Robots are increasingly found to operate together in the same environment where they must coordinate their motion. Such an operation is simple if the motion is quasi-static. Under second-order dynamics, the problem becomes challenging even for a known environment. Planning must guarantee safety by ensuring collision-free paths for the considered period by not bringing the robot to states where collisions are inevitable. This can be addressed with communication among robots, but it becomes complicated when the replanning cycles of different robots are not synchronized and robots make planning decisions at different times. This thesis shows how to guarantee safety for communicating second-order vehicles, whose replanning rates do not coincide, through a distributed motion planning framework without a global time reference. The method is evaluated through simulation where each robot has its own address space, and communicates with message passing. A proof of safety is presented, and simulation results are used to investigate performance of the framework.