Vehicle routes and trajectories (i.e., car-following and
lane-changing behaviors) at the intersection are optimized in one unified
framework for system optimality in terms of total vehicle delay. Considering
varying traffic conditions, the planning horizon is adaptively adjusted in the
implementation procedure of the proposed model to make a balance between
solution feasibility and computational burden. Numerical studies validate the
advantages of the proposed LAF control in terms of both vehicle delay and
throughput with different demand structures and temporal safety gaps.
