In the paper, basic idea and some results of a central control system for two dimensional moving vehicles, e. g. ships or free-course carriers in a factory, are shown, where optimum courses for each of a group of vehicles rushing into a limited area are solved, avoiding collisions and yet keeping the minimum distance course for each vehicle as close as possible. In the group control problems, proper functions of miss distances and deviations from minimum distance courses are formulated as criterion functions, and optimizing algorithm and characteristics of optimum trajectories are analysed for various cases. The problems can be easily solved by small-size mini-computers for several vehicles, and time and energy losses in collision avoidance can be decreased to the minimum by taking such optimum courses, where all vehicles clear predetermined miss distances to other vehicles effectively. A back up system for each vehicle to assure safety is also investigated in the case the central control system should go down while it controls the traffic. Such back up system is indispensable to realize the above central control system, because effectiveness in the optimum course decreases the margin for the safety. The back up system is based on a simplified coordinating algorithm of two vehicular collision avoidance solutions, and from some numerical examples, it is shown that it can work well even in the crowded case.