Conflict-free optimal control of connected automated vehicles at unsignalized intersections: A condition-based computational framework with constrained terminal position and speed

Conventional intersection management relies on traffic signals to coordinate conflicting traffic flows and distribute right-of-way. However, delays caused by traffic signals remain a major burden on urban transportation systems. Emerging connected automated vehicles (CAVs) are expected to improve the intersection management by coordinating vehicle movements without relying on traffic signals. Hence, this paper primarily focuses on coordinating CAVs at unsignalized intersections, especially common unsignalized intersections composed of major and minor roads, which exhibit inherent asymmetries such as higher speed limits and vehicle arrival rates on major roads compared to minor roads. We propose a conflict-free optimal control method to achieve highly efficient coordination of CAVs at these unsignalized intersections. The method employs a hierarchical coordination framework, in which an upper layer optimizes the passing order for CAVs through the intersection, and a lower layer designs a second-order optimal control model with constrained terminal position and speed for trajectory planning. Specifically, the upper layer adopts an improved Incremental Learning Monte Carlo Tree Search to efficiently generate a nearly global-optimal passing order for CAVs within a very short planning time. The lower layer introduces a condition-based computational framework that enhances the standard iterative solution procedure used in the constrained Hamiltonian analysis, and derives a closed-form analytical solution for the constrained optimal control problem without any recursive steps. The results of numerical experiments show that the proposed method can achieve real-time conflict-free optimal trajectory planning for all CAVs. Compared with fully-actuated signal control, the proposed method reduces the average delay for all CAVs by 19.92s, 16.46s, and 15.47s under both symmetric and asymmetric traffic demands (i.e., the ratios of CAV arrival rates on the major to minor roads are 1:1, 2:1, and 3:1, respectively).