  We consider the localization problem between agents while they run a
formation control algorithm. These algorithms typically demand from the agents
the information about their relative positions with respect to their neighbors.
We assume that this information is not available. Therefore, the agents need to
solve the observability problem of reconstructing their relative positions
based on other measurements between them. We first model the relative
kinematics between the agents as a left-invariant control system so that we can
exploit its appealing properties to solve the observability problem. Then, as a
particular application, we will focus on agents running a distance-based
control algorithm where their relative positions are not accessible but the
distances between them are.
