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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 …