In this paper we consider two examples of synchronization problems, i.e., a network of oscillators and a network of rigid bodies. We propose a controller that requires only the knowledge of the relative distances among the neighboring systems in the network. The controller is based on an extremum seeking controller, that steers the overall system to the minimum of an optimization problem on a manifold. Using a Lie bracket approximation for extremum seeking systems, we show that the controller leads to a synchronization of the overall network in both examples.