This article investigates the online motion coordination problem for a group of mobile robots moving in a shared workspace, each of which is assigned a linear temporal logic specification. Based on the realistic assumptions that each robot is subject to both state and input constraints and can have only local view and local information, a fully distributed multirobot motion coordination strategy is proposed. For each robot, the motion coordination strategy consists of three layers. An offline layer precomputes the braking area for each region in the workspace, the controlled transition system, and a so-called potential function. An initialization layer outputs an initially safely satisfying trajectory. An online coordination layer resolves conflicts when one occurs. The online coordination layer is further decomposed into three steps. First, a conflict detection algorithm is implemented, which detects conflicts with neighboring robots. Whenever conflicts are detected, a rule is designed to assign dynamically a planning order to each pair of neighboring robots. Finally, a sampling-based algorithm is designed to generate local collision-free trajectories for the robot, which at the same time guarantees the feasibility of the specification. Safety is proven to be guaranteed for all robots at any time. The effectiveness and the computational tractability of the resulting solution is verified numerically by two case studies.