<p>This paper investigates the motion synchronization of underactuated brachiating robots that communicate with each other over a network represented by a digraph. The synchronization is accomplished by leveraging the concept of a virtual leader, which leads to synchronization in stride time. For motion synchronization, three controllers are proposed: two model-dependent controllers and a model-free sliding-mode controller. All of the proposed controllers lead to a stable network operation. With a stable network, it is mathematically illustrated that all nodes synchronize their motion to the virtual leader. The performance of motion synchronization is evaluated quantitatively through measurements of errors and error rates for each physical robot in the network. Over time, a decrease in these metrics signifies improved synchronization and reduced deviation from the synchronized state. Simulation results demonstrate the efficacy of the controllers in achieving and maintaining synchronization across the network of physical robots. Model-based controllers can be limited because of the need to accurately know the system parameters for better performance. In this regard, we discuss a parameters estimation technique to approximate lumped parameters of the system.</p>