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

On the observability of relative positions in left-invariant multi-agent control systems and its application to formation control