  We present a unified formal framework for expressing mobile robots models,
protocols, and proofs, and devise a protocol design/proof methodology dedicated
to mobile robots that takes advantage of this formal framework. As a case
study, we present the first formally certified protocol for oblivious mobile
robots evolving in a two-dimensional Euclidean space. In more details, we
provide a new algorithm for the problem of universal gathering mobile oblivious
robots (that is, starting from any initial configuration that is not bivalent,
using any number of robots, the robots reach in a finite number of steps the
same position, not known beforehand) without relying on a common orientation
nor chirality. We give very strong guaranties on the correctness of our
algorithm by proving formally that it is correct, using the COQ proof
assistant. This result demonstrates both the effectiveness of the approach to
obtain new algorithms that use as few assumptions as necessary, and its
manageability since the amount of developed code remains human readable.
