A consensus-based distributed trajectory control in a signal-free intersection

This paper develops a distributed cooperative control logic to determine conflict-free trajectories for connected and automated vehicles (CAVs) in signal-free intersections. The cooperative trajectory planning problem is formulated as vehicle-level mixed-integer non-linear programs (MINLPs) that aim to minimize travel time of each vehicle and their speed variations, while avoiding near-crash conditions. To push vehicle-level solutions towards global optimality, we develop a coordination scheme between CAVs on conflicting movements. The coordination scheme shares vehicle states (i.e., location) over a prediction horizon and incorporates such information in CAVs' respective MINLPs. Therefore, the CAVs will reach consensus through an iterative process and select conflict-free trajectories that minimize their travel time. The numerical experiments quantify the effects of the proposed methodology on traffic safety and performance measures in an intersection. The results show that the proposed distributed coordinated framework converges to near-optimal CAV trajectories with no conflicts in the intersection neighborhood. While the solutions are found in real-time, the comparison to a central intersection control logic for CAVs indicates a maximum marginal objective value of 2.30%. Furthermore, the maximum marginal travel time, throughput, and average speed do not exceed 0.5%, 0.1%, and 0.5%, respectively. The proposed control logic reduced travel time by 43.0-70.5%, and increased throughput and average speed respectively by 0.8-115.6% and 59.1-400.0% compared to an optimized actuated signal control, while eliminating all near-crash conditions.