This paper studies pose synchronization on the Special Euclidean group SE(3) for a network of rigid bodies. In particular, we extend our earlier results on the topic to expand a class of interaction graphs for which synchronization is proved. We first give the definitions of rigid body networks and pose synchronization as the controlled system and goal of this work, respectively. We next introduce our previous results as the preliminaries. Then, by introducing a condensation graph and stability theory of perturbed systems, we derive a necessary and sufficient condition in terms of interconnection topologies for pose synchronization on SE(3). We finally demonstrate the effectiveness of the present analysis through simulation.
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