In this paper, a new geometric technique for planning collision-free motions for multiple vehicles in industrial environments is presented. This planner is executed at high speed, as frequent as new position and speed estimations are available. The proposed motion planner is based on the prediction of collisions between pairs of industrial vehicles. Such a prediction is measured as the minimum translational distance between their motions. A predicted collision is avoided by generating intermediate temporal-positions for each vehicle. These intermediate positions are restricted to the feasible path of involved vehicles. Cooperation among mobile vehicle is computed for each pair of vehicles based on priority indices