  We study the problem of coordinating multiple robots along fixed geometric
paths. Our contribution is threefold. First we formalize the intuitive concept
of priorities as a binary relation induced by a feasible coordination solution,
without excluding the case of robots following each other on the same geometric
path. Then we prove that two paths in the coordination space are continuously
deformable into each other if and only if they induce the \emph{same priority
graph}, that is, the priority graph uniquely encodes homotopy classes of
coordination solutions. Finally, we give a simple control law allowing to
safely navigate into homotopy classes \emph{under kinodynamic constraints} even
in the presence of unexpected events, such as a sudden robot deceleration
without notice. It appears the freedom within homotopy classes allows to much
deviate from any pre-planned trajectory without ever colliding nor having to
re-plan the assigned priorities.
