With a full fleet of autonomous vehicles (AV) in the future, the concept of signal-free intersections has attracted transportation researchers. Multiple studies have investigated different methods and protocols to facilitate vehicle decision-making at intersections. Most of these methods have relied on strong centralized or inter-vehicle communications. This research aims to develop a new protocol for managing vehicle movement at four-leg intersections assuming a fully automated fleet. The main concept of the proposed protocol is to maintain a continuous movement of vehicles entering the intersection, without stopping in queues, by controlling their sequence of movements. In the methodology a dynamic occupancy grid (DOG) approach is applied by initially dividing the intersection into dynamic grids (i.e. cells). The cells are in a virtual movement, emanating away from each lane-group without overlapping, like a gear machine. Each vehicle sits on a specific cell to traverse the intersection safely at a predetermined time. In other words, vehicles approaching an intersection must register their speed and position by certain sensors, and in return receive the appropriate acceleration and speed to finally be allocated to the suitable moving grids. The efficiency of the applied protocol was demonstrated by a practical example that presented a higher intersection capacity value exceeding the ideal saturation flow rate in some cases. This reflects the efficiency of the implemented protocol and its applicability to different low to high traffic flows. Moreover, the protocol shows more flexibility in dealing with different weather, geometric and traffic conditions.