Intersection crossing represents a bottleneck for transportation systems and Connected Autonomous Vehicles (CAVs) may be the groundbreaking solution to the problem. This work proposes a novel framework, i.e, AVOID-PERIOD, where an Intersection Manager (IM) controls CAVs approaching an intersection in order to maximize intersection capacity while minimizing the CAVs' gas consumption. Contrary to most of the works in the literature, the CAVs' location uncertainty is accounted for and periodic communication and re-optimization allows for the creation of safe trajectories for the CAVs. To improve scalability for high-traffic intersections, an event-triggering approach is also developed (AVOID-EVENT) that minimizes computational and communication complexity. AVOID-EVENT reduces the number of re-optimizations required by 92.2%, while retaining most of the benefits introduced by AVOID-PERIOD.