This paper 1 presents a geometry-based approach for multiple mobile robot motion coordination. The problem is to coordinate the motions of several robots moving along fixed independent paths to avoid mutual collisions. The proposed algorithm is based on a bounding box representation of the obstacles in the so-called coordination diagram. The algorithm is resolution-complete but it is shown to be complete for a large class of inputs. Despite the exponential dependency of the coordination problem, the algorithm efficiently solves problems involving up to ten robots in worst-case situations and more than 100 robots in practical ones.