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This paper presents a methodology to control the trajectory of cooperative connected automated vehicles (CAVs) at roundabouts with a mixed fleet of CAVs and human-driven vehicles (HVs). We formulate an optimization program in a two-dimensional space for this purpose. A model predictive control-based solution technique is developed to optimize the trajectories of CAVs at discretized time steps based on the estimated driving behavior of HVs, while the actual behavior of HVs is controlled by a microscopic traffic simulator. At each time step, the location and speed of vehicles are collected, and a decomposition-based methodology optimizes CAV trajectories for a few time steps ahead of the system time. The optimization methodology has convexification, alternating direction method of multipliers, and cutting plane decomposition components to tackle the complexities of the problem. We tested the solution technique in a case study roundabout with different traffic demand flow rates and CAV market penetration rates. The results showed that increasing the CAV market penetration rate from 20% to 100% reduced total travel times by 2.8% to 35.8%. The analyses indicate that the presence of cooperative CAVs in roundabouts can lead to considerable improvements.

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