  This paper 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 multi-robot motion coordination
strategy is proposed. For each robot, the motion coordination strategy consists
of three layers. An offline layer pre-computes 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. Firstly,
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.
