This paper investigates the online motion coordination problem for a group of mobile robots moving in a shared workspace. Based on the realistic assumptions that each robot is subject to both velocity and input constraints and can have only local view and local information, a fully distributed multi-robot motion coordination strategy is proposed. Building on top of a cell decomposition, a conflict detection algorithm is presented first. Then, a rule is proposed to assign dynamically a planning order to each pair of neighboring robots, which is deadlock-free. Finally, a two-step motion planning process that combines fixed-path planning and trajectory planning is designed. The effectiveness of the resulting solution is verified by a simulation example.